Abstract:
Methods and apparatus for determining rotor position in a motor including a rotor and stator windings. The method includes measuring inductive sense values for each pair of the stator windings by performing an inductive sense routine on the motor, measuring stator winding voltage values, induced by mutual inductance between windings, for each of the stator windings by performing a mutual inductance sensing routine on the motor, and determining the rotor position based on the inductive sense values and the stator winding voltage values.

Description:
BACKGROUND 
     1. Technical Field 
     This disclosure relates to electric motors and, more particularly, to sensing the initial position of the rotor of a brushless DC motor while the rotor is stationary. 
     2. Discussion of Related Art 
     A basic three-phase brushless DC(BLDC) motor includes a permanent magnet rotor and three stator windings. The windings are energized with appropriate currents and phase relationships to produce a rotating field which causes rotation of the rotor. In a typical configuration, the motor windings are energized with a 120° phase relationship between the currents of the three windings. 
     In order to obtain rotation of the rotor, the stator windings are energized and de-energized in a sequence that relates to the current position of the rotor. Accordingly, the motor position is sensed during operation, and the sensed motor position is used to control a commutation sequence for energizing the stator windings. In one approach, pulse-width-modulated (PWM) signals are applied to the motor windings according to the sensed motor position. 
     Known techniques for sensing motor position include mounting position sensors within the motor. Other known techniques include measurement of back electromotive force (BEMF) but this requires the rotor to be rotating at sufficiently high speed in order for the BEMF to be detectable. Before we can even start rotating the rotor, it is crucial to determine its initial position so that the correct first phase is energized to avoid back rotation or stalling of the rotor. One widely used technique to determine the initial position is known as inductive sense. However, inductive sense accuracy is affected by the mismatch between the phases of the motor coils in terms of resistance and inductance and the current limit measurement apparatus. 
     Manufacturing BLDC motors and/or measurement apparatus with tight tolerance is both high in cost and complexity. Accordingly, there is a need for improved methods that are more tolerant to these manufacturing defects. 
     SUMMARY 
     According to a first aspect, a method is provided for determining rotor position in a motor including a rotor and stator windings. The method comprises measuring inductive sense values for each pair of the stator windings by performing an inductive sense routine on the motor, measuring stator winding voltage values, induced by mutual inductance between windings, for each of the stator windings by performing a mutual inductance sensing routine on the motor, and determining the rotor position based on the inductive sense values and the stator winding voltage values. 
     In embodiments, measuring inductive sense values comprises determining a time for a current through each pair of the stator windings to reach a current limit. 
     In embodiments, determining the time to reach a current limit comprises sensing a voltage across a single sense resistor associated with the stator windings. 
     In embodiments, determining the time to reach a current limit comprises sensing a voltage across sense resistors associated with respective stator windings. 
     In embodiments, measuring stator winding voltage values comprises determining if a winding voltage is positive or negative when a current is supplied through two other stator windings. 
     In embodiments, determining the rotor position comprises accessing an entry in a table based on the inductive sense values and the stator winding voltage values. 
     In embodiments, the motor includes three stator windings and measuring inductive sense values includes measuring six inductive sense values. 
     In embodiments, the motor includes three stator windings and measuring stator winding voltage values comprising measuring six stator winding voltage values. 
     In embodiments, measuring stator winding voltage values comprises supplying a current through a pair of the stator windings and measuring a voltage across a third winding of the stator windings. 
     In embodiments, measuring the voltage across the third winding comprises determining zero crossings of the voltage across the third winding. 
     According to a second aspect, a method is provided for determining rotor position in a motor including a rotor and three stator windings. The method comprises: measuring inductive sense values for each pair of the stator windings by determining a time for a current through each pair of stator windings to reach a current limit; measuring stator winding voltage values, induced by mutual inductance between windings, for each of the stator windings by supplying a current through a pair of the stator windings and measuring the zero crossings of a voltage across a third winding of the stator windings; and determining the rotor position by accessing an entry in a table based on the measured inductive sense values and the measured stator winding voltage values. 
     According to a third aspect, apparatus is provided for determining rotor position in a motor including a rotor and stator windings. The apparatus comprises: first circuitry configured to measure inductive sense values for each pair of the stator windings by performing an inductive sense routine on the motor; second circuitry configured to measure stator winding voltage values, induced by mutual inductance between windings, for each of the stator windings by performing a mutual inductance sensing routine on the motor; and processing circuitry configured to determine the rotor position based on the inductive sense values and the stator winding voltage values. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a better understanding of the embodiments, reference is made to the accompanying drawings, which are incorporated herein by reference and in which: 
         FIG. 1  is a schematic block diagram of a three-phase BLDC motor system with one current sense resistor; 
         FIG. 2  is a schematic block diagram of a three-phase BLDC motor system with three current sense resistors; 
         FIG. 3  is a schematic block diagram of a BLDC motor system performing inductive sense of the BC pulse at the instant Δt time after the phases are being driven; 
         FIG. 4  is a schematic block diagram of a BLDC motor system performing inductive sense of the BC pulse at the instant Δt time before the current limit Ilimit is reached; 
         FIG. 5  shows the BLDC motor winding current profile with the  Ilimit _latch signal while performing an inductive sense routine; 
         FIG. 6  is a graph of inductive sense count as a function of rotor position for each of six inductive sense pulses; 
         FIG. 7  is a graph of inductive sense period as a function of rotor position for each of six inductive sense pulses if a mismatch of 0.75 times the inductive sense variation is introduced; 
         FIG. 8  is a timing diagram that illustrates the phase relationship between the ETON waveform, BEMF and inductive sense count as a function of rotor position; 
         FIG. 9  shows the various digitized ETON waveforms, taken while the motor winding currents are low, and the corresponding inductive sense counts; 
         FIG. 10  shows the various digitized ETON waveforms, taken while the motor winding currents are high, and the corresponding inductive sense counts; 
         FIG. 11  shows the relationship between two adjacent inductive sense counts, namely BCis and BAis, together with the corresponding digitized ETON waveforms BCzc and BAzc; 
         FIG. 12  shows the phase difference between the inductive sense region and the mutual inductance region; 
         FIG. 13  shows the phase relationship between the constructed A, B and C regions and the six inductive sense counts as a function of rotor position, and six mutual inductance regions are defined; and 
         FIG. 14  is flowchart for performing the enhanced inductive sense process. 
     
    
    
     DETAILED DESCRIPTION 
     A schematic block diagram of a motor system  10  is shown in  FIGS. 1 and 2 .  FIG. 1  illustrates a motor system with a single sense resistor Rs, and  FIG. 2  illustrates a motor system with three sense resistors Rsa, Rsb, and Rsc. In  FIGS. 1 and 2 , a BLDC motor  12  is represented schematically by stator windings A, B and C, each having one end connected to a center tap  14 . Stator winding A is represented by a series connection of an inductor LA and a resistor RA; stator winding B is represented by a series connection of an inductor LB and a resistor RB; and stator winding C is represented by a series connection of an inductor LC and a resistor RC. The motor  10  also includes a permanent magnet rotor (not shown). 
     The opposite ends of stator windings A, B and C are connected to drive circuits  20 ,  22  and  24 , respectively. Each drive circuit  20 ,  22 ,  24  includes a switch  26  coupled to a supply voltage +VCC and a switch  28  coupled to ground. Each of the stator windings A, B and C can be connected by switch  26  to voltage +VCC or by switch  28  to ground. The drive circuits  20 ,  22  and  24  are controlled by a state machine/sequencer  32 . 
     Each of the stator windings A, B and C is coupled to an input of a multiplexer  40  which receives a control input from state machine/sequencer  32 . A selected winding signal is provided by multiplexer  40  to a negative input of a comparator  42 . The center tap  14  of the stator windings is coupled to a positive input of comparator  42 , and the output of comparator  42  is supplied to state machine/sequencer  32 . 
     In the embodiment of  FIG. 1 , a single sense resistor  44  (RS) is utilized for inductive sensing of each winding pair. An embodiment using three current sense resistors is shown in  FIG. 2 . In particular, a sense resistor  80  (RSA), connected between drive circuit  20  and ground, senses the current in winding A; a sense resistor  82  (RSB), connected between drive circuit  22  and ground, senses the current through winding B; and a sense resistor  84  (RSC), connected between drive circuit  24  and ground, senses the current through winding C. Use of a single sense resistor, as shown in  FIG. 1 , avoids a mismatch between three separate sense resistors. However, in some embodiments, the resistance of the switch connecting the winding to ground can be used as the sense resistor. 
     In  FIG. 1 , the voltage VS corresponds to a voltage across sense resistor RS when the total current flows through switches  28  of drive circuits  20 ,  22  and  24  and through resistor RS to ground. The motor system  10  of  FIG. 1  further includes a comparator  60  to sense the current limit Ilimit during inductive sensing. In particular, comparator  60  receives voltages VS at a positive input. The positive input is then compared with a threshold voltage VTHRES supplied to a negative input of comparator  60 . 
     In  FIG. 2 , the voltage VSA corresponds to a voltage across sense resistor RSA when current flows through switch  28  of drive circuit  20  and through sense resistor RSA to ground. The voltage VSB corresponds to a voltage across sense resistor RSB when current flows through switch  28  of drive circuit  22  and through sense resistor RSB to ground. The voltage VSC corresponds to a voltage across sense resistor RSC when current flows through switch  28  of drive circuit  24  and through sense resistor RSC to ground. Likewise, when switch  28  of drive circuit  20 ,  22  or  24  is open, no current flows through sense resistor RSA, RSB or RSC, respectively, and as such, voltage VSA, VSB or VSC becomes 0. 
     The motor system  10  of  FIG. 2  further includes comparator  60  to sense the current limit Ilimit during inductive sensing. In particular, comparator  60  receives voltages VSA, VSB and VSC at respective positive inputs. The sum of the inputs is compared with threshold voltage VTHRES supplied to a negative input of comparator  60 . 
     In  FIGS. 1 and 2 , the threshold voltage VTHRES applied to the negative input of comparator  60  corresponds to the current limit Ilimit. The output of comparator  60  is supplied through an OR gate  62  to a reset input of a SR latch  70  so that SR latch  70  is reset by a current limit event. SR latch  70  is also reset when the state machine/sequencer  32  provides a signal through OR gate  62 . 
     In the discussion that follows, it is assumed that the embodiment of  FIG. 2  with three separate sense resistors is utilized. In any case, sense resistors RSA, RSB, RSC and voltages VSA, VSB, VSC shown in  FIG. 2  can be replaced by sense resistor RS and voltage VS in  FIG. 1 . 
     A start signal from state machine/sequencer  32  is applied to a set input of SR latch  70  and to a reset input of a timer  72 . The start signal from state machine/sequencer  32  indicates the start of a current pulse applied to a pair of the windings A, B and C, such as windings B and C. A Q output of SR latch  70  is applied to timer  72  as an increment input. 
     In operation, the state machine/sequencer  32  supplies a current pulse through a winding pair, such as windings B and C. In the example of windings B and C, switch SWBH of switch  22  is closed to connect winding B to voltage +VCC and switch SWCL of switch  24  is closed to connect winding C to ground. The current through windings B and C begins to increase and produces a voltage VSC across sense resistor RSC. The winding current I is given by I=VSC/RSC. The sense voltage VSC ( FIG. 2 ) is applied to the positive input of comparator  60 . When the voltage VSC is greater than the threshold voltage applied to the negative input of comparator  60 , the comparator  60  produces an output logic signal Ilimit which resets latch  70  and causes the increment input of timer  72  to go low, hence stopping timer  72 . The timer count when timer  72  is stopped is an inductive sense count IS supplied to state machine/sequencer  32 . 
     Comparator  42  senses the zero crossings of the voltage between one of the windings A, B and C and the center tap  14 . The comparator  42  senses an ETON signal and provides an output ZC which changes state on the zero crossings of the ETON signal. The ETON signal for winding A can be represented as ETON=VA−VCT, (LAB−LAC)dI/dt, where VA is the voltage on winding A, VCT is voltage on center tap  14 , LAB is the mutual inductance of windings A and B, LAC is the mutual inductance of windings A and C, and dI/dt is the rate of change of the current through windings B and C. The ETON signals for windings B and C can be represented in a corresponding manner. The comparator output ZC is supplied to the state machine/sequencer  32 . 
     In operation, the drive circuits  20 ,  22 ,  24  supply pulses to each of the windings A, B and C, with the pulse timing and the pulse widths determined by a PWM generator within the state machine/sequencer  32 , to cause rotation of the rotor (not shown). The state machine/sequencer  32  provides the timing of the drive signals based on the sensed signals from comparator  42 . 
     A simplified schematic diagram of a BLDC motor system performing inductive sense of the BC pulse at the instant Δt time after the phases are driven is shown in  FIG. 3 , where time Δt (typically a few μs) represents a short duration of time such that the current built up in the motor coil is small, yet sufficiently long that the driver switch is fully closed.  FIG. 4  is similar to  FIG. 3  but shows the BLDC motor system performing inductive sense of the BC pulse at the instant before the current limit Ilimit is reached. At the higher current of  FIG. 4 , the magnetic core of the windings is more saturated than at the lower current of  FIG. 3 . 
     In both  FIGS. 3 and 4 , the comparator  42  senses the voltage across stator winding A when a current is supplied through stator windings B and C by coupling stator winding B to supply voltage +VCC and coupling stator winding C to ground. The comparator  42  receives the winding signal ETON, which is the voltage induced in winding A due to the change of current through windings B and C. For the configuration shown in  FIGS. 3 and 4 , the comparator  42  detects the zero crossings of the winding A signal ETON when windings B and C are energized and outputs zero crossing signal BC ZC . Zero crossing signal CBzc is obtained from comparator  42  when the current direction through windings B and C is reversed. In a similar manner, zero crossing signals BAzc, ABzc, ACzc, and CAzc are obtained by changing the windings that are energized and the winding connected to comparator  42 . 
       FIG. 5  shows the BLDC motor coil current profile while performing the inductive sense routine. A dummy pulse is performed prior to the six inductive sense pulses to equalize the effect of the power supply on the subsequent measurements. The inductive sense pulse width is represented by the duration in which the  Ilimit _latch signal stays high and is the time required for the current through respective stator winding pairs to reach the threshold value. On a BLDC motor, the alignment of the rotor can be determined by identifying the shortest pulse. In  FIG. 5  this is CB and AB, so we can conclude the rotor is aligned at the intersection between CB and AB. 
       FIG. 6  is a graph of inductive sense period as a function of rotor position for each of six inductive sense pulses BAis, CAis, CBis, ABis, ACis, and BCis. The actual values of the inductive sense period are less important than the relationships between the inductive sense pulses as a function of rotor position, as can be seen from  FIG. 6 . 
     To simplify calculations, we can represent manufacturing defects that cause mismatches between the three phases by a shift in the Ilimit measurement. If the shift between motor phases is as much as 0.75× of the amplitude of the inductive sense counts variation, the worst case distortion of inductive sense counts is as shown in  FIG. 7 . It is clear that we would not be able to identify the rotor position accurately. In this case, the worst case error in position detection is 120°, as region A would be mis-detected as region B. 
       FIG. 8  illustrates the relationship between various waveforms as a function of rotor position for the case where inductive sense of the BC pulse is performed. Waveform  100  is the ideal ETON amplitude and as shown has two cycles for one electrical cycle. Waveform  102  represents the actual ETON amplitude, taking into account the saturation effect. The higher the current in the motor windings, the higher the saturation effect, and the larger the deviation from the ideal ETON waveform. Waveform  110  represents the back EMF magnitude as a function of rotor position, and waveform  112  represents an inductive sense pulse BCis amplitude as a function of rotor position with its y-axis value on the right side. 
     From  FIG. 8  it is clear that we can avoid the saturation effect on the ETON waveform by using the information at the time when the inductive sense count is lower than its mean (e.g. between 0° to 180° in  FIG. 8 ). But when the inductive sense count is higher than its mean value, sampling the ETON waveform is unreliable, as it is subjected to the saturation effect. 
       FIG. 9  shows the various ETON waveforms, digitized by comparator  42 , while the cores are driven close to linear to minimize the saturation effect, and the corresponding inductive sense pulses using the measurement setup as illustrated in  FIG. 3 .  FIG. 10  shows the various ETON waveforms, digitized by comparator  42 , slightly before the winding current reaches the current limit, and the corresponding inductive sense pulses using the measurement setup as illustrated in  FIG. 4 . Both  FIGS. 9 and 10  show measurements taken from an actual BLDC motor. 
     It is clear that the digitized ETON waveform in  FIG. 9  more resembles a square wave than the one shown in  FIG. 10 . It is therefore important to choose a time Δt that is appropriate to minimize this saturation effect. The deviation from square wave mainly occurs when the inductive sense pulse is high, but as concluded previously, the saturation effect is nonexistent when the corresponding inductive sense pulse is low. 
       FIG. 11  shows two adjacent inductive sense counts, namely BCis and BAis, together with their digitized ETON waveforms BCzc and BAzc. The shaded box covers the region where both BCzc and BAzc are low, whereas the dotted box covers the 180° region centered on the mid-point where both BCis and BAis are low. The region where the dotted box intersects the shaded box, which covers the middle 60° region of the dotted box, is a region where both BAis and BCis are low, and therefore, the ETON waveforms are not affected by the saturation effect. The above argument can be extended to all six adjacent pairs of inductive sense pulses. 
     Referring to  FIG. 12 , the shaded box again represents the region as defined by ETON waveforms BCzc and BAzc, whereas the dotted box represents the region defined by the normal inductive sense when BAis is the shortest pulse. This shows that the mutual inductance region is 30° misaligned with the normal inductive sense region. 
     This disclosure supplements the known inductive sense routine with information on the ETON waveforms to achieve better rotor position detection accuracy. All we need to do is use the known inductive sense count information to determine this 180° dotted box region, and then use the mutual inductance information to zero in further to the 60° region. Since we do not need to use the inductive sense information to gain 60° resolution, we are able to tolerate much higher mismatches between phases. 
     Six 180° regions are defined by regions A&gt;0, B&gt;0, C&gt;0, A&lt;0, B&lt;0 and C&lt;0 where regions A, B and C are defined as follows:
 
 A=BAis−ABis−CBis+BCis   (1)
 
 B=CBis−BCis−ACis+CAis   (2)
 
 C=ACis−CAis−BAis+ABis   (3)
 
       FIG. 13  shows the relation between the A, B and C regions, and the six inductive sense counts as well as the six mutual inductance regions. 
     Based on the A, B and C regions and the six digitized ETON waveforms, we can then build a truth table that is used to determine the rotor position. Such a table is shown in Table 1. In Table 1, A&gt;0, B&gt;0 and C&gt;0 are represented as A=1, B=1 and C=1, and, A≦0, B≦0 and C≦0 are represented as A=0, B=0 and C=0. As can be seen in Table 1, the maximum position detection error is only 30° if the saturation effect is avoided by sampling the six ETON waveforms while the motor coil current is still low and if the manufacturing defects are confined to 0.75 times the normal inductive sense variation. In the unlikely event that the saturation effect is not avoided, the maximum error becomes 90° which stills compares favorably to the old inductive sense routine (120°). Due to the nature of a BLDC motor, Table 1 covers only 264 out of the total 512 possible states for a nine input truth table. A BLDC motor simply would not yield an input not defined by Table 1. Table 1 is attached hereto as an appendix and is hereby incorporated by reference in its entirety. 
       FIG. 14  illustrates one possible flowchart to perform the enhanced inductive sense process as described in this disclosure. It will be understood that the enhanced inductive sense routine may include additional acts and that one or more of the acts shown in  FIG. 14  may be omitted, according to embodiments. 
     To avoid the saturation effect and improve accuracy, the process of  FIG. 14  is performed using the motor system shown in  FIG. 3 . However, since the saturation effect is dependent on individual motors, it is not a valid assumption that the saturation effect could be eliminated completely and Table 1 is built considering the saturation effect. The process of  FIG. 14  may be performed by the state machine/sequencer  32 , which may include a processing device and a computer-readable storage device encoded with instructions that, when executed by the processing device, perform the process. During execution of the process, the state machine/sequencer  32  controls the circuitry shown in  FIG. 3  to perform the acts of the process. In other embodiments, the process of  FIG. 14  may be performed by a computing device separate from state machine/sequencer  32 . 
     In act  700 , winding pair CA is driven as a dummy cycle. In act  704 , the process waits until the current limit Ilimit is reached. Since this is a dummy cycle, no measurement is taken. 
     In act  710 , winding pair CB is driven. The process waits Δt microseconds in act  712  and measures ETON waveform CBzc in act  714 . The process then waits until the current limit Ilimit is reached in act  716  and measures the inductive sense count CBis in act  720 . Act  720  also includes letting the motor current decay, and then driving winding pair AB. 
     The process is repeated for winding pair AB. In particular, process waits Δt microseconds in act  722  and measures ETON waveform ABzc in act  724 . The process then waits until the current limit Ilimit is reached in act  726  and measures the inductive sense count ABis in act  730 . Act  730  also includes letting the motor current decay and then driving winding pair AC. 
     In a similar manner, ETON waveform ACzc and inductive sense count ACis are measured in acts  732 ,  734 ,  736  and  740 . Likewise, ETON waveform BCzc and inductive sense count BCis are measured in acts  742 ,  744 ,  746  and  750 ; ETON waveform BAzc and inductive sense count BAis are measured in acts  752 ,  754 ,  756  and  760 ; and ETON waveform CAzc and inductive sense count CAis are measured in acts  762 ,  764 ,  766 , and  768 . 
     In act  768 , the ETON waveform values and the inductive sense count values are used to reference an entry in Table 1 which provides the position of the rotor. In particular, the values of the six digitized ETON waveforms are listed in the table, and the values of regions A, B and C are determined according to equations (1), (2), and (3) as described above. The value in the table matching the values of regions A, B and C and the six digitized ETON waveform values is identified as the position of the rotor. 
     Although not the main objective of this disclosure, since the mutual inductance and inductive sense information have a phase misalignment of 30°, we could also use both information to double the position sensing resolution at the expense of having less accurate information due to lower tolerance to manufacturing defects. 
     Having thus described at least one illustrative embodiment of the invention, various alterations, modifications and improvements will readily occur to those skilled in the art. Such alterations, modifications, and improvements are intended to be part of this disclosure, and are intended to be within the spirit and the scope of the present invention. Accordingly, the foregoing description is by way of example only and is not intended to be limiting. The present invention is limited only as defined in the following claims and the equivalents thereto. 
     
       
         
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 Max. 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 Possible 
                 Detected 
                 Detection 
               
               
                 A 
                 B 
                 C 
                 CBzc 
                 ABzc 
                 ACzc 
                 BCzc 
                 BAzc 
                 CAzc 
                 Region 
                 Region 
                 Error 
               
               
                   
               
             
             
               
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 1 
                 0 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 1 
                 1 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 1 
                 0 
                 0 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 1 
                 0 
                 1 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 1 
                 1 
                 0 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 1 
                 1 
                 1 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 0 
                 1 
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
                 0 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 0 
                 1 
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
                 1 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 0 
                 1 
                 0 
                 1 
                 0 
                 0 
                 1 
                 0 
                 0 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 0 
                 1 
                 0 
                 1 
                 0 
                 0 
                 1 
                 0 
                 1 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 0 
                 1 
                 0 
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 0 
                 1 
                 0 
                 1 
                 0 
                 0 
                 1 
                 1 
                 1 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 1 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 1 
                 1 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 1 
                 0 
                 1 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 1 
                 1 
                 1 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 1 
                 0 
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 1 
                 0 
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 1 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 1 
                 0 
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
                 0 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 1 
                 0 
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
                 1 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 1 
                 0 
                 0 
                 1 
                 0 
                 0 
                 1 
                 0 
                 0 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 1 
                 0 
                 0 
                 1 
                 0 
                 0 
                 1 
                 0 
                 1 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 1 
                 0 
                 0 
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 1 
                 0 
                 0 
                 1 
                 0 
                 0 
                 1 
                 1 
                 1 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 1 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 1 
                 0 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 1 
                 1 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
                 1 
                 0 
                 0 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
                 1 
                 0 
                 1 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
                 1 
                 1 
                 0 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
                 1 
                 1 
                 1 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 1 
                 1 
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 1 
                 1 
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 1 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 1 
                 1 
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
                 0 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 1 
                 1 
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
                 1 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 1 
                 1 
                 0 
                 1 
                 0 
                 0 
                 1 
                 0 
                 0 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 1 
                 1 
                 0 
                 1 
                 0 
                 0 
                 1 
                 0 
                 1 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 1 
                 1 
                 0 
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 1 
                 1 
                 0 
                 1 
                 0 
                 0 
                 1 
                 1 
                 1 
                 R0 
                 R0 = AC 
                 30° 
               
               
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
                 1 
                 0 
                 0 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
                 1 
                 0 
                 1 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
                 1 
                 1 
                 0 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 0 
                 1 
                 0 
                 0 
                 1 
                 1 
                 1 
                 0 
                 0 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 0 
                 1 
                 0 
                 0 
                 1 
                 1 
                 1 
                 0 
                 1 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 0 
                 1 
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 0 
                 1 
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 1 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
                 1 
                 0 
                 0 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
                 1 
                 0 
                 1 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
                 1 
                 1 
                 0 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
                 1 
                 1 
                 1 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 0 
                 1 
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 0 
                 1 
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 1 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 0 
                 1 
                 0 
                 1 
                 1 
                 1 
                 1 
                 1 
                 0 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 0 
                 1 
                 0 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
                 0 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
                 1 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 1 
                 0 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 0 
                 1 
                 1 
                 0 
                 1 
                 1 
                 1 
                 0 
                 0 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 0 
                 1 
                 1 
                 0 
                 1 
                 1 
                 1 
                 0 
                 1 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 0 
                 1 
                 1 
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 0 
                 1 
                 1 
                 1 
                 0 
                 1 
                 1 
                 0 
                 0 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 0 
                 1 
                 1 
                 1 
                 0 
                 1 
                 1 
                 0 
                 1 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 0 
                 1 
                 1 
                 1 
                 0 
                 1 
                 1 
                 1 
                 0 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 0 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 0 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 0 
                 1 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 0 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 0 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 1 
                 1 
                 0 
                 0 
                 0 
                 1 
                 1 
                 0 
                 0 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 1 
                 1 
                 0 
                 0 
                 0 
                 1 
                 1 
                 0 
                 1 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 1 
                 1 
                 0 
                 0 
                 0 
                 1 
                 1 
                 1 
                 0 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 1 
                 1 
                 0 
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 1 
                 0 
                 0 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 1 
                 0 
                 1 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 1 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 1 
                 1 
                 0 
                 1 
                 0 
                 1 
                 1 
                 0 
                 0 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 1 
                 1 
                 0 
                 1 
                 0 
                 1 
                 1 
                 0 
                 1 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 1 
                 1 
                 0 
                 1 
                 0 
                 1 
                 1 
                 1 
                 0 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 1 
                 1 
                 0 
                 1 
                 0 
                 1 
                 1 
                 1 
                 1 
                 R1 
                 R1 = BC 
                 30° 
               
               
                 0 
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 1 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 0 
                 1 
                 0 
                 0 
                 1 
                 0 
                 0 
                 1 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 0 
                 1 
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 0 
                 1 
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 0 
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 0 
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
                 1 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 0 
                 1 
                 1 
                 0 
                 1 
                 0 
                 0 
                 0 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 0 
                 1 
                 1 
                 0 
                 1 
                 0 
                 0 
                 1 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 0 
                 1 
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 0 
                 1 
                 1 
                 1 
                 0 
                 0 
                 0 
                 1 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
                 0 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
                 1 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
                 0 
                 0 
                 0 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
                 0 
                 0 
                 1 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 1 
                 0 
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 1 
                 0 
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
                 0 
                 0 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
                 0 
                 0 
                 0 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
                 0 
                 0 
                 1 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 1 
                 0 
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 1 
                 0 
                 1 
                 1 
                 0 
                 0 
                 0 
                 1 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 1 
                 0 
                 1 
                 1 
                 1 
                 0 
                 0 
                 0 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 1 
                 0 
                 1 
                 1 
                 1 
                 0 
                 0 
                 1 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 1 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
                 0 
                 0 
                 0 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
                 0 
                 0 
                 1 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 1 
                 1 
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 1 
                 1 
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 1 
                 1 
                 0 
                 1 
                 1 
                 0 
                 0 
                 0 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 1 
                 1 
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 1 
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 1 
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
                 1 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 1 
                 1 
                 1 
                 0 
                 1 
                 0 
                 0 
                 0 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 1 
                 1 
                 1 
                 0 
                 1 
                 0 
                 0 
                 1 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
                 0 
                 1 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 1 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
                 0 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 1 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
                 1 
                 R2 
                 R2 = BA 
                 30° 
               
               
                 0 
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 0 
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 0 
                 0 
                 1 
                 0 
                 0 
                 1 
                 0 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 0 
                 0 
                 1 
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 0 
                 0 
                 1 
                 0 
                 1 
                 0 
                 0 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 0 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 0 
                 0 
                 1 
                 0 
                 1 
                 1 
                 0 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 0 
                 0 
                 1 
                 0 
                 1 
                 1 
                 1 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 0 
                 0 
                 1 
                 1 
                 0 
                 0 
                 0 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 0 
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 0 
                 0 
                 1 
                 1 
                 0 
                 1 
                 0 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 0 
                 0 
                 1 
                 1 
                 0 
                 1 
                 1 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 0 
                 0 
                 1 
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 0 
                 0 
                 1 
                 1 
                 1 
                 0 
                 1 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 0 
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 0 
                 1 
                 1 
                 0 
                 0 
                 0 
                 1 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
                 0 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 0 
                 1 
                 1 
                 0 
                 1 
                 0 
                 0 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 0 
                 1 
                 1 
                 0 
                 1 
                 0 
                 1 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 0 
                 1 
                 1 
                 0 
                 1 
                 1 
                 0 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 0 
                 1 
                 1 
                 1 
                 0 
                 0 
                 0 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 0 
                 1 
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 0 
                 1 
                 1 
                 1 
                 0 
                 1 
                 0 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 1 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 0 
                 1 
                 1 
                 1 
                 1 
                 1 
                 0 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 1 
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 1 
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 1 
                 0 
                 1 
                 0 
                 0 
                 1 
                 0 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 1 
                 0 
                 1 
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 1 
                 0 
                 1 
                 0 
                 1 
                 0 
                 0 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 1 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 1 
                 0 
                 1 
                 0 
                 1 
                 1 
                 0 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 1 
                 0 
                 1 
                 0 
                 1 
                 1 
                 1 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 1 
                 0 
                 1 
                 1 
                 0 
                 0 
                 0 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 1 
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 1 
                 0 
                 1 
                 1 
                 0 
                 1 
                 0 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 1 
                 0 
                 1 
                 1 
                 0 
                 1 
                 1 
                 1 
                 1 
                 R3 
                 R3 = CA 
                 30° 
               
               
                 0 
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 1 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 0 
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
                 0 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 0 
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
                 1 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 0 
                 0 
                 1 
                 0 
                 0 
                 1 
                 0 
                 1 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 0 
                 0 
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 0 
                 0 
                 1 
                 0 
                 0 
                 1 
                 1 
                 1 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 0 
                 0 
                 1 
                 0 
                 1 
                 0 
                 0 
                 1 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 0 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
                 0 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 0 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
                 1 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 0 
                 0 
                 1 
                 0 
                 1 
                 1 
                 0 
                 1 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 0 
                 0 
                 1 
                 0 
                 1 
                 1 
                 1 
                 0 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 0 
                 0 
                 1 
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 1 
                 0 
                 0 
                 0 
                 0 
                 1 
                 0 
                 0 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 1 
                 0 
                 0 
                 0 
                 0 
                 1 
                 0 
                 1 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 1 
                 0 
                 0 
                 0 
                 0 
                 1 
                 1 
                 0 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 1 
                 0 
                 0 
                 0 
                 0 
                 1 
                 1 
                 1 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 1 
                 0 
                 0 
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 1 
                 0 
                 0 
                 0 
                 1 
                 0 
                 0 
                 1 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 1 
                 0 
                 0 
                 0 
                 1 
                 0 
                 1 
                 0 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 1 
                 0 
                 0 
                 0 
                 1 
                 0 
                 1 
                 1 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 1 
                 0 
                 0 
                 0 
                 1 
                 1 
                 0 
                 0 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 1 
                 0 
                 0 
                 0 
                 1 
                 1 
                 0 
                 1 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 1 
                 0 
                 0 
                 0 
                 1 
                 1 
                 1 
                 0 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 1 
                 0 
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 1 
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 1 
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 1 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 1 
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
                 0 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 1 
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
                 1 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 1 
                 0 
                 1 
                 0 
                 0 
                 1 
                 0 
                 0 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 1 
                 0 
                 1 
                 0 
                 0 
                 1 
                 0 
                 1 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 1 
                 0 
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 1 
                 0 
                 1 
                 0 
                 0 
                 1 
                 1 
                 1 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 1 
                 0 
                 1 
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 1 
                 0 
                 1 
                 0 
                 1 
                 0 
                 0 
                 1 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 1 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
                 0 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 1 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
                 1 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 1 
                 0 
                 1 
                 0 
                 1 
                 1 
                 0 
                 0 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 1 
                 0 
                 1 
                 0 
                 1 
                 1 
                 0 
                 1 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 1 
                 0 
                 1 
                 0 
                 1 
                 1 
                 1 
                 0 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 1 
                 0 
                 1 
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 R4 
                 R4 = CB 
                 30° 
               
               
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
                 0 
                 0 
                 1 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
                 0 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
                 1 
                 0 
                 0 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
                 1 
                 0 
                 1 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
                 1 
                 1 
                 0 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
                 1 
                 1 
                 1 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 0 
                 0 
                 1 
                 1 
                 1 
                 0 
                 0 
                 0 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 0 
                 0 
                 1 
                 1 
                 1 
                 0 
                 0 
                 1 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 0 
                 0 
                 1 
                 1 
                 1 
                 0 
                 1 
                 0 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 0 
                 0 
                 1 
                 1 
                 1 
                 0 
                 1 
                 1 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 1 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 1 
                 0 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 0 
                 1 
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 0 
                 1 
                 1 
                 1 
                 0 
                 0 
                 0 
                 1 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 0 
                 1 
                 1 
                 1 
                 0 
                 0 
                 1 
                 0 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 0 
                 1 
                 1 
                 1 
                 0 
                 1 
                 0 
                 0 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 0 
                 1 
                 1 
                 1 
                 0 
                 1 
                 0 
                 1 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 0 
                 1 
                 1 
                 1 
                 0 
                 1 
                 1 
                 0 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
                 0 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
                 1 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 1 
                 0 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 0 
                 1 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 0 
                 1 
                 1 
                 1 
                 1 
                 1 
                 0 
                 1 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 0 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 0 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 1 
                 0 
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 1 
                 0 
                 1 
                 1 
                 0 
                 0 
                 0 
                 1 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 1 
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
                 0 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 1 
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 1 
                 0 
                 1 
                 1 
                 0 
                 1 
                 0 
                 0 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 1 
                 0 
                 1 
                 1 
                 0 
                 1 
                 0 
                 1 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 1 
                 0 
                 1 
                 1 
                 0 
                 1 
                 1 
                 0 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 1 
                 0 
                 1 
                 1 
                 0 
                 1 
                 1 
                 1 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 1 
                 0 
                 1 
                 1 
                 1 
                 0 
                 0 
                 0 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 1 
                 0 
                 1 
                 1 
                 1 
                 0 
                 0 
                 1 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 1 
                 0 
                 1 
                 1 
                 1 
                 0 
                 1 
                 0 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 1 
                 0 
                 1 
                 1 
                 1 
                 0 
                 1 
                 1 
                 R5 
                 R5 = AB 
                 30° 
               
               
                 1 
                 1 
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
                 R1, R5 
                 R0 = AC 
                 90° 
               
               
                 1 
                 1 
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 1 
                 R1, R5 
                 R0 = AC 
                 90° 
               
               
                 1 
                 1 
                 0 
                 1 
                 1 
                 1 
                 1 
                 1 
                 0 
                 R1, R5 
                 R0 = AC 
                 90° 
               
               
                 1 
                 1 
                 0 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 R1, R5 
                 R0 = AC 
                 90° 
               
               
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 R0, R2 
                 R1 = BC 
                 90° 
               
               
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 1 
                 R0, R2 
                 R1 = BC 
                 90° 
               
               
                 0 
                 1 
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 R0, R2 
                 R1 = BC 
                 90° 
               
               
                 0 
                 1 
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 1 
                 R0, R2 
                 R1 = BC 
                 90° 
               
               
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 R1, R3 
                 R2 = BA 
                 90° 
               
               
                 0 
                 1 
                 1 
                 0 
                 1 
                 1 
                 1 
                 1 
                 1 
                 R1, R3 
                 R2 = BA 
                 90° 
               
               
                 0 
                 1 
                 1 
                 1 
                 0 
                 1 
                 1 
                 1 
                 1 
                 R1, R3 
                 R2 = BA 
                 90° 
               
               
                 0 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 R1, R3 
                 R2 = BA 
                 90° 
               
               
                 0 
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 R2, R4 
                 R3 = CA 
                 90° 
               
               
                 0 
                 0 
                 1 
                 0 
                 0 
                 1 
                 0 
                 0 
                 0 
                 R2, R4 
                 R3 = CA 
                 90° 
               
               
                 0 
                 0 
                 1 
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 R2, R4 
                 R3 = CA 
                 90° 
               
               
                 0 
                 0 
                 1 
                 0 
                 1 
                 1 
                 0 
                 0 
                 0 
                 R2, R4 
                 R3 = CA 
                 90° 
               
               
                 1 
                 0 
                 1 
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 R3, R5 
                 R4 = CB 
                 90° 
               
               
                 1 
                 0 
                 1 
                 1 
                 1 
                 0 
                 1 
                 1 
                 1 
                 R3, R5 
                 R4 = CB 
                 90° 
               
               
                 1 
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 1 
                 1 
                 R3, R5 
                 R4 = CB 
                 90° 
               
               
                 1 
                 0 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 R3, R5 
                 R4 = CB 
                 90° 
               
               
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 R0, R4 
                 R5 = AB 
                 90° 
               
               
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 1 
                 0 
                 R0, R4 
                 R5 = AB 
                 90° 
               
               
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 1 
                 0 
                 0 
                 R0, R4 
                 R5 = AB 
                 90° 
               
               
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 1 
                 1 
                 0 
                 R0, R4 
                 R5 = AB 
                 90° 
               
             
          
           
               
                 OTHER UNREACHABLE INPUTS 
                 UNDETERMINED 
                 180°