Method of and apparatus for obtaining image data used for filling inner or outer region of graphic figure

Abstract: Segment data expressing segments which form the contour of a graphic figure are provided. Connection mode data expressing the connection modes between the segments are generated. The loops included in the graphic figure are detected on the basis of the segment data and the connection mode data. Even if the segments imperfectly define the contour, the loops can be detected through the step of correcting the segment data and the connection mode data.

Description: The present invention relates to a method and an apparatus for inputting graphic data provided in the form of a set of segments, to convert the same into image data used for filling the inner or outer region of a graphic figure whose contour line is expressed by the segments, with the features of a first part of claim 1 and 11, resp. Such method and apparatus are known from IEEE COMPUTER GRAPHICS AND APPLICATIONS, vol. 6, no. 7, July 1986, pages 61-70, New York, US; R.D. HERSCH: "Descriptive contour fill of partly degenerated shapes". In the field of process printing, inner or outer region of a graphic figure is often filled with a monochromatic color to produce a process cut mask or a pattern mask used for making a printed circuit board. One of the conventional techniques for conducting the filling process employs a cutting machine. For example, consider a mask film 2 shown in Fig. 28A of the accompanying drawings, in which the inner region of the graphic figure 1 should be filled with a monochromatic color. In manufacturing the mask film 2, data expressing segments 3a-3d (Fig. 28BV) defining the contour line of the graphic figure 1 are prepared by means of a computer aided design technique (CAD). In Fig. 28B, the segments 3a-3d are illustrated as vectors in order to indicate the respective directions of the segments 3a-3d. The data expressing the segments 3a-3d are then delivered to a cutting machine (not shown). The cutting machine is operable to automatically cut a peel-off film 4 shown in Fig. 28C to form slits 5a-5d thereon corresponding to the segments 3a-3d. A part of the peel-off film 4 corresponding to the inner region 6 (Fig. 28D) surrounded by the slits 5a-5d is then manually taken off, to obtain a cut mask film in which only the inner region 6 is transparent. The cut mask film is inversely printed on another film through a contact printing process, to obtain the mask film 2 (Fig. 28A) in which only the inner region of the graphic figure 1 is opaque. In another conventional technique, a photoplotter is employed. For manufacturing the mask film 2 with this technique, graphic data expressing the graphic figure 1 are prepared by means of CAD, similarly to the first conventional technique. However, the graphic data are not identical to those in the first technique, in that they express a set of segments 7 (Fig. 29A) filling the inner region 6 rather than the segments 3a-3d defining the contour line. The graphic data expressing the segments 7a are then delivered to the photoplotter (not shown). The photoplotter scans the surface of a photosensitive film with a light beam along the segments 7 while controlling the light beam so that it is in ON state on the segments 7 and in OFF state on the other region, whereby the photosensitive film 2 shown in Fig. 29B is exposed along the trace 8 of the exposure light beam. The exposed photosensitive film 2 is developed, to obtain the desired film 2 of Fig. 28A having the filled region. The first conventional technique employing the cutting machine has an advantage in that the graphical data can be easily prepared, since it requires only the data expressing the segments 3a-3d which define the contour line of the graphical figure 1. The segments 3a-3d may be crossed without terminating at a common point, since the respective parts of the slits 5a-5d extending over the other slits do not substantially hinder the opaque character of the outer region in the film 4. However, the technique has a disadvantage in that an operator must be skilled in the manual operation of taking off the region 6 of the peel-off film 4. Further, the efficiency of the manual operation is low, and the desired film cannot be easily obtained. On the other hand, the second conventional technique employed the photoplotter does not require a manual operation, and the desired film 2 can be obtained automatically. However, since the diameter of the exposure beam spot is small, a long time is required to fill the inner region of a graphic figure which has relatively wide area, as compared with the first conventional technique, and a part between adjacent segments is sometimes left unfilled even after the scanning with the exposure beam is completed. Further, a long time is required also in preparation of the graphic data with CAD. Under the circumstances, it is desirable to develop a system in which graphic data is prepared through CAD or the like only for a contour line, and a filling operation is automatically conducted at a high speed. The desirable system may be constructed with a laser plotter in which an exposure scanning with a laser beam is controlled according to run length data. For obtaining the run length data, graphic data must be prepared to include information with respect to a contour line which can be drawn with a single stroke, as shown in Fig. 28E, and other information indicating whether the inner region of the contour line is to be filled or to be left unfilled. A contour line which can be drawn with a single stroke is hereinafter referred as "single stroke contour line". Although such graphic data can be prepared through CAD dedicated to the laser plotter, it is desired to obtain the graphic data from graphic data prepared for the cutting machine. However, a contour line expressed by the graphic data prepared for the cutting machine is not always a single stroke contour line. Therefore, when the graphic data for the cutting machine is employed for controlling the laser plotter, it is necessary to distinguish the inner region from the outer region of the graphic figure 1 on the basis of the graphic data indicating the segments 3a-3d of Fig. 28B which imperfectly express the contour line. The distinguishing process will be a complicated process, since graphic figures have many variations. Thus, the desired system will not be obtained unless a technique is developed in which imperfection in segment connection is detected and a single stroke contour line is reproduced at high efficiency and high speed. SUMMARY OF THE INVENTION The present invention is intended for a method of obtaining an image data and the converter therefor, as set out in claims 1 and 11, said image data being used for filling an inner region or an outer region of a graphic figure. According to the present invention, the method comprises the steps of: (a) preparing segment data expressing segments which form a contour of a graphic figure, (b) generating connection mode data expressing connection modes between the segments on the basis of the segment data, (c) extracting an imperfect segment from the segments with reference to the connection mode data, where the imperfect segment is defined as an segment having a floating terminal point, (d) correcting the segment data and the connection mode data so as to remove the floating terminal point of the imperfect segment, thereby to convert the imperfect segment into a perfect segment whose terminal point exists on another segment, (e) detecting a loop formed with the segments with reference to the connection mode data after being subjected to the step (d), thereby to obtain loop data expressing the loops, and (f) obtaining image data used for filling an inner region or an outer region of the loop with an image filler, on the basis of the loop data and the segment data. Preferably, the step (b) includes the steps of: (b-1) specifying rectangles surrounding the segments, respectively, in an image plane on which the graphic figure is defined, (b-2) extracting interrelated rectangles from the rectangles, where the interrelated rectangles are defined as rectangles belonging to areas overlapped with each other on the image plane, respectively, and (b-3) finding a connection mode between segments surrounded by the interrelated rectangles, to generate the connection mode data. According to an aspect of the present invention, the step (b-2) is attained though the steps of (b-21) dividing the image plane repeatedly, thereby to obtain a tree of divisional areas in which each of the divisional areas is related to a node of the tree according to a sequence of division, (b-22) comparing each of the rectangles with the divisional areas, thereby to find respective minimum divisional areas including the rectangles, respectively, (b-23) detecting the interrelated rectangles within rectangles whose respective minimum divisional areas belong to a same node or direct nodes in the tree. Preferably, the connection modes are previously classified into a perfect connection mode and a imperfect connection mode, where the perfect connection mode is defined as a mode in which a terminal point of a segment exists on another segment and the imperfect connection mode is defined as a mode other than the perfect connection mode. The step (c) may be attained through the steps of: (c-1) detecting a segment being connected to another segment in the imperfect connection mode with reference to the connection mode data, and (c-2) extracting the segment detected in the step (c-1) from the segments expressed by the segment data. In a preferred embodiment of the present invention, the step (e) includes the steps of: (e-1) detecting one or more fundamental loops in which segments are serially connected only in a fundamental connection mode, the fundamental connection mode being defined as a mode where a terminal point of a segment exists at a terminal point of another segment, (e-2) detecting one or more bridging loops formed by bridging between already detecting loops with a segment, the loop data is generated with respect to both of the fundamental loops and the bridging loops. According to another aspect of the present invention, an image data converter for inputting segment data expressing segments which form a contour of a graphic figure, to convert the segment data into image data used for filling an inner region or an outer region of the graphic figure, comprising: (a) mode data generating means for generating connection mode data expressing a connection mode between the segments on the basis of the segment data, (b) a memory means for storing the connection mode data as a data base, (c) a correction means for correcting the segment data and the connection mode data being stored in the memory means so as to express a state where terminal points of each segment exist on other segments, respectively, (d) a loop detecting means for detecting a loop formed with the segments with reference to the connection mode data after subjecting a correction in the correction means, thereby to obtain a loop data expressing the loop, and (e) image data generating means for generating an image data used for filling an inner region or an outer region of the loop with an image filler, on the basis of the loop data and the segment data. The construction is illustrated in Fig. 1, as a function block diagram. The present invention also provides method of sorting segments defined on an image plane into segment groups to detect a loop formed of the segments in each of the segment groups, the method comprising the steps of: (a) receiving segment data expressing the segments, (b) specifying rectangles surrounding the segments in the image plane, respectively, (c) finding areas in which the rectangles are located, on the image plane, respectively, (d) sorting the rectangles into rectangle groups so that rectangles belonging to a common area fall under a common rectangle group, and (e) sorting the segments into the segment groups according to rectangle groups into which respective rectangles corresponding to the segments are sorted in the step (d). Accordingly, an object of the present invention is to provide a method of obtaining an image data required for filling an inner or outer region of a graphic figure with an image filler at high speed, even if the contour of the graphic figure is imperfectly exressed by segment data. Another object of the present invention is to automatically fill the inner or outer region at a high efficiency. A further object of the present invention is to detect mutual connections of segments at a high speed. Yet another object of the present invention is to provide a method in which loops inlcuded in a graphic image are systematically detected. These and other objects, features, aspects and advantages of the present invention will become more apparent from the following detailed description of the present invention when taken in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS Fig. 1 is a function diagram showing the construction of the present invention, Fig. 2 is a block diagram showing an overall structure of an image processing system having an image converter according to a preferred embodiment of the present invention, Fig. 3A through Fig. 3H are diagrams showing data conversion sequence with respect to graphic figures, Fig. 4 is a flowchart showing the overall operation of the preferred embodiment, Fig. 5A and Fig. 5B are explanatory diagrams showing a rectangular approximation, Fig. 6 is a flowchart showing a process of conducting the rectangular approximation, Fig. 7A through Fig. 7C are explanatory diagrams showing divisions of an image plane according to a quadruple branching classification method, Fig. 8 is an explanatory diagram showing the quadruple branching classification method employed in a classification of segments, Fig. 9 is a flowchart showing a segment classification process employing the quadruple branching classification method, Fig. 10 is an explanatory diagram showing connection modes and connection codes, Fig. 11 is a flowchart showing a connection mode data generation process, Fig. 12 is an explanatory diagram of a terminal correction, Fig. 13 and Fig. 14 are flowcharts showing a terminal point correction process, Fig. 15 through Fig. 18 are diagrams showing examples of the terminal point correction, Fig. 19 is an explanatory diagram showing the relationships between loops, Fig. 20 is a schematic block diagram showing a loop data generation process, Fig. 21 is an explanatory diagram showing loop detection, Fig. 22 is a flowchart showing a loop detection process, Fig. 23 is a diagram showing an example subjected to the loop detection, Fig. 24 is an explanatory diagram showing a bridging loop detection process, Fig. 25 is an explanatory diagram showing a quadruple branching classification method for investigating an inclusion relationship between loops, Fig. 26 is an explanatory diagram showing a principle for investigating the inclusion relationship between the loops, Fig. 27 is a flowchart showing a process for generating an image data to be delivered to a laser plotter, and Fig. 28 and Fig. 29 are explanatory diagrams showing image data processing for filling an inner region of a graphic figure. DESCRIPTION OF THE PREFERRED EMBODIMENTS A. Overall Structure and Overall Operation of the Preferred Embodiment Fig. 2 is a block diagram showing the overall structure of an image processing system having an image data converter according to a preferred embodiment of the present invention. Data with respect to the contour line of a graphic figure to be recorded is produced in a CAD system 10. The CAD system 10 has a CRT 11, a keyboard 12, a microcomputer 13 and a digitizer 14. When it is desired to fill the hatched region defined with graphic figures shown in Fig. 3H, for example, segment data with respect to segments a-t (Fig. 3A) expressing the respective contour lines of the graphic figures are inputted to the CAD system 10 through operation of the digitizer 14 ( process step S1 in Fig. 4A). The segment data include respective start point coordinates and end point coordinates of the segments a-t. With respect to the segment a in Fig. 3A, for example, the two dimensional coordinates of the start point a S and the end point a E thereof are provided in the segment data. The segment t is a circle, and its shape and position in the image plane are identified by the coordinates of its central point t O and the value of its radius t R , which are also input to the CAD system 10. The input operation of the segment data to the CAD system 10 is conducted similarly to that in the system employing a cutting machine. Therefore, the segments a-t expressed by the segment data may be crossed or separated from each other. In other words, the segments a-t may not be in "perfect connection mode" which is defined as state where the terminal points, i.e., the start point and the end point of each segment, are just connected to the terminal points of another segment, respectively. For example, as shown in Fig. 3A, the end point a E of the segment a is not located at the position of the end point q E of the segment q . Connection states other than the perfect connection state will be hereinafter referred as "imperfect correction modes". A terminal point which is not located on another segment such as the end points a E and a q will be referred as "a floating terminal point" or "a floating start (end) point". Now back to Fig. 2, the segments data prepared in the CAD system 10 are delivered to an image data converter 20 through on-line or off-line transmission. The image data converter 20 has a CRT 21, a keyboard 22 and a microcomputer 23, the microcomputer 23 being provided with a CPU 24 and a memory 25. The image data converter 20 receives the segment data with respect to the segments a-t, and converts the segment data into image data expressing the image shown in Fig. 3G. The conversion includes the following processes (a) through (e), details of which will be described later. (a) Connection Mode Data Generating Process In the process (a), the connection mode between the respective terminal points of the segments a-t are detected, to generate "connection mode data" expressing the connection mode between the segments a-t. In the preferred embodiment, the process (a) is conducted through the following sub-processes (a-1) and (a-2). (a-1) Segment Classification Process This is a sub-process to roughly find which segments may be connected with each other within the segments a-t, as a preliminary process of the connection mode data generation. More particularly, an image plane on which the segments a-t are given is imaginarily divided into a plurality of divisional areas, and it is found which divisional area each of the segments a-t belongs to. The segments a-t are classified into segment groups according to their respective belonging areas. Since segments belonging to different areas cannot be connected with each other, a pair of segments belonging to different areas is not subjected to the following sub-process (a-2) of detecting a connection mode between segments. By conducting the sub-process (a-1) before the subprocess (a-2), the following sub-process (a-2) can be carried out at high efficiency, since a pair of segments having no possibility of mutual connection is eliminated as subjects for connection mode detection. As will be described later in detail with reference to Fig. 3B, the sub-process (a-1) is carried out through "rectangular approximation" and "quadruple branching classification method", as indicated in the process step S2 in Fig. 4A. The data obtained in the sub-process (a-1) and indicating the contents of the segment groups are called "segment classification data". (a-2) Segment Connection Mode Detection Process In the sub-process (a-2), the connection modes between the segments a-t are detected through detecting the connection modes between the respective terminal points of the segments a-t while taking the result of the classifiction process (a-1) into consideration. Connection mode data are generated on the basis of the detected segment connection modes. For example, the connection mode between the end points a E and q E is detected and recognized as in "connection mode A2 (Fig. 10B)", according to a classification rule described later. For each of the segments a-t, the connection mode data has information as to: to what other segment the segment is connected; in what connection mode the segment is connected to the other segment; and by what characteristic point the connection is represented. For example, the connection between the segments a and q in Fig. 3C is represented by the characteristic point p2 which is the cross point of the segments a and q . The sub-process (a-2) is indicated as the process step S3 in Fig.4A. (b) Connection Mode Data Storage Process The connection mode data obtained through the process (a) are stored in the memory 25 in the form of a data base. (the process step S4 in Fig. 4A). The data base is utilized in the following processes (c), (d) and the like. In the present invention, the term "data base" is used for indicating a data system in which data included therein are arranged according to a predetermined data arrangement rule, and the data can be systematically accessed or corrected from the exterior of the memory storing the data system. Since the connection mode data with respect to the segments a-t are systematically classified and arranged into the data base, the following processes can be carried out at high efficiency and high speed. (c) Terminal Point Correction Process The process (c) is intended for correction of the terminal point coordinates of a segment in the imperfect connection mode. The terminal point coordinates are corrected on the basis of the connection mode data stored in the memory 25, so that the segment in the imperfect connection mode is converted into that in the perfect connection mode (the process step S5 in Fig. 4A). In other words, the chain of the segments is corrected into a graphical figure having a single stroke contour line. In the process (c), the connection mode data and the segment data are corrected with reference to the contents of the connection mode data themselves. Through the process (c), data expressing the corrected graphical figures shown in Fig. 3D, for example, are obtained. (d) Loop Detection Process When the process (c) is completed, there is no segment in the imperfect connection mode, and all of the chains of the segments are in the form of single stroke contour lines corresponding to the closed graphical figures which fit the operator's will. Each of the chains of segments is traced with reference to the data base, through which a contour line forming a loop is detected. In Fig. 3E, loops A-F to be detected are illustrated. In the preferred embodiment, the loop detection is carried out through the following sub-processes (d-1) and (d-2) so that the loops are detected at high efficiency. (d-1) Fundamental Loop Detection Process The connection modes between the terminal points of segments are classified into "a fundamental connection mode" in which the terminal point of one segment is located at the same position with the terminal point of another segment, and other connection modes. The fundamental connection mode is shown in Fig. 10C as "connection mode A3". In the process (d-1), a loop in which segments are serially connected in only the fundamental connection mode is detected through the step of tracing segments serially connected in the fundamental connection mode (the process step S6a in Fig. 4A). In the present application, such a loop is called "a fundamental loop". The loops L a and L b shown in Fig. 19C and Fig. 21B are examples of fundamental loop, details of which will be described later. (d-2) Bridging Loop Detection Process In the sub-process (d-2), a chain of segments at least one of which is connected with another segment in a connection mode other than the fundamental connection mode is traced, to detect "a bridging loop" which is formed by bridging between points on one or more fundamental loops. The loop L c in Fig. 19C is an example of the bridging loop. More particularly, a chain of segments not belonging to a fundamental loop is traced along the chain, whereby "a loop linkage line" linking the points on one or more fundamental loops with each other is first detected (the process step S6b in Fig. 4B). Examples of the loop linkage line are shown in Fig. 21B as lines Ca and Cb. Although the linkage line links the points on one or more fundamental loops with each other, a closed loop cannot be formed only by the linkage line. For obtaining a closed loop, a plurality of linkage lines each of which links two fundamental loops together are combined with each other according to a predetermined combination rule (the process step S6c in Fig. 4B). The information with respect to the combined loop linkage lines is coupled with information as to a segment belonging to an already detected loop, whereby a bridging loop including a connection mode other than the fundamental connection mode is found (the process step S6d in Fig. 4B). Note that the original segment data were so prepared in the CAD system 10 as to express a set of segments forming loops perfectly or imperfectly. Therefore, when the detection of the fundamental loop and the bridging loop is completed, no segments remain which are unused for detecting the loops. After the detection, both of the fundamental loop and the bridging loop are subjected to the following processes as "loops" without discrimination between the fundamental loop and the bridging loop. The data expressing the loop, which is obtained in the loop detection process, is called "loop data". (e) Process of Generating Image Data for Filling After detecting the loops, it is found whether the inner region or the outer region of each loop should be filled, on the basis of the "inclusion relationship" between the loop and the other loops. The term "inclusion relationship" is defined as a relationship where one or more other loops are included or located in the inner region of the loop now considered. The information indicating what region is to be filled is generated in this process, and it is added to the segment data for indicating which side of the segment is to be subjected to the filling. More particularly, the inclusion relationship between the loops are first detected (the step S7 in Fig. 4B). For example, the loop B-F in Fig. 3E are included in the loop A. Through the detection of the inclusion relationship, it can be found what region is to be filled. In the preferred embodiment, the information indicating a region to be filled is given to the segment data by so resetting the direction of each segment that the left side region of each segment with respect to the direction of the segment or vector corresponds to a region to be filled. Through the process, the image data for filling is generated (the process step S8 in Fig. 4B). The steps S2-S8 hereinabove described are carried out in the image data converter 20. The image data obtained in the image data converter 20 are delivered to a laser plotter 30, which has a raster converter 31 for converting the image data into run-length data (the process step S9). The run-length data are transmitted to an interface circuit 32, which controls a laser beam generated in a laser oscillator 33 according to the run-length data, the control being ON/OFF control of the laser beam. The laser beam is supplied to the photosensitive surface of a photosensitive film 34, which is wound around a rotary drum 35. The rotary drum 35 is coupled with a motor (not shown) and driven by the motor to rotate in the direction α. The laser oscillator 33 is translationally moved in the axial direction Y of the rotary drum 35 with a drive mechanism (not shown). Therefore, through the ON/OFF control of the laser beam being synchronized with the rotation of the rotary drum 33 and the translational movement of the laser oscillator 33, an image shown in Fig. 3H is recorded on the photosensitive film 34 in the form of an exposure pattern (the process step S10 in Fig. 4B). The record is a serial record along scanning lines, and the direction X and Y are main scanning and subscanning directions, respectively. The laser plotter 30 may be that of a flat bed type, a stationary drum type in which the inner surface of the drum is scanned, or the like, in place of the rotary drum type. The laser beam may be one beam or multi-beam. The image data processing system shown in Fig. 2 has the overall structure and overall operation hereinabove described, detail of which will be described in the following sections. B. Details of Segment Classification Process For the graphic figures shown in Fig. 3A, the segment data D seg with respect to the segments a-t, which are prepared in the CAD system 10, have information specifying the respective coordinates of the respective terminal points (start points and end points) of the segments a-t, as shown in Table 1. The coordinates of the start points, the end points and the central point are provided in the form of two dimensional coordinates (X, Y) defined on the image plane 100 which is not illustrated in Fig. 3A but illustrated in Fig. 3B. The segment data D seg are stored in the memory 25, and the CPU 24 generates data expressing rectangular regions R a -R t (Fig. 3B) which include the segments a-t therein, respectively, on the basis of the segment data D seg . For the rectangular region R r , for example, the respective X coordinates r SX and r SE of the both terminal points: r S = (r SX , r SY ) r E = (r EX , r EY ) are compared with each other, and the larger value and the smaller value within them are employed as a maximum value r XMAX and a minimum value r XMIN , respectively. In the example shown in Fig. 3A: r XMAX = r SX r XMIN = r EX as shown in Fig. 5A. Similarly, a maximum value r YMAX and a minimum value r YMIN with respect to the Y coordinates are defined as: r YMAX = r EY r YMIN = r SY Then, values r X1 and r Y1 which are larger than the maximum values r XMAX and r XMIN by Δ X₁ and Δ Y₁, respectively, are defined, where the values Δ X₁ and Δ Y₁ are predetermined margins. Similarly, values r X2 and r Y2 are defined as being smaller than the minimum values r X2 and r Y2 by Δ X₁ and Δ Y₁, respectively. Namely, the values r X1 , r X2 , r Y1 and r Y2 are defined through the following expressions (7)-(10), and they are illustrated in Fig. 5A as points on the coordinate axes. r X1 = r XMAX + Δ X 1 r Y1 = r YMAX + Δ Y 1 r X2 = r XMIN - Δ X 1 r Y2 r YMIN - Δ Y 1 Then, two lines being in parallel to the Y axis: L r1 : X = r X1 L r2 : X = r X2 and other two lines being in parallel to the X axis: L r3 : Y = r Y1 L r4 : Y = r Y2 are specified. The rectangular region R r for the segment r is defined as a region surrounded by the four lines or sides L r1 -L r4 . The process is illustrated in Fig. 6, as a flowchart. With respect to the segment (circle) t shown in Fig. 5B, the rectangular region R t is defined as a region whose contour is defined by the four lines L t1 -L t4 . The lines L t1 -L t4 are defined through the expressions (15)-(18), where (t ox , t or ) is a two dimensional coordinate of the central point t on the image plane. L t1 : X = t OX + t R +ΔX 1 L t2 : X = t OX - t R -ΔX 1 L t3 : Y = t OY + t R +ΔY 1 L t4 : Y = t OY - t R -ΔY 1 The data expressing the rectangular regions R a -R t are stored in the memory 25. After obtaining the rectangular regions R a -R t , it is found to what area in the image plane each of the rectangular regions R a -R t belongs. For example, the segment b is considered in the following description. First, the image plane 100 shown in Fig. 3B is divided into four divisional areas 110, 120, 130 and 140, by dividing the image plane 100 with one vertical line and one horizontal line. Then, it is found whether or not the rectangular region R b corresponding to the segment b is perfectly included in one of the divisional areas 110-140, and if included, it is further found in what divisional area the rectangular region R b belongs. In the example shown in Fig. 3B, it can be found that the rectangular region R b is perfectly included in the divisional area 120. The divisional area 120 including the rectangular region R b is further divided into four divisional areas 121-124, and it is found whether or not the rectangular region R b is included in one of the divisional areas 121-124. As understood from Fig. 3B, no divisional area within the areas 121-124 perfectly includes the rectangular region R b , since the rectangular region R b extends over the two areas 121 and 122. When the term "minimum inclusion area" is so defined as to express a divisional area which has a minimum size within the divisional areas perfectly including the rectangular region now considered, the minimum inclusion area for the rectangular region R b is the divisional region 120. In general, when a rectangular region is given, the image plane 100 is divided into four divisional areas repeatedly, as shown in Fig. 7A. Then, inclusion relationships between the rectangular region and the four divisional areas in each repeated division are investigated, through which a minimum inclusion area corresponding the rectangular region is found. Since the rectangular region is so defined as to include a segment, the minimum inclusion area thus found can be regarded as a divisional area which has a minimum size within the divisional areas including the segment. Rectangular regions or segments whose respective minimum inclusion areas are identical with each other are classified into a same class. The process will be understood more clearly, with reference to the "classification tree" schematically shown in Fig. 8. The tree is repeatedly branched into four or quadruple branches from the "root" which is defined by the whole area corresponding to the image plane 100. In the first branching, four divisional areas or "nodes" 110-140 are obtained. The second branching gives four sets of four divisional areas 111-114, ..., 131-134, ... as secondary "nodes", although the secondary divisional areas obtained from the areas 120 and 140 are not illustrated in Fig. 8. The branching can be repeated an infinite number of times in a geometrical scheme, but, in practice, the minimum inclusion area will be found after branching a finite number of times, since each of the segments has a finite size. Therefore, in the preferred embodiment, the number of times for the repetition is previously determined so that the repetitions are completed when the divisional areas smaller than the predetermined small area are once obtained through the divisions. The minimum divisional areas obtained through the repeated divisions, which are the areas 132a-132d in Fig. 8, for example, are called "leaves". When all of the root, the nodes and the leaves are called "nodes" in the extended meaning, all of the rectangular regions R a -R t or the segments a-t are classified into their corresponding nodes which are the minimum inclusion areas therefor. For example, the rectangular region R b or the corresponding segment b belongs to the node 120, since the minimum inclusion area for the rectangular region R b is the divisional area 120. Such a classification rule is applied to all rectangular regions R a -R t , and the result of the classification for all regions R a -R t is illustrated in the blocks BL in Fig. 8 which associate with the respective nodes. The data expressing the classified relationships between the rectangular regions R a -R t (or the segments a-t) and the nodes are the "segment classification data". For the set of rectangular regions R a -R t , the nodes 110-140 are "leaves". The segment classification data D SH are stored in the memory 25, in the form shown in Table 2. Segment Classification Data D SM Node Segment 100 {a, i, j, q} 110 {d, r, s} 120 {b, c, k, ℓ} 130 {t} 140 {e, f, g, h, m, n, o, p} The classification process is also illustrated in Fig. 9, as a flowchart. Through the classification, it can be found which pairs of segments cannot be connected with each other. Within the nodes or the divisional areas shown in Fig. 8, two segments whose respective rectangles belong to direct nodes in the tree may be connected with each other, but two segments belonging to indirect nodes cannot be connected with each other, where the term "direct nodes" is used on the analogy of a family line or family tree. An example of the former is a pair of segments one of which belongs to the node 100 and the other belongs to the node 110, and that of the latter is a pair of segments belonging the nodes 110 and 120, respectively. Of course, two segments belonging to the same node may be connected with each other. Accordingly, from the result of the classification using the quadruple branching classification method, the number of pairs of segments to be subjected to the following connection mode detection process can be reduced. In other words, when "interrelated rectangles" are defined as rectangles belonging to divisional areas overlapped with each other on the image plane, pairs of segments surrounded with the interrelated rectangles are subjected to the connection mode detection process. In the classification process, the margins ΔX₁ and ΔY₁ are introduced in order to prevent the error in that the possibility of a connection is denied for two segments existing mutually adjacent divisional areas and being connected with each other at the boundary between the divisional areas. The quadruple branching classification method may be so carried out that the image plane is repeatedly divided into four divisional areas only with vertical division lines (Fig. 7B) or only with horizontal division lines (Fig. 7C). The former is especially suitable for a graphic figure having many vertical segments, and the latter is suitable for that having many horizontal segments. In general, N-branching classification method may be employed for the segment classification, where N is a positive integer equal to or larger than two. C. Details of Segment Connection Mode Detection Process In this process, mutual connection modes between the segments a-t are detected with referecne to the segment classification data stored in the memory 25. In order to systematically carry out the detection, connection modes between segments are previously classified into plural types. The types of connection mode are shown in Fig. 10A to Fig. 10L, respectively, and they consist of twelve types of connection mode A1-A4, B1-B5, and C1-C3. The mode A3 indicates "fundamental connection mode" in which the respective terminal points of the two segments are located at a common position. The other mode types are not corresponding to the fundamental connection mode, and for example, the mode A4 indicates a connection mode in which the terminal point of one segment is connected with the other segment at a point other than the terminal points of the other segment. As understood from Fig. 10, the connection modes A1-A4 correspond to connection modes between two line segments each of which has two terminal points, while the modes B1-B5 are those for two segments one of which has two terminal points and the other is a closed segment, e.g., a circle. The remaining modes C1-C3 are those for two closed segments. The connection modes A1 and C1 are so defined as to include connection conditions in which the minimum distance d is between the two segments satisfies the unequality (19) with respect to the predetermined gap margin d max . O < d is < d max This is because such nearly connected segments should be regarded as connected segments, when the small gap between the segments is provided through a rough preparation of the segment data in the CAD system 10 although they are to be connected. In other words, only segments separated from each other by a distance larger than the gap margin d max are treated as being ot connected. In the preferred embodiment, the values of the gap margin d max and the margins ΔX₁ and ΔY₁ are identical with each other. In generating the connection mode data, the characteristic point representing or characterizing the connection mode is specified for each connection between the segments. The characteristic points in respective connection modes are shown in Fig. 10 as black dots each surrounded with a small circle. For the segments a-t shown in Fig. 3C, the connection modes between the segments a-t are detected and classified into the connection mode types shown in Fig. 10. The detection process is carried out for the segments belonging to the same mode and for the segments belonging to different nodes existing in the same direct line, where "direct line" means a straight series of branches 100, 130, 132 and 132a, for example. On the contrary, the segments belonging to different nodes existing different branch lines or chains, e.g., the nodes 120 and 130, are not subjected to the detection. In parallel to the detection of the connection mode, a characteristic point with respect to each connection mode is also detected. This process is expressed in Fig. 11, as a flowchart, and the result of the detection is shown in Table 3, where the "connection code" is data expressing the connection mode by a code system, although they are indicated in the same symbols A1-A4, ... in Table 3. On the basis of the result shown in Table 3, the connection mode data D CR shown in Table 4 are generated in the CPU 24. In Table 4, "related segment" means another segment connected to the segment indicated in the first column, and "number of related segments" means the number thereof. The "serial number of related segment" is an address at which the related segment is stored in the memory 25. The "characteristic point data" consists of the coordinates P n of the characteristic point and "terminal point flag F C " indicating what positional relationship holds between the terminal point of the related segment and the segment in the first column. The terminal point flag F C indicates the positional relationship according to the rule shown in Table 5. Terminal Point Flag F C F C Contents F1 The character point is the start point of the segment. F2 The character point is the end point of the segment. F3 The character point is located on the segment. F4 The character point is located out of the segment. The connection mode data D CR are stored in the memory 25, in the form a data base where the relationships between the information included therein can be easily found by access from the exterior of the memory 25. Therefore, the relationships between the information shown in the respective columns in Table 4 is easily found from the exterior of the memory 25, and the connection mode data D CR can be arbitarily read and corrected in the following processes. D. Detail of Terminal Point Correction Process The CPU 24 corrects a pair of segments interconnected in an imperfect connection mode into segments having perfect connection mode A3 or B2. A segment having no floating terminal point such as a segment in mode C1, C2 or C3 is not subjected to the correction. Therefore, a segment to be corrected is one which is in one of the seven connection modes A1, A2 (A4), B1, B3, B4 and B5. As to the connection mode A4, the correction is carried out only for the segment connected with another segment having a floating terminal point T a shown in Fig. 12A, since it is not necessary to correct the segment when the terminal point T b (Fig. 12B) of the other segment connected therewith has no floating terminal point. The correction process is shown in Fig. 13. In Fig. 13, one of the segments is extracted, and one of terminal points of the selected segment is further extracted. Then, the connection mode between the extracted terminal point and another segment is found with reference to the connection mode data (the process steps S11-S13). When the terminal point is connected with another segment in the mode A3, which is the fundamental and perfect connection mode, the process progresses to the steps S19 and S20, and then returns to the step S12. Namely, the terminal point is not subjected to the correction, and another terminal point is extracted to be subjected to the steps S11-S13. On the other hand, when it is found in the process step S14 that the terminal point is not connected with another segment in the connection mode A3, it is judged whether or not the terminal point is connected with another segment in the connection mode A1, A2 or A4 (the process step S15). When it is connected in the connection mode A1, A2 or A4, the terminal point is so corrected as to be connected with the other segment in the perfect connection mode through the process step S16, details of which will be described later. If it is found in the process step S15 that the terminal point is not connected with another segment in the connection mode A1, A2 or A4, it is judged in the process step S17 whether or not the terminal point is connected with another segment in the connection mode B2. When a connection in the connection mode B2 is found, the terminal point is not subjected to the correction in the process step S18, since the mode B2 is one of the perfect connection modes. On the other hand, if a connection in the mode B2 is not found, it can be concluded that the terminal point is connected with another segment in the mode B1, B3, B4 or B5. This is because the modes C1-C3 are out of consideration from the fact that "terminal point" cannot be defined for a circle. In the process step S18, the terminal point in the mode B1, B3, B4 or B5 is corrected into that in the mode B2, or the data expressing the terminal point is deleted form the data base. Detail of the process step S18 will be also described later. Through the process steps S19-S20, such a routine is repeated for respective terminal points of all segments. Fig. 14A and Fig. 14B are flowcharts showing the detail of the process step S16 in Fig. 13. In the process step S30, it is judged in which mode within the modes A1, A2 and A4 the subjected terminal point is connected to another segment. When in mode A1 or A2, the terminal point T a is so corrected to be positioned on the other segment S b (the process steps S31 and S32). The correction is executed through a correction of the connection mode data and the coordinate value of the terminal point included in the segment data. Through the correction, the terminal point in the mode A1 or A2 is preliminarily converted into that in the mode A4. When the connection mode of the terminal point is originally in mode A4, no correction is executed and the mode A4 is reserved. Then, it is judged in the process step S33 whether or not the terminal point T b of the other segment S b is a floating terminal point. When it is a floating terminal point, the terminal point T b is shifted to the corrected point T a , whereby the connection mode A3 is obtained (the process step S34). If the terminal point T b is not a floating temrinal point, the correction or shift of the terminal point T b is not required. Fig. 14C is a flowchart showing the detail of the process step S18 in Fig. 13. When the connection mode is the mode B1 or B3, the terminal point T a is so shifted that the connection mode thereof is converted into the mode B2. If the connection mode of the terminal point T a is the mode B4 or B5, the data respecting the segment S a is deleted from the connection mode data and the segment data. This is because the modes B4 and B5 are not appropriate for constructing a closed loop, as seen from Fig. 10, and it can be regarded that the segment having the mode B4 or B5 is prepared by mistake. With respect to the segments a-t in Fig. 3C, the above indicated process is conducted as follows: First, it should be noted that the seven segments a , q , i , j , f , g , and n are in the imperfect connection modes, within the segments a-t, since each of the seven segments has a connection mode other than the connection modes A3 and B2 in the connection mode data D CR in Table 4. As to the segment a , it is found from Table 4 that the connection with the segment q is "imperfect", and the position of the terminal point a E shown in Fig. 15A is corrected to the position of the character point p2, through the process step S32 in Fig. 14A. More particularly, in the row having NS = a and NRS = q in the connection mode data D CR (Table 4), the connection code A2 is rewritten to A4, and the terminal point flag with respect to the characteristic point p2 is rewritten to "F2" indicating an end point. Therefore, within the connection made data for the segment a , the data: "q A2 p2 (F3)" is rewritten to: "q A4 p2 (F4)" and, correspondingly, the connection mode data for the segment q is rewritten from: "a A2 p2 (F3)" to: "a A4 p2 (F3)" In parallel with or in series with the rewrite processes, the coordinate value of the terminal point a E of the segment a , which is included in the segment data, is rewritten to that of the characteristic point p2. The state thus obtained is shown in Fig. 15B. Next, the data for the characteristic point q included in the connection mode data with respect to the segment q is rewritten from "a A4 p2 (F3)" to "a A3 p2 (F3)" through the process steps S32 and S33, so that the connection mode in which the segments a and q are interconnected at the characteristic point p2 is corrected to the "perfect connection mode", as shown in Fig. 15C. Similarly, the respective connection modes between the segments q and i , and that between the segments i and j are corrected through the process order shown in Fig. 15D through Fig. 15F. As a result, the corrected connection mode data for the segments a , q , i and j are obtained as shown in Table 6. NS NBR NRS CC DC a 2 j A3 p1 (F1) q A3 p2 (F2) i 2 j A3 p3 (F2) q A3 p5 (F1) j 2 a A3 p1 (F1) i A3 p3 (F2) q 2 a A3 p2 (F1) i A3 p5 (F2) In Table 6, the data with respect to the characteristic point p4 is not present, since the characteristic points p4 and p5 coincident with each other after the correction. As shown in Table 4, the connection mode A2 belonging to the "imperfect connection mode" exists also in the segment data for the segments f , g and n . However, the segment data for these segments are not subjected to the correction process, since each of the respective opposite segments to which the segments f , g and n are connected in the mode A2 has terminal points connected to other segments, respectively. For example, the segment f shown in Fig. 3C is connected to the segment n at the characteristic point p16 in the connection mode A2, however, the connection mode data for the segment f is not corrected because the terminal points of the segment f connect to the segments e and h , respectively. If the connection is in the state shown in Fig. 16B rather than that shown in Fig. 16A, correction is required. In other words, a connection mode data for a segment connected to another segment in the connection mode A2 is corrected only when the latter segment has a floating terminal point. The routine for judging whether a mode data in the connection mode A2 should be corrected or not is also attained in the process step S32 in Fig. 14A. With respect to the connection mode A1 shown in Fig. 10A, the correction can be carried out through various procedures. For example, when the segment S a and S b shown in Fig. 17A are imperfectly interconnected in the connection mode A1, the terminal point T a may be corrected through an extension of the segment S a as shown in Fig. 17B, or alternatively through a translational shift of the segment S a as shown in Fig. 17C. A new segment S c shown in Fig. 17D or that shown in Fig. 17E may be added to the segment S a , in place of the procedures shown in Fig. 17B and 17C. In the preferred embodiment, one of the procedures is selected to be used according to the type of positional relationship between the segments S a and S b . If the positional relationship is that shown in Fig. 18A, for example, the procedure shown in Fig. 17B is not suitable for the correction since the perfect connection mode is not obtained through the procedure of Fig. 17B, as shown in Fig. 18B. In such a case, the other procedure shown in Fig. 17C can be selected to be used, because the perfect connection mode shown in Fig. 18C can be obtained through the correction according to the procedure shown in Fig. 17C. On the other hand, if the type of positional relationship is not that shown in Fig. 18A, the perfect connection mode is obtained by shifting the terminal point. Through the correction process, a set of segments shown in Fig. 3D each of which having no "floating terminal point" is obtained. E. Detail of Loop Detection Process After the connection mode data and the segment data corresponding to the state shown in Fig. 3D are obtained, loops each of which is formed by a series connection of segments are detected. Since the connection mode data include all of the information with respect to interconnections between segments, all of the loops can be detected through the process where a chain of the segment is traced from an arbitrary segment. However, when the segment data are prepared in the CAD system 10 as those for a cutting machine, the graphic figure shown in Fig. 19A, for example, is often expressed by a set of the linked loops L a , L b and L e shown in Fig. 19C, rather than a single or independent loop shown in Fig. 19B. Therefore, when the basic tracing method described above is employed in the loop detection process, a relatively long time is required to detect all of the loops. Accordingly, the following improved detection process is employed in the preferred embodiment, in order to detect the loops at a high efficiency and a high speed. In the improved detection process schmatically shown in Fig. 20, "connection point data" is first obtained on the basis of the connection mode data after it is subjected to the terminal point correction. The connection point data consists of the two dimensional coordinates of a connection point, and information indicating two segments which are interconnected at the connection point. The "connection point" corresponds to the "characteristic point" which is indicated in the connection mode data. The connection point data is referred in order to know which segments are interconnected at a connection point. For example, the connection point data with respect to the connection point Q1 in Fig. 21A is obtained as shown in Table 7, where the graphic figure shown in Fig. 21A corresponds to that in Fig. 19C except for the difference in size, and the "first" and "second" segments indicated in Table 7 indicate two segments interconnected at the connection points, respectively. Connection Point: Q1 First Segment: G1 Second Segment: G4 Coordinates of Connection Point: (X₁, Y₁) The respective connection point data for the other connection points Q2-Q12 are also obtained, similarly to that for the connection point Q1. As shown in Fig. 20, "connection line data" is then generated on the basis of the segment data. The connection line data has information designating all of the segments G1-G12 (Fig. 21A) in the initial state in the loop detection process. Namely, Connection Line Data =(G1, G2, ..., G11, G12), in the initial state. The number of the segments designated by the connection line data decreases as the loop detection process progresses, the detail of which will be described later. Furthermore, "loop data" is so defined as to have information representing a detected loop, and it is given for each loop. For example, when the loop L a shown in Fig. 21B is detected, loop data for the loop L a is generated as shown in Table 8. Loop Data for Loop L a Serial Number of Loop: L a Number of Segments: 4 Serial Number of Segment: G1, G2, G3, G4 Serial Number of Connection Point Sequence Table: TB(L a ) In Table 8, the "number of segments" indicates the number of the segments belonging to the loop, and the segments are listed in the row entitled "serial number of segment". The "connection point sequence table" is a data table in which the connection points Q5 and Q6 connecting the loop L a to other loops are listed along the clockwise direction in the segment point sequnece Q1-Q6 existing on the loop L a . The connection point sequence table TB (L a ) for the loop L a is indicated in Table 9, and other tables with respect to the other loops L b and L c are also generated. Connection Point Sequence Table for Loop L a Serial Number of Connection Poit Sequence Table: TB (L a ) Contents of Table: Q5, Q6 A storage area is reserved in the memory 25 for storing the "loop data set" (Fig. 20) including all of the loop data. In the initial stage, no loop has been detected yet, and therefore, Loop Data Set (in Initial State) = (), where the symbol () expresses an empty set. Under the condition where these data are prepared, the CPU 23 starts the process shown in Fig. 22A. In the first process step S50, a fundamental loop (apex interconnecting loop) in which segments are interconnected only in the fundamental connection mode A3 is detected. The detail of the detection step is shown in Fig. 22B, and a tracing start segment at which the tracing is to be started is arbitrary selected from the all segments (the process step S51). Supposing that the segment G5 shown in Fig. 21A is selected, for example, it is judged in the process step S52 whether or not another segment is connected to the segment G5 in the fundamental connection mode A3, with reference to the connection mode data for the segment G5. As seen from Fig. 21A, the segment G6 is connected to the segment G5 in the mode A3, and therefore, the process proceeds to the process step S53 for judging whether or not the segment G6 is the tracing start segment G5. Since the result of the judgement in the process step S52 is "NO", the subject segment is changed to the segment G6 in the process step S54, and then, the process is return to the step S52. In the process step S52 to which the process is returned, it is found that no segment is connected to the segment G6 in the connection mode A3, where the segment G5 which has been subjected to the process step S52 is omitted in the current judgement in the process step S52. Then, it is also found that the sequence or chain consisting of the segments G5 and G6 cannot form a fundamental loop, and a new tracing step is started after the process returned to the process step S51 through the step S56. When the segment G1 is selected as the new tracing start segment, the chain of the segments G1-G4 is traced, since these segments G1-G4 are serially interconnected in the connection mode A3. Then, the tracing reaches the tracing start segment G , and the process proceeds to the process step S55, in which it is detected that the set of segments G1-G4 forms the fundamental loop L a . After the detection of the loop L a , information as to the segments G1-G4 is deleted from the connection line data, and the loop data for the loop L a shown in Table 8 is produced. Similar process is conducted on the basis of the connection line data from which the segments G1-G4 were deleted, so that another fundamental loop L b is detected. When the detection of the loops L a and L b is completed, the connection line data is changed to: (G5, G6, G11, G12), and the loop data set is provided as: L a = (G 1 , G 2 , G 3 , G 4 ), L b = (G 7 , G 8 , G 9 , G 10 ) The segment data G₁, G₂, G₃ and G₄ forming the loop L a are so registered in the memory 25 that the loop L a is specififed as an anticlockwise loop in the Table 8. In other words, the angular direction of the loop should be detected, and, if it is found that the loop was traced in the clockwise direction, the segment data are registered in reverse direction to the tracing direction. The other loop L b is also registered in the same rule to the loop L a . The reason for unifying the respective directions of loops to the anticlockwise direction will be described later. The detected loops L a and L b , and the remaining segments indicated by the current connection line data are indicated in Fig. 21B. After the detection of the fundamental loops L a and L b , detection of a bridging loop is conducted in the process step S60 (Fig. 22A), the detail of which is illustrated in Fig. 22C and Fig. 22D. In the process step S61, one fundamental loop is arbitrarily selected from the detected fundamental loops L a and L b . Supposing that the loop L a is selected, the loop L a is registered as a "linkage line starting loop" from which a loop linkage line starts to extend toward another fundamental loop, in the process step S62 (Fig. 22D). In the process step S63, it is judged whether or not there is another connected to the linkage line starting loop L a in the connection mode A3 or A4, through a search in the segments remaining in the connection line data. Since the segments G1-G4 have been deleted from the connection line data, they are not subjected to the search. When the segment connected to the loop L a in the mode A3 or A4 is found, the process proceeds to the next process step S64. Fig. 23 shows an example in which two segments are connected to the loop L a in the mode A3. On the other hand, in the example shown in Fig. 21B, two segments G5 and G12 are found to be connected to the loop L a in the mode A4. If two or more segments are found through the search, one of them, e.g., the segment G5, is arbitrarily selected, and then the process proceeds to the process step S64. In the step S64, it is judged whether or not there is another segment connected to the segment G5 in the connection mode A3. As seen from Fig. 21B, the segment G6 is connected to the segment G5 in the mode A3, and therefore, the process further proceeds to the step 66. Since the segment G6 is connected to the fundamental loop L b , the segments G5 and G6 are registered as a set of segments forming a loop linkage line through the steps S66 and S67. Incidentally, the step S65 is provided for ignoring a segment in the mode A2, when the result of the judgement in the step 64 is "NO", e.g., it is found that one or more segments are connected to the subjected segment only in the connection mode A4 or A2. This is because the interconnected segments in the connection mode A2 are intercrossed segments shown in Fig. 16A, and it is not necessary to detect the intercrossed segments for the loop linkage line detection. Examples of the intercrossed segments are found in Fig. 3D, and they are the segments f - n at the point p16 and the segments f - g at the point p19. It is to be noted that there are neither segments interconnected in the mode A1 nor those interconnected in the mode A2 without being intercrossed, since they have been corrected to the perfect connection mode through the terminal point correction process already described in the section "D". After the loop linkage line C a (Fig. 21B) consisting of the segments G5 and G6 is detected, it is judged whether or not the fundamental loop (linkage line ending loop) L b which the loop linkage line C a reaches is the linkage line starting loop L a . Since the loops L a and L b are different loops, the fundamental loop L b is newly set as a linkage line starting loop in the step S73, and the segment chain tracing process described above is repeated. A segment from which the tracing starts is selected from the segments connected to the new starting loop with reference to the connection point sequence table, the detail of which will be described later. Through the repetition process, another loop linkage line C b shown in Fig. 21B is detected, and the process proceeds to the step S69 through the step S68. In the step S69, the respective data expressing the loop linkage lines C a and C b are combined. The information expressing the segments G3, G7 and G10 belonging to the fundamental loop L a or L b is added to the data for the loop linkage lines C a and C b in the process step S70, where the information of the segments G3, G7 and G10 are used in the form of an information expressing partial segments g3, g7 and g10 (Fig. 21C) obtained by clipping respective parts of the segments G3, G7 and G10. More particularly, the partial segments g3, g7 and g10 are defined as parts in the sections Q6-Q5, Q7-Q12 and Q11-Q7 respectively, where the points Q5, Q6, Q11 and Q12 are connection points between the fundamental loop L a or L b and the loop linkage line C a or C b . Accordingly, the partial segments have the following start points and end points, respectively: g3 = start point Q6, end point Q5, g7 = start point Q7, end point Q12, g10 = start point Q11, end point Q7. In the clipping process, the connection point data is referred to. For example, in order to clip the partial segment g3, it is detected which segments in the fundamental loop L a the connection points Q6 and Q5 belong to, respectively, with reference to the connection point data. Then, the respective coordinates of the start and end points of the partial segment g3 are obtained from the coordinates of the points Q6 and Q5. Then, the angular direction of the loop L c shown in Fig. 21D, which consists of the segments G5, G6, G1 and G12, and the partial segments g3, g7 and g10, is detected. When the loop L c is in clockwise direction, the loop detection is regarded as an error and the process is returned to the step S63 through the step S70a for renewing the loop detection process. On the other hand, if the loop L c is in anticlockwise direction, the loop L c is specified as a bridging loop in the step S71, and loop data for the bridging loop L c is added to the loop data set. The reason for employing only a loop in anticlockwise direction as a bridging loop will be described later. In the example shown in Fig. 21, no segment remains after the bridging loop L c is detected, and therefore, the loop detection process is completed through the process step S72. When the graphic figure to be processed is that shown in Fig. 19E or Fig. 19D rather than that shown in Fig. 19C, the loops L p , L q and L r are detected as "fundamental loops" and the loop L c is detected as a "bridging loop". Incidentaly, in the process where a bridging loop is detected after another bridging loop is already detected, the "loop" referred in the steps S61, S70 and S66 means both of a fundamental loop and a bridging loop already detected. Now, the production rule and the utilization method of the connection point sequence table will be described. A connection point sequence table is produced an stored up every time a new loop is detected. For example, when the loop L a is detected, the connection mode data is investigated to find that the fundamental loop L a is accompanied by the connection points Q5 and Q6. Then, the data expressing the connection points Q5 and Q6 are written in a new connection point sequence table in which the connection points Q5 and Q6 are listed along the clockwise direction in the loop (see Table 9). In a process of detecting a bridging loop, the connection point sequence table is referred, and a connection point just following the connection point at which the tracing reached the fundamental loop is selected as a next tracing start point. In order to detect a bridging loop without mistaking the angular direction thereof, the respective directions of the detected loops are set at the anticlockwise direction, and the sequence order or direction at which the connection points are registered in the connection point table is set at the clockwise direction. The reason therefor is as follows: In the example shown in Fig. 24A, when the fundamental loops L a and L b are registered in the anticlockwise direction and the sets of the connection points (Q20, Q21) and (Q22, Q23) belonging to the loops L a and L b , respectively, are registered in the clockwise direction in the connection point sequence table, the bridging loop L c in the anticlockwise direction can be detected by tracing the connection points in the connection point sequence table along the sequence at which the connection points are registered. In other words, the upward direction from the point Q21 to the point Q20 corresponds to the anticlockwise direction in the loop L a in Fig. 24A, while the downward direction from Q20 to Q21 corresponds to the anticlockwise direction in the loop L c , and therefore, it is required to register the points Q20 and Q21 in the connection point sequence table in the direction opposite to that in the loop data in order to unify the respective directions of the all loops. As will be understood by those skilled in the art, it is allowed that the connection points are registered in the clockwise direction as a loop data while they are registered in the connection point sequence table in the anticlockwise direction, in place of the registering rule indicated above. Namely, either rule may be employed as long as the angular direction of a loop and the sequence or direction of the connection points in the connection point sequence table are opposite to each other. However, even when such a restriction for the angular direction of a loop and the registering order in the connection point sequence table is employed, an ambiguity in the direction of the bridging loop L c may remain. For example, when the tracing is started from the point Q20 as shown in Fig. 24B, the points Q22, Q23 and Q21 are serially detected in that order, to obtain a clockwise loop L c ′. If such a clockwise loop is included in the loop data, the following process for identifying filling regions and unfilling regions will cause errors in some cases. In order to prevent the errors, the direction of the loop just found is detected and, when it is the clockwise direction, the loop is abandoned and another tracing start point Q21 in Fig. 24C is selected to repeat the loop detection process until an anticlockwise loop L c is obtained. This is the reason for providing the step S70a in Fig. 22C. By constructing the connection point sequence table according to the above indicated rule and the connection points therein are traced in the registered sequence, the anticlockwise bridging loop L c can be obtained without an ambiguity in the angular direction thereof. The sequence in the connection point sequence table is interpreted as a cyclical order, and therefore, the connection point following the point Q6 in Table 9 is the point Q5. Through the loop detection process for the graphic figures shown in Fig. 3D, loops A-F shown in Fig. 3E are detected. Once all of the loops are detected, it is not necessary to distinguish the fundamental loop and the bridging loop, and each of them is referred as a "loop". F. Detail of Image Data Generation for Filling After the loop detection is completed, inclusion relationships between the detected loops are investigated, in which the rectangular approximation and the quadruple branching classification are employed again. Contrarily to the segment classification process already conducted, the margins ΔX₁ and ΔY₁ are set at zero in the present process, since the imperfect connection mode has been already corrected and the loops formed by the segments a-t have perfect shapes. Furthermore, the rectangular approximation is applied to the loops A-F rather than the segments a-t. Therefore, rectangles V A -V F shown in Fig. 3F are obtained from the loops A-F shown in Fig. 3E, through the rectangular approximation. When the rectangles V A -V F are subjected to the quadruple branching classification, a tree shown in Fig. 25 is obtained. The rectangles V A -V F or the loops A-F belong to the whole area 100 of the image plane and the divisional areas 110-140, in the relationship of: [100] = (V A ) [110] = (V C ) [120] = (V B ) [130] = (V D ) [140] = (V E , V F ) After the classification process is completed, the inclusion relationships between the loops A-F are investigated. In the investigation process, the inclusion relationships between the rectangular regions belonging to the higher rank region or node 100 and that belonging to the lower rank regions or nodes 110-140 are investigated as well as the inclusion relationship between the rectangular regions both of which belong to a common node. The inclusion relationships between the regions 110-140 belonging to different branches are not subjected to the investigation, because the lower rank regions 110-140 are relatively exclusive and it can be previously found that the rectangular regions belonging to the nodes, e.g., 110 and 140, classified into the different branches have not an inclusion relationship therebetween. The investigation may be conducted through a comparison between the respective apex coordinates of the rectangular regions V A -V F . In the example shown in Fig. 3, it is found through the investigation that the rectangular regions V B -V F are included in the rectangular region V A . Then, the inclusion relationships between the respective loops A-F corresponding to the regions V A -V F are investigated, where the investigation process is conducted only for the loops belonging to the rectangular regions between which an inclusion relationship is found. Therefore, only the respective pairs of loops A-B, A-C, ... and A-F are subjected to the investigation process, in the example shown in Fig. 3E. More particularly, it is first judged whether or not the subjected loops A and B , for example, cross each other, and then it is further judged whether or not a point arbitrarily selected from points existing on one loop is located in the area surrounded by the other loop when the loops do not cross each other. In the example shown in Fig. 26, a rectangular region V H is included in another rectangular region V I , however, it is found that a loop H is not included in a loop I since the loops H and I cross each other. The detection of a cross may be achieved through the step of judging whether there are the connection modes A2, A4, B5 and/or C3 in the respective connection mode data of the loops H and I . With respect to the example shown in Fig. 3E, it can be found that all of the loops B-F are included in the loop A . In the next step, regions to be filled with a solid or a tint through an exposure are designated automatically. When the inner region of the most outer loop A is to be filled, the respective inner region of the inner loops B-F are designated as non-filling region. In other words, "filling" and "non-filling" are alternately designated from the higher rank loop to the lower rank loop according to the inclusion order. The designation is conducted through resetting the respective directions of the segments or vectors a-t forming the loops A-F, i.e., through resetting the respective start and end points of the segments or vectors a-t within the respective terminal points thereof. When the filling rule is previously so determined that the left hand side region of a segment with respect to the direction of the segment is to be filled while the right hand side region thereof is not to be filled, the respective directions of the segments a-t (Fig. 3G) are so reset that the loop A is an anticlockwise loop and the other loops B - F are clockwise loops. The region W shown in Fig. 3G exists in the respective left hand side with respect to the loops A - F , and it can be detected in the following recording process that the region W is a "filling region" rather than a "non-filling region". The inversion of a segment direction is achieved by exchanging the start and end points of the segment, and the resets of the respective directions of the segments are carried out in the segment data. In other words, information indicating the positional relationship between the segment and the filling region is given to the segment data through resetting the respective coordinates of the start and end points of the segments. Since the rectangular approximation and the quadruple branching classification method are employed in the detection of the inclusion relationships between the loops, the detection efficiency is further improved in the preferred embodiment. The segment data after being subjected to the above indicated processing are delivered from the image data converter 20 to the laser plotter 30 as image data for filling the inner or outer regions of the graphic figures. The delivery of the image data may be attached through either on-lin communication or off-line communication. The process described above is also indicated in Fig. 27. G. Detail of the Operation in the Laser Plotter 30 The segment data corresponding to the graphic figures shown in Fig. 3G are delivered to the raster converter 31 in the laser plotter 30. The raster convertor 31 calculates the respective coordinates of the points (e.g., the points u₁-u₆ in Fig. 3H) at which a main scanning line SL crosses the segments forming the loops A-F. Although only one main scanning line is illustrated in Fig. 3H, there are many main scanning lines parallel to each other, and the process is carried out with respect to each of the main scanning lines. From the coordinates thus obtained, run-lengths ℓ₁-ℓ₇ in the image plane 100 are calculated. For example, the run-length ℓ₂ is obtained as ℓ₂ =u₁ - u₂. The interface circuit 32 controls the laser beam supplied from laser oscillator 33 to the photosensitive material 34 on the basis of the run-length data ℓ₁-ℓ₇ so that the laser beam is continuosly activated in the period in which the main scanning sweeps the interval ℓ₁, and then continuously inactivated in the next period in which the main scanning sweeps the interval ℓ₂. Similar operation is performed with respect to the intervals ℓ₃-ℓ₇, too. The judgement whether the laser beam is to be turned-on or turned-off when the scanning crosses a segment is carried out through a comparison between the respective subscanning coordinates of the start and end points of the segment. If the subscanning coordinate of the start point is smaller than that of the end point, the vector expressing the segment is directed downward in the image plane 100. Therefore, the main scanning started at the left side of the image plane 100 runs from the right hand side of the segment to the left hand side thereof with respect to the direction of the segment, i.e., the downward direction, and the laser beam is turned-on when the main scanning crosses the segment. On the other hand, if the subscanning coordinate of the start point is larger than that of the end point, i.e., the vector expressing the segment is directed upward, the laser beam is turned-off when the main scanning crosses the segment. Furthermore, when the main scanning successively crosses two segments both of which are directed downward, a designation for turn-off is twice given, whereby the laser beam is continuously inactivated until a designation for turn-on is twice given. Through the operation where the above indicated process is carried out while scanning the photosensitive film 34 with the laser beam, whereby regions on the photosensitive film 34 corresponding to the hatched parts in Fig. 3H are filled with the exposure, to obtain a desired record image. H. Modifications The segment data may be prepared in an apparatus other than the CAD system, and the image data converter according to the present invention can be applied to several systems in which image data expressed by a set of segment data is converted to other type image data for recording scan. The image in which a desired region thereof is filled with an image filler such as a solid color or a tint may be recorded on a medium or displayed on a CRT. The present invention can be also applied to a dot image recorder. In the present invention, since the connection mode data are generated on the basis of the connection relationships between the respective terminal points of the segments and the terminal point correction is conducted in response to the connection mode data, the image data required for automatically filling the inner or outer region of the graphic figure can be obtained at a high speed and at a high efficiency even if the segment data are imperfectly prepared. The features disclosed in the foregoing description, in the claims and/or in the accompanying drawings may, both separately and in any combination thereof, be material for realising the invention in diverse forms thereof.

Claims: A method of converting first vector data expressing vectors expressing a contour of a graphic figure into raster image data for filling an inner region or an outer region of said graphic figure for each scanning line, wherein said first vector data includes respective coordinates of terminal points of each vector on an image plane, characterized in that said method comprises the steps of (a) comparing respective coordinates of said terminal points (aS, aE, bS, bE, ...) of respective vectors each other to determine whether or not each vector has a floating terminal point not located on terminal points of other vectors, (b) extracting imperfect-connection ve tors from said vectors, wherein said imperfect-connection vectors are defined as vectors having floating terminal points, (c) moving said floating terminal points of said imperfect-connection vectors to terminal points of other ones of said vectors to obtain second vector data including only vectors having no floating terminal points, (d) detecting a plurality of loops (La, Lb, Lc, ...) formed by said vectors having no floating terminal points, and (e) obtaining said raster image data for filling the inner or outer region of said graphic figure with an image filler for each scanning line, comprising the steps of (e-1) finding mutual inclusion relationship among said plurality of loops, (e-2) resetting the directions of said vectors such that a clockwise loop and an anticlockwise loop appear alternately in an inclusion order of the loops and respective regions to be filled are located on a designated side of each vector, and (e-3) determining run-length between cross points of respective loops and each scanning line to generate said raster image data. The method of claim 1, characterized in that the step (a) comprises the steps of (a-1) specifying rectangles surrounding said segments, respectively, in an image plane on which said graphic figure is defined, (a-2) extracting interrelated rectangles from said rectangles, where said interrelated rectangles are defined as rectangles belonging to areas overlapped with each other on said image plane, respectively, and (a-3) comparing the terminal points of the vectors surrounded by said interrelated rectangles with each other to determine whether or not each vector has a floating terminal point. The method of claim 2, characterized in that the step (a-2) comprises the steps of (a-21) dividing said image plane repeatedly, thereby to obtain a tree of divisional areas in which each of said divisional areas is related to a node of said tree according to a sequence of division, (a-22) comparing each of said rectangles with said divisional areas, thereby to find respective minimum divisional areas including said rectangles, respectively, and (a-23) detecting said interrelated rectangles within rectangles whose respective minimum divisional areas belong to a same node or direct nodes in said tree. The method of claim 3, characterized in that said rectangles are so defined as to surround said segments with a predetermined margin, respectively. The method of claim 4, characterized in that said raster image data is delivered to an image recorder in which said inner region or said outer region of said loop is filled for each scanning line, and each of said rectangles has two pairs of opposite sides being parallel to a main scanning direction and a subscanning direction in said image recorder, respectively. The method of claim 5, characterized in that the step (b) comprises the steps of (b-1) generating connection mode data for discriminating said imperfect-connection vectors from other vector data having no floating terminal points, and (b-2) storing said connection mode data in a memory as a data base. The method of any of the preceding claims, characterized in that said connection modes are previously classified into a perfect connection mode and an imperfect connection mode, where said perfect connection mode is defined as a mode in which a terminal point of a segment exists on another segment and said imperfect connection mode is defined as a mode other than said perfect connection mode. The method of claim 1, characterized in that the step (d) comprises the steps of (d-1) detecting one or more fundamental loops in which segments are serially connected only in a fundamental connection mode, said fundamental connection mode being defined as a mode where a terminal point of a segment exists at a terminal point of another segment, and (d-2) detecting one or more bridging loops formed by bridging between already detected loops with a segment, and said plurality of loops are obtained by both of said fundamental loops and said bridging loops. The method of claim 8, characterized in that the step (d) further comprises the steps of (d-3) generating a connection point sequence table every time a loop is detected, where said connection point table has an information as to a sequence of connection points existing on said loop, and said connection points are points at which said loops is connected to segments other than segments forming said loops, and the step (d-2) has the steps of (d-21) tracing a chain of segments from a first loop already detected, (d-22) referring said connection point sequence table when a tracing of the step (d-21) reaches a second loop already detected, to select one connection point in said connection point sequence table according to a rule where, along said sequence, said one connection point follows a connection point at which said tracing reaches said second loop, and (d-23) resuming a tracing of a segment chain from said connection point selected in the step (d-22). The method of claim 9, characterized in that said vector data is prepared as data which can be also used in a cutting machine employed for cutting a peel-off film in response to said vector data. An image data converter for converting first vector data expressing vectors expressing a contour of a graphic figure into raster image data for filling an inner region or an outer region of said graphic figure for each scanning line, wherein said first vector data includes respective coordinates of terminal points of each vector on an image plane, characterized by (a) means for comparing respective coordinates of said terminal points (aS, aE, bS, bE, ...) of respective vectors each other to determine whether or not each vector has a floating terminal point not located on terminal points of other vectors, (b) means for extracting imperfect-connection vectors from said vectors, wherein said imperfect-connection vectors are defined as vectors having floating terminal points, (c) means for moving said floating terminal points of said imperfect-connection vectors to terminal points of other ones of said vectors to obtain second vector data including only vectors having no floating terminal points, (d) means for detecting a plurality of loops (La, Lb, Lc, ...) formed by said vectors having no floating terminal points, and (e) means for obtaining said raster image data for filling the inner or outer region of said graphic figure with an image filler for each scanning line, comprising (e-1) means for finding mutual inclusion relationship among said plurality of loops, (e-2) means for resetting the directions of said vectors such that a clockwise loop and an anticlockwise loop appear alternately in an inclusion order of the loops and respective regions to be filled are located on a designated side of each vector, and (e-3) means for determining run-length between cross points of respective loops and each scanning line to generate said raster image data. The apparatus of claim 11, characterized in that said means (a) comprises means for (a-1) specifying rectangles surrounding said segments, respectively, in an image plane on which said graphic figure is defined, (a-2) extracting interrelated rectangles from said rectangles, where said interrelated rectangles are defined as rectangles belonging to areas overlapped with each other on said image plane, respectively, and (a-3) comparing the terminal points of the vectors surrounded by said interrelated rectangles with each other to determine whether or not each vector has a floating terminal point. 13. The apparatus of claim 12, characterized by means for preparing said vector data as data which can be also used in a cutting machine employed for cutting a peel-off film in response to said vector data.

Inventors: KISHIMOTO KATSUMI, SHIMAZU SHIGEAKI, KISHIMOTO, KATSUMI, SHIMAZU, SHIGEAKI, KISHIMOTO, KATSUMI DAINIPPON SCREEN MFG. CO., LTD., SHIMAZU, SHIGEAKI DAINIPPON SCREEN MFG. CO., LTD.
Applicants: DAINIPPON SCREEN MFG, DAINIPPON SCREEN MFG. CO., LTD.
Application year: 1988
Main classification: G06T11
IPC codes: G06T11, G06F17