Patent Publication Number: US-9411796-B2

Title: Smoothing paths in a graphical interface generated by drawing inputs

Description:
TECHNICAL FIELD 
     This disclosure relates generally to computer-implemented methods and systems and more particularly relates to smoothing paths in a graphical interface generated by drawing inputs. 
     BACKGROUND 
     Computing applications use drawing inputs to specify paths or shapes on a graphical interface. For example, a graphical interface may be displayed on a touch screen. A user may “draw” a line, a curve, or other path in the graphical interface by using a stylus or a finger to trace the path on the touch screen. 
     Such drawing inputs may imperfectly represent a desired path on the graphical interface. Defects in the path can include unwanted curves, lines, interruptions, or other unwanted features. The unwanted features can be caused by unintentional movement of the user&#39;s hand during a drawing input and/or due to noise introduced by the touch screen hardware. 
     It is desirable to decrease defects in a path generated by a drawing input caused by unintentional user movement during the drawing input and/or noise introduced by the input hardware. 
     SUMMARY 
     One embodiment involves determining a value of a motion attribute associated with a drawing input to a graphical interface. The embodiment also involves modifying a value of a smoothing parameter for a smoothing operation based on the determined value of the motion attribute. The smoothing parameter at least partially determines smoothing performed by a smoothing operation on input points generated by the drawing input. The embodiment also involves generating a path for rendering in the graphical interface. The path can be generated by applying the smoothing operation to the input points using the determined value of the smoothing parameter. 
     These illustrative embodiments are mentioned not to limit or define the disclosure, but to provide examples to aid understanding thereof. Additional embodiments are discussed in the Detailed Description, and further description is provided there. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
       These and other features, embodiments, and advantages of the present disclosure are better understood when the following Detailed Description is read with reference to the accompanying drawings, where: 
         FIG. 1  is a block diagram depicting an example computing system for implementing certain embodiments; 
         FIG. 2  is a modeling diagram depicting a drawing input to a graphical interface; 
         FIG. 3  is a modeling diagram depicting performance of a smoothing operation using input points obtained from a drawing input; 
         FIG. 4  is a modeling diagram depicting a path generated by the smoothing operation from the input points; 
         FIG. 5  is a modeling diagram depicting an example smoothing operation in which a cursor is modeled as a physical object dragged by an input device; 
         FIG. 6  is a modeling diagram depicting a movement of the input device causing a corresponding movement of the cursor; 
         FIG. 7  is a modeling diagram depicting a movement of the input device that is insufficient to cause a movement of the cursor; and 
         FIG. 8  is a flow chart illustrating an example method for smoothing paths in a graphical interface generated by drawing inputs. 
     
    
    
     DETAILED DESCRIPTION 
     Computer-implemented systems and methods are disclosed for smoothing paths in a graphical interface generated by drawing inputs. 
     The following non-limiting example is provided to help introduce the general subject matter of certain embodiments. A computing application can apply a smoothing operation to a drawing input. The smoothing operation can reduce or eliminate unwanted features in a path caused by unintentional movement of a user&#39;s hand during the drawing input. The computing application can determine that a greater amount of smoothing is desirable for rapid movements of a stylus and that a lower amount of smoothing is desirable for slower movements of the stylus. For example, a slowly drawn line may be more susceptible to defects caused by shaking of a user&#39;s hand than a quickly drawn line. The computing application can determine a speed associated with the drawing input (e.g., a speed at which a stylus moves across a touch screen). The computing application can modify a smoothing operation to provide higher amounts of smoothing for lower speeds and lower amounts of smoothing for higher speeds. 
     In accordance with one embodiment, a graphics module is provided for smoothing paths in a graphical interface generated by drawing inputs. The graphics module can determine a value of a motion attribute associated with a drawing input to a graphical interface. Non-limiting examples of a motion attribute include velocity of a drawing input, acceleration of a drawing input, curvature of the drawing input, etc. The graphics module can modify a value of a smoothing parameter for a smoothing operation based on the determined value of the motion attribute. The smoothing parameter at least partially determines an amount of smoothing performed by a smoothing operation on input points generated by the drawing input. For example, the graphics module may model a cursor as a mass being dragged in response to the drawing input. The amount of the mass can vary the amount of smoothing. The graphics module may increase the modeled mass value for lower velocities of the drawing input and may decrease the modeled mass value for higher velocities of the drawing input. The graphics module can generate a path to be rendered for display by the graphical interface. The path can be generated by applying the smoothing operation to the input points using the determined value of the smoothing parameter. 
     As used herein, the term “drawing input” is used to refer to a command to draw a line, curve, or other path in a graphical interface. A drawing input can be generated using any suitable input device such as (but not limited to), a touch screen, a touch pad, a mouse, etc. 
     As used herein, the term “motion attribute” is used to refer to an attribute of a physical motion with respect to an input device that generates the drawing input. Non-limiting examples of a motion attribute include the velocity or acceleration of the physical motion, a curvature of the motion, a pressure applied to an input device such as a touch screen during the motion, etc. 
     As used herein, the term “input point” is used to refer to a point along a path indicated by a drawing input. In one non-limiting example, a drawing input may be generated for a touch screen by capturing a series of images of a stylus or finger as the stylus or finger moves along a surface of the touch screen. Each image can be used to determine a respective input point identifying a respective position of the stylus or finger along the path indicated by the drawing input. In another non-limiting example, sensors on top of or beneath a touch surface or touch screen can detect pressure from a finger or stylus along the path indicated by the drawing input to generate the input points. 
     As used herein, the term “smoothing operation” is used to refer to an operation for modifying a path defined by the input points to generate a modified path to be rendered in a graphical interface. For example, a user may move a stylus along a horizontal axis for the purpose of drawing a line in the graphical interface. The motion of the stylus may include unintentional movements in a vertical direction caused by shaking of the user&#39;s hand. The path defined by the input points may thus include vertical spikes or curves rather than the flat horizontal line intended by the user. A smoothing operation can include modifying and/or removing one or more input points defining the vertical spikes or curves, thereby eliminating the unwanted features of the path caused by unintentional movements of the stylus. 
     As used herein, the term “smoothing parameter” is used to refer to any parameter that can modify an amount of smoothing performed by a smoothing operation. For example, a smoothing operation may modify or remove a given input point that deviates from a path by a given amount. A smoothing parameter can control the amount of deviation that causes the input point to be modified or removed. 
     As used herein, the term “output point” is used to refer to a point along a path to be rendered for display in a graphical interface in response to a drawing input. A group of output points defining the path to be rendered can be generated by applying a smoothing operation to the input points generated by a drawing input. 
     As used herein, the term “amount of smoothing” is used to refer to an amount by which a drawing input including multiple input points is modified to obtain a path including multiple output points. A greater amount of smoothing can include a greater portion of a drawing input being modified and/or a greater degree of modification to one or more portions of a drawing input. A smaller amount of smoothing can include a smaller portion of a drawing input being modified and/or a smaller degree of modification to one or more portions of a drawing input. 
     Referring now to the drawings,  FIG. 1  is a block diagram depicting an example computing system  102  for implementing certain embodiments. 
     The computing system  102  can include a processor  104  that is communicatively coupled to a memory  106  and that executes computer-executable program instructions and/or accesses information stored in the memory  106 . The processor  104  may comprise a microprocessor, an application-specific integrated circuit (“ASIC”), a state machine, or other processing device. The processor  104  can include any of a number of computer processing devices, including one. Such a processor can include or may be in communication with a computer-readable medium storing instructions that, when executed by the processor  104 , cause the processor to perform the steps described herein. 
     The computing system  102  can also include a bus  108 . The bus  108  can communicatively couple one or more components of the computing system  102 . 
     The computing system  102  can also include and/or be communicatively coupled to a number of external or internal devices, such as input or output devices. For example, the computing system  102  is shown with an input/output (“I/O”) interface  110 , a display device  112 , and an input device  114 . Non-limiting examples of a display device  112  include a screen integrated with the computing system  102 , a monitor external and coupled with the computing system, etc. Non-limiting examples of an input device  114  include a touch screen, a touch pad, an external mouse, etc. In some embodiments, the display device  112  and the input device  114  can be separate devices. In other embodiments, the display device  112  and the input device  114  can be integrated in the same device. For example, a display device  112  may be a screen and the input device  114  may be one or more components providing touch-screen functions for the display device, such as cameras for imaging a touch area or pressure sensors for detecting pressure changes caused by a touch. 
     The computing system  102  can modify, access, or otherwise use electronic content. The electronic content may be resident in any suitable computer-readable medium and execute on any suitable processor. In one embodiment, the electronic content can reside in the memory  106  at the computing system  102 . In another embodiment, the electronic content can be accessed by the computing system  102  from a remote content provider via a data network. 
     The memory  106  can include any suitable computer-readable medium. A computer-readable medium may include, but is not limited to, electronic, optical, magnetic, or other storage device capable of providing a processor with computer-readable instructions or other program code. Other examples comprise, but are not limited to, a floppy disk, CD-ROM, DVD, magnetic disk, memory chip, ROM, RAM, an ASIC, a configured processor, optical storage, magnetic tape or other magnetic storage, or any other medium from which a computer processor can read instructions. The instructions may comprise processor-specific instructions generated by a compiler and/or an interpreter from code written in any suitable computer-programming language, including, for example, C, C++, C#, Visual Basic, Java, Python, Perl, JavaScript, and ActionScript. 
     A graphics module  116  stored in the memory  106  can configure the processor  104  to prepare electronic content for rendering in a graphical interface and/or render the electronic content in the graphical interface. In some embodiments, the graphics module  116  can be a stand-alone application executed by the processor  104 . In other embodiments, the graphics module  116  can be a software module included in or accessible by a separate application executed by the processor  104  that is configured to modify, access, or otherwise use the electronic content. 
     The computing system  102  can include any suitable computing device for executing the graphics module  116 . Non-limiting examples of a computing device include a desktop computer, a tablet computer, a laptop computer, or any other computing device suitable for rendering the electronic content. 
       FIG. 2  is a modeling diagram depicting a drawing input  204  to a graphical interface  202 . The graphical interface  202  can be rendered for display by the display device  112 . The drawing input  204  can be provided to the computing system  102  via the input device  114 . For example, the drawing input  204  can be generated by a finger or stylus moving along an input device  114  such as a touch screen or touch pad. In some embodiments, a cursor  206  can be rendered for display by the display device  112 . The cursor  206  can visually depict the drawing input  204  received via the input device  114 . In other embodiments, a cursor  206  can be omitted. 
       FIG. 3  is a modeling diagram depicting performance of a smoothing operation  304  using input points  302  obtained from a drawing input  204 . The graphics module  116  can receive input points  302  from the input device  114 . The input points  302  can include points along a path defined by the drawing input  204 . The graphics module  116  can perform a smoothing operation  304  using the input points  302 . The smoothing operation  304  can generate output points  306  from the input points  302 . The output points  306  can be rendered in the graphical interface  202 . For example,  FIG. 4  is a modeling diagram depicting a path  402  generated by the smoothing operation  304  from the input points  302 . The smooth path  402  can be defined by the output points  306 . 
     In some embodiments, the smoothing operation  304  can involve modeling the cursor  206  as a physical object having a mass and modeling movement of the cursor  206  as a physical motion having a velocity. A modeled frictional force can resist the motion of the modeled physical object. 
     For example,  FIG. 5  is a modeling diagram depicting an example smoothing operation  304  in which a cursor  206  is modeled as a physical object dragged by an input device  114 . In a non-limiting example, a Dynadraw smoothing operation can model the cursor  206  as a physical object attached to the input device  114  by a spring  502  and moved along a surface  504  corresponding to the graphical interface  202 . 
     The graphics module  116  can model the cursor  206  as a physical object by assigning a mass m to the cursor  206 . The graphics module  116  can associate an amount of friction (or “drag”) with a movement of the cursor  206  having the assigned mass m. The drag can be represented by a drag constant c drag . 
     Modeling the cursor  206  as a physical object attached to a spring and having a mass and associated friction can allow the graphics module  116  to filter or otherwise ignore undesirable movements of an input device  114  during a drawing input  204 . For example, in the absence of the modeled mass, friction, and spring  504 , each movement of the input device  114  can be applied to the cursor  206 . In the presence of the modeled mass, friction, and spring  504 , a modeled resistive force generated by the modeled friction and mass and/or one or more modeled force associated with the spring  502  can reduce the effect of moving the input device  114  on the movement of the cursor  206 . In one non-limiting example, a movement of the input device  114  may be sufficient to “extend” the modeled spring  502 . The extension of the spring  502  can be modeled as exerting a force on the cursor  206 . The modeled force F exerted on the cursor  206  can cause the cursor  206  having a modeled mass m to move toward a position of the input device  114  with an acceleration a based on the function F=ma. For a smaller modeled mass m, the acceleration a can be larger such that the cursor  206  tracks closely to the input device  114 . For a larger modeled mass m, the acceleration a can be smaller such that the cursor  206  is less responsive to movement of the input device  114 , thereby smoothing out those movements of the input device  114 . In another non-limiting example, a modeled friction between with the cursor  206  and the model surface  504  can generate a modeled frictional force. The modeled frictional force can resist a modeled horizontal force applied to the cursor  206 . The frictional force can be selected so as to limit oscillation around the input device  114  of the cursor  206  “attached” to the spring  502 . The frictional force can prevent the spring  502  from causing the cursor  206  to accelerate such that the cursor  206  moves past the input device  114  and oscillates around the input device  114 . 
     A movement of the input device  114  sufficient to overcome a modeled resistive force generated by the drag constant c drag  for a mass m can result in a movement of the cursor  206 . For example,  FIG. 6  is a modeling diagram depicting a movement  602  of the input device  114  causing a corresponding movement  604  of the cursor  206 . The movement  602  can correspond to the drawing input  204  generated using the input device  114 . The movement  602  of the input device  114  is modeled as applying a force through the spring  502  to the cursor  206 . The modeled force can be proportional to the extension of the spring  502 . The modeled force F acting on the cursor  206  can be the sum of the forces due to spring  502  extension and force associated with the drag constant c drag . The acceleration of the cursor  206  in movement  604  can be determined by applying F=ma. 
     A movement with respect to the input device  114  may be insufficient to overcome an inertia associated with the cursor  206  having a modeled mass m. The inertia of the cursor  206  can be a function of the mass of the cursor  206 . A higher mass can be associated with a higher inertia, thereby making the cursor less responsive to movements of the input device. The inertia can cause the graphics module  116  to filter out or otherwise ignore the movement with respect to the input device  114 , thereby limiting movement of the cursor  206 . For example,  FIG. 7  is a modeling diagram depicting a movement  702  of the input device  114  that is insufficient to cause a movement of the cursor  206 . The movement  702  can correspond to an undesirable movement with respect to the input device  114 . In one non-limiting example, the movement  702  may be a small, rapid movement of the input device  114  that may occur due to noise in the input. The movement  702  being small can cause the modeled force applied to the cursor  206  to be correspondingly small. The movement  702  being rapid can cause the movement  702  to be applied for a short amount of time. The movement  702  being small and having a short duration can cause a correspondingly small acceleration to be applied to the cursor  206 . A small acceleration being applied to the cursor  206  can limit the movement of cursor  206  in response to the movement  702 . In another non-limiting example, an undesirable movement with respect to the input device  114  may be caused by a shaking of a user&#39;s hand while performing the movement that generates the drawing input  204 . The graphics module  116  can determine that the movement  702  is sufficiently small that a modeled force generated by the movement  702  is insufficient to overcome an inertia associated with the cursor  206 . The inertia resists movement of the cursor  206  and thereby limit movement of the cursor  206 . Limiting movement of the cursor  206  in response to the undesirable movement  702  can smooth a path  402  generated in response to the drawing input  204 . 
     The path  402  can be defined by the output points  306 . The graphics module  116  can generate n output points  306  based on the input points  302 . For a given output point p out,n , the graphics module  116  can determine a model force F associated with the movement of the cursor  206  based on the function
 
 F=k ( p   in   −p   out,n-1 ),
 
where p in  represents the received input position, p out,n-1  represents a recent filtered output point, and k is a constant describing the strength of the spring  502 . The function can be simplified by using k=1, which can effectively consolidate the spring constant with the mass m and drag constant. A filtered output point can be one of the output points  306  defining the smooth path  402  and generated by filtering or otherwise modifying one or more of the input points  302 . The graphics module  116  can select a time value of t=1 to simplify the function above to obtain the function
 
 F=p   in   −p   out,n-1 .
 
     The graphics module  116  can determine a model acceleration a associated with the model force F and the assigned mass m based on the function 
     
       
         
           
             a 
             = 
             
               
                 F 
                 m 
               
               . 
             
           
         
       
     
     An initial velocity v 0  of the drawing input  204  can be updated based on the acceleration a. An updated velocity v 1  can be determined from the function
 
 v   1   =v   0   +at.  
 
The graphics module  116  can select a time value of t=1 to simplify the function above to obtain the function
 
 v   1   =v   0   +a  
 
The velocity v 1  can be further updated based on the drag factor to have a velocity v 2  as determined by the function
 
 v   2   =v   1   ×c   drag .
 
     The output point p out,n  can be determined from the recent output point p out,n-1  based on the function
 
 p   out,n   =p   out,n-1   +v   2   t.  
 
The graphics module  116  can select a time value of t=1 to simplify the function above to obtain the function
 
 p   out,n   =p   out,n-1   +v   2   t.  
 
     In some embodiments, a Dynadraw smoothing operation as described above or other similar smoothing operation can generate an inexact estimate for one or more of the points p out,n . The inexact estimate can result from using an assigned drag constant. The value of the drag constant can control an amount of oscillation in the path  402 . The oscillation can be generated by modeling the cursor  206  as a mass attached to a spring. Different values of the drag constant can result in different oscillation values. The value of the drag constant can also control an amount of overshoot or undershoot in the output points  306  generated by the smoothing operation  304 . Incorrect or sub-optimal selection of the drag constant value can result in the output points  306  defining a path  402  having reduced fidelity to the desired path indicated by the drawing input  204 . 
     Deficiencies of the Dynadraw process or other similar process can be remedied by improving tuning of a drag factor and providing a more accurate simulation of the mass spring system to improve the smoothness of the output points  306 . 
     In some embodiments, the output points  306  can be generated with greater fidelity to the desired path by applying a smoothing operation  304  without a drag constant having a set value. For example, the graphics module  116  can model a path between each of the input points  302  as a straight line. Modeling a path between each of the input points  302  as a straight line can allow the graphics module  116  to generate the output points  306  using a differential equation using the position of the drawing input  204 , as described below. 
     For example, a path including the output points  306  can be determined from the function p(t). An output path p(t) can be determined by solving the following differential equation for p(t):
 
 p ″( t )+γ p ′( t )+ p ( t )= p   in,n-1   +Dt  
 
The p″ (t) is a second derivative of the function (p)(t) and p′ (t) is a first derivative of the function (p)(t). The point p in,n-1  is a prior un-smoothed input point. A distance D between an input point p in  and a prior un-smoothed input point p in,n-1  can be represented by the function D=p in −p in,n-1  
 
     The graphics module  116  can automatically determine a drag factor γ based on the mass factor m using the function
 
γ=2√{square root over (m)}.
 
The drag factor γ can minimize oscillation and/or overshoot/undershoot of the cursor  206  with respect to the input device  114 .
 
     For a time value of 1, the graphics module  116  can determine the term dp′(t) from the velocity v at which the output point is moving, as represented by the function 
               v   =         ⅆ   p       ⅆ   t       =         (     xr   +     y   ⁡     (     1   +   rt     )         )     ⁢     ⅇ   rt       +   D         ,     
     ⁢   where               r   =       -   1       m                     x   =       (       p     out   ,     n   -   1         -     p     in   ,     n   -   1           )     +     γ   ⁢           ⁢   D         ,   and               y   =       v   out     -   D   -   xr           
for a previously determined output point p out,n-1  and a prior input point p in,n-1 , where v out  is a velocity corresponding to p out,n-1 .
 
     The graphics module  116  can determine the solution for the differential equation above to obtain an output point p for a received input point p in  at time t=1. The output point can be represented by the function
 
 p ( t )=( x+yt ) e   rt   +z,  
 
where
 
 z=p+D ( t −γ).
 
     The graphics module  116  can thereby obtain a function p(t) for a smooth path  402  based on the input points p in  and p in,n-1  (which are determinative of distance D), a previously determined output point p out,n-1  and the velocity v out  for the previously determined output point p out,n-1 , and the mass factor m (which is determinative of r and drag factor γ). 
     In some embodiments, the graphics module  116  can vary the amount of smoothing applied to different input points  302 . For example, for drawing inputs having a lower velocity v, a larger mass factor can be desirable. A larger mass factor m can produce a smooth result for drawing inputs having a lower velocity v. A potential disadvantage of increasing the mass factor m can be increasing the distance (or lag) between the current input position and the corresponding rendered output position. An excessive lag may be sufficiently long that a user can perceive the lag, thereby decreasing a quality of the user&#39;s experience. In another example, for drawing inputs having a higher velocity v, a lower amount of smoothing can be desirable. The higher velocity may reduce the effects of noise or other undesirable motion of the cursor  206 . Decreasing the mass factor at higher velocities can reduce the lag without adversely affecting the smoothness of the output path  402 . 
     In some embodiments, the graphics module  116  can vary the mass factor m based on one or more motion attributes of the motion of the drawing input. Non-limiting examples of motion attributes include the velocity and acceleration of the motion of the drawing input. For example, the value of the mass factor m can be decreased as the velocity v increases and increased as the velocity v decreases. Varying the mass m based on the velocity v or other motion attribute can modify the amount of smoothing performed by the smoothing operation  304 . Modifying the amount of smoothing performed by the smoothing operation  304  can provide a smooth output path  402  having reduced or minimal lag for a range of drawing speeds. 
     In a non-limiting example, the graphics module  116  can vary the mass factor m as a function of the velocity v of the drawing input. The variable mass factor m can be represented by the function: 
             m   =         m   0         w   ⁡     (         m   0     /     m   1       -   1     )       +   1       .           
The parameter w can be represented by the function
 
             w   =       (     v   -     v   0       )       (       v   1     -     v   0       )             
where v 0  represents a minimum velocity, v 1  represent as maximum velocity, m 0  represents a mass factor value for use with the minimum velocity v 0 , and m 1  represents a mass factor value for use with the maximum velocity v 1 . The variable mass m can be used to determine an output point p out,n  using the function p out,n =(a+bt)e rt +c, as described above. The maximum velocity v 1  and minimum velocity v 0  can vary based on characteristics of the input device  114  and can be selected experimentally in order to produce a suitably smooth output and a reduced or minimal lag.
 
 FIG. 8  is a flow chart illustrating an example method  800  for smoothing paths in a graphical interface generated by drawing inputs. For illustrative purposes, the method  800  is described with reference to the system implementation depicted in  FIG. 2  and the operations described with respect to  FIGS. 3-7 . Other implementations, however, are possible.
 
     The method  800  involves determining a value of a motion attribute associated with a drawing input to a graphical interface, as shown in block  810 . The processor  104  of the computing system  102  can execute the graphics module  116  or other suitable programming instructions to determine the value of the motion attribute associated with a drawing input  204  to a graphical interface  202 . 
     In some embodiments, a motion attribute can be associated with a speed of the drawing input  204 , such as (but not limited to) the velocity and/or the acceleration of the drawing input  204 . The processor  104  can execute the graphics module  116  or other suitable programming instructions to determine the velocity and/or acceleration. Determining the velocity and/or acceleration associated with the drawing input  204  may involve associating a time value with each of the input points  302  identifying when the input point was generated by the input device  114 . In one non-limiting example, the processor  104  can determine the velocity based on the total distance of the drawing input and the duration of the drawing input. The processor  104  can determine a distance between the first received point and the last received point of the input points  302 . The processor  104  can determine a duration of the drawing input  204  from a difference between the time values for the first received point and the last received point. The processor  104  can determine a velocity for the drawing input  304  based on the determined distance and duration associated with the drawing input  304 . In another non-limiting example, the processor  104  can determine a velocity at each of the input points  302  based on a distance between sequential pairs or groups of the input points  302  and the difference in time values between the sequential pairs or groups. The processor  104  can determine an acceleration at each of the input points  302  based on changes in the determined velocity between sequential pairs of the input points  302 . 
     In additional or alternative embodiments, a motion attribute can be a curvature associated with the drawing input  204 . For example, the processor  104  can determine that the drawing input  204  generally defines a straight line, a curve, or other shapes. For example, the mass can be increased in regions of high local curvature that may correspond to a noisy part of the input. The graphics module  116  can estimate a discrete curvature of the drawing input  204 . For example given 3 input points A, O, B, an estimate of curvature can be
 
 k= 4 S /( abc )
 
where S is the area of the triangle AOB and a, b, c are the distances AO, OB and BC respectively.
 
     In additional or alternative embodiments, a motion attribute can be a pressure associated with one or more of the input points  302  generated by the drawing input  204 . For example, an input device  114  may be a touch device, such as a touch screen or touch pad, that can detect an amount of pressure applied by a finger or stylus to a touch surface. 
     In some embodiments, the drawing input  204  can be received in a two-dimensional plane. In other embodiments, the drawing input  204  can be received in a three-dimensional space. The input device  114  can include one or more devices that can image a three-dimensional space and capture the position of a stylus, finger, or other object in the three-dimensional space. The processor  104  can determine the motion attribute based on the positions of each of the input points  302  in the three-dimensional space. 
     The method  800  further involves modifying a value of a smoothing parameter for a smoothing operation based on the determined value of the motion attribute, as shown in block  820 . The processor  104  of the computing system  102  can execute the graphics module  116  or other suitable programming instructions to modify the value of a smoothing parameter for a smoothing operation  304  based on the determined value of the motion attribute, as described above with respect to  FIGS. 5-7 . 
     The smoothing parameter can at least partially determine an amount of smoothing performed by the smoothing operation  304 . In some embodiments, the smoothing parameter can be a variable mass factor for the cursor  206 . In other embodiments, the smoothing parameter can be a variable drag factor for the cursor  206 . In one non-limiting example, the drag factor can be increased at higher velocities. Increasing the drag factor can accentuate curves in the input stream. At lower velocities, the drag factor can remain constant or be decreased to prevent accentuating noise and wobbles in the input, which may be undesirable. The same formula can be used to vary the drag factor as for varying the mass factor by substituting drag factor for the mass factor in the formula. 
     In one non-limiting example, a smoothing parameter such as variable mass factor m can be varied based on a motion parameter such as a velocity according to the function 
               m   =       m   0         w   ⁡     (         m   0     /     m   1       -   1     )       +   1         ,         
as described above.
 
     In another non-limiting example, a smoothing parameter such as a variable mass factor can be varied based on a motion parameter such as a pressure associated with one or more of the input points  302 . An increased pressure can indicate that less smoothing is required and a decreased pressure can indicate that more smoothing is required. The graphics module  116  can decrease the value of the mass factor based on an increase in pressure and can increase the value of the mass factor based on a decrease in pressure. The graphics module  116  can use same formula as used as for varying mass with velocity by substituting pressure values for the velocity. 
     The method  800  further involves generating a path for rendering in the graphical interface by applying the smoothing operation to the plurality of input points using the determined value of the smoothing parameter, as shown in block  830 . The processor  104  of the computing system  102  can execute the graphics module  116  or other suitable programming instructions to generate a path  402  for rendering in the graphical interface  202  by applying the smoothing operation  304  to the input points  302 , as described above with respect to  FIGS. 3-7 . 
     In some embodiments, the graphics module  116  can determine the output points  306  defining a path  402  by using a differential equation that describes relationships among the position, velocity and acceleration of the output, an assigned mass factor for the cursor  206 , and one or more of the input points  302 . The graphics module  116  can assign a variable mass factor to the cursor  206 , as described above. The graphics module  116  can determine the acceleration and velocity of the drawing input  204  based on the input points  302 , as described above with respect to block  810 . The graphics module  116  can determine a differential equation relating the velocity, the acceleration, the mass factor, and the input points  302 . The graphics module  116  can determine each of the output points  306  by solving the differential equation, as described above. 
     In other embodiments, a Dynadraw process or other suitable smoothing operation can be used to generate the path  402 . The graphics module  116  can assign a mass factor and a drag factor to a cursor  206  used to indicate the drawing input, as described above with respect to  FIGS. 5-7 . The graphics module  116  can determine a model force associated with a movement of the cursor  206  by the drawing input  204 . The model force can be determined based on the mass factor, the drag factor, and the input points  302  of the drawing input  204 . The graphics module  116  can generate the output points based on an acceleration associated with the model force and the drag factor. The graphics module  116  can modify at least one of the mass factor and the drag factor based on one or more motion attributes of the drawing input. 
     In additional or alternative embodiments, the graphics module  116  can modify a smoothing parameter (e.g., a variable mass factor) during the drawing input  204  based on detecting differences in the motion attribute (e.g., differences in velocity) during different portions of the drawing input  204 . For example, the graphics module  116  can determine a first value of the motion attribute for a first portion of the drawing input  204  (e.g., a first velocity) and a second value of the motion attribute for a second portion of the drawing input  204  (e.g., a second velocity greater than or less than the first velocity). The graphics module  116  can select first and second values for a smoothing parameter (e.g., assign first and second values to a mass factor) based on the respective first and second values of the motion attribute during first and second portions of the drawing input  204 . The graphics module  116  can apply a first amount of smoothing to the first portion of the drawing input  204  based on the first value of the smoothing parameter. The graphics module  116  can apply a second amount of smoothing greater than or less than the first amount of smoothing to the second portion of the drawing input  204  based on the second value of the smoothing parameter. 
     GENERAL CONSIDERATIONS 
     Numerous specific details are set forth herein to provide a thorough understanding of the claimed subject matter. However, those skilled in the art will understand that the claimed subject matter may be practiced without these specific details. In other instances, methods, apparatuses, or systems that would be known by one of ordinary skill have not been described in detail so as not to obscure claimed subject matter. 
     Unless specifically stated otherwise, it is appreciated that throughout this specification discussions utilizing terms such as “processing,” “computing,” “calculating,” “determining,” and “identifying” or the like refer to actions or processes of a computing device, such as one or more computers or a similar electronic computing device or devices, that manipulate or transform data represented as physical electronic or magnetic quantities within memories, registers, or other information storage devices, transmission devices, or display devices of the computing platform. 
     The system or systems discussed herein are not limited to any particular hardware architecture or configuration. A computing device can include any suitable arrangement of components that provide a result conditioned on one or more inputs. Suitable computing devices include multipurpose microprocessor-based computer systems accessing stored software that programs or configures the computing system from a general purpose computing apparatus to a specialized computing apparatus implementing one or more embodiments of the present subject matter. Any suitable programming, scripting, or other type of language or combinations of languages may be used to implement the teachings contained herein in software to be used in programming or configuring a computing device. 
     Embodiments of the methods disclosed herein may be performed in the operation of such computing devices. The order of the blocks presented in the examples above can be varied—for example, blocks can be re-ordered, combined, and/or broken into sub-blocks. Certain blocks or processes can be performed in parallel. 
     The use of “adapted to” or “configured to” herein is meant as open and inclusive language that does not foreclose devices adapted to or configured to perform additional tasks or steps. Additionally, the use of “based on” is meant to be open and inclusive, in that a process, step, calculation, or other action “based on” one or more recited conditions or values may, in practice, be based on additional conditions or values beyond those recited. Headings, lists, and numbering included herein are for ease of explanation only and are not meant to be limiting. 
     While the present subject matter has been described in detail with respect to specific embodiments thereof, it will be appreciated that those skilled in the art, upon attaining an understanding of the foregoing may readily produce alterations to, variations of, and equivalents to such embodiments. Accordingly, it should be understood that the present disclosure has been presented for purposes of example rather than limitation, and does not preclude inclusion of such modifications, variations, and/or additions to the present subject matter as would be readily apparent to one of ordinary skill in the art.