JP2013130998A - Image forming apparatus - Google Patents

Abstract

PROBLEM TO BE SOLVED: To represent diagrams in the same manner before and after division if a diagram including a Bezier curve overlaps.SOLUTION: Orientation of a boundary between two diagrams is performed to determine a point of intersection of the two diagrams (S33, S34); if the point of intersection exists on a tertiary Bezier curve (S38), the tertiary Bezier curve is divided at a position of respective end points and the point of intersection; the respective line segments produced by the division are approximated with a tertiary Bezier curve having a parameter area of [0, 1] (S42); and closed curves of divided portions of the two diagrams are described using the approximated line segments.

Description

  In the present invention, when graphics having color attributes are overlapped, a process of dividing a figure into a portion that overlaps each other and a portion that does not overlap at the stage of a vector object, and determining a color attribute of the overlapped portion is a printing process The present invention relates to an image forming apparatus performed as a part of the image forming apparatus.

  In an image forming apparatus equipped with a printer function, when two color figures represented by vector objects overlap each other and the upper figure has transparency, each of these two figures is rasterized and converted into bitmap data. If the process of determining the color of the overlapped part is performed after that, the memory size of the work area increases and the processing time becomes longer.

  Therefore, in the following Patent Document 1 in which the inventor is the same as the inventor, the figure is divided into a superposed portion and other portions at the stage of the vector object, and the color of each figure is determined and then rasterized. The problem is solved.

Patent No. 3935127

  However, the figure illustrated in Patent Document 1 is a rectangle, and when the figures represented by using Bezier curves are overlapped, there is no disclosure of the figure expression by the mathematical expression after the figure division. The curve figure is generally represented by a cubic Bezier curve, but if the same Bezier curve is used before and after the division, the area of the parameter differs for each Bezier curve, so the rasterization process is performed uniformly as before. Cannot be used, and the existing rasterizing process cannot be used, and changing this complicates the rasterizing process.

  In view of such problems, the object of the present invention is to provide an image forming apparatus in which existing rasterization processing need not be changed by unifying graphic representation before and after division when a graphic including a Bezier curve is superimposed. There is to do.

In a first aspect of the image forming apparatus according to the present invention, a processor and a storage unit storing a program are provided, and the program gives transparency as a color attribute to the upper layer of the first graphic having the color attribute. Regarding the print data in which the second graphic is superimposed and the first graphic and the second graphic are each described by a vector object,
(A) dividing the first graphic and the second graphic into a portion that overlaps each other and a portion that does not overlap each other;
(B) The color attribute of the superimposed portion is determined based on at least the color attributes of both figures,
(C) Bitmap development is performed for each of the overlapped portion and the other portions to form an image.
In the image forming apparatus, each boundary line of the first graphic and the second graphic is represented by a cubic Bézier curve or a straight line, and the program further includes a step (a) for the processor.
If there is an intersection on the cubic Bezier curve, the cubic Bezier curve is divided at each end point and the position at the intersection, and each divided line segment has a parameter area of [0, 1] 3 It is approximated by a second-order Bezier curve, and if the segment of the closed curve of the divided portion is the third-order bezier curve thus divided, this is described by the approximated third-order Bezier curve.

In a second aspect of the image forming apparatus according to the present invention, in the first aspect, the program is further transmitted to the processor in step (a).
The first and second differential values of x with respect to y in the position where the parameter value of the divided Bezier curve is 0 and 1, respectively, in the xy orthogonal coordinate system at the position are the values before the division. An approximate expression for the Bezier curve before the division of the divided Bezier music is determined so as to coincide with those at corresponding points of the Bezier curve.

In a third aspect of the image forming apparatus according to the present invention, in the first aspect, the program is further transmitted to the processor in step (a).
The parameter value of the divided Bezier curve is 0, 0.5, and 1 at each position, and the first differential value of x with respect to y in the xy orthogonal coordinate system at the position is the Bezier before division. Let the approximate expression for the bezier curve before the division of the divided Bezier music be determined so as to match those at corresponding points of the curve.

In a fourth aspect of the image forming apparatus according to the present invention, in any one of the first to third aspects, the program is further transmitted to the processor in step (a).
(A1) For each of the first graphic and the second graphic, direction information is added to the boundary line so as to turn in one direction on the boundary line,
(A2) When dividing the line segment of the boundary line at the intersection, the direction information of the line segment after the division is matched with the direction information of the line segment before the division,
(A3) For each intersection, select one line segment having direction information whose starting point is the direction in which the one direction is away from the starting end, and determine the moving direction as the one direction.
(A4) logically move on the line segment to the next intersection in the determined direction;
(A5) If the intersection after movement is not the start point, the intersection is moved to the corresponding point of the other figure, the movement direction is determined to be opposite to the direction in step (a4), and then step (a4) If it is the start point, the closed curve is determined as the closed curve of the portion that does not overlap with each other.

According to a fifth aspect of the image forming apparatus of the present invention, in any one of the first to fourth aspects, the program executes a step (a) for the processor with respect to one intersection and one direction.
(A6) One line segment in the one direction starting from the intersection is selected,
(A7) Move on the line segment in the one direction logically to the next intersection,
(A8) If the intersection after movement is not the start point, move to the corresponding point of the other figure at the intersection, and then return to step (a7). If there is one closed curve stored by the processing of steps (a6) to (a8), the process returns to step (a6). If there are two closed curves, the other closed curves included in one of both closed curves are superimposed on each other. The closed curve of the part to be
The one direction is either the direction indicated by the direction information of the line segment or the opposite direction.

  According to the configuration of the first aspect, when an intersection exists on a cubic Bezier curve that is a part of a boundary line between two figures, the cubic Bezier curve is divided at each end point and the position at the intersection. Then, each divided line segment is approximated by a cubic Bezier curve whose parameter area is [0, 1], and this is used to describe the closed curve of the divided part of two figures. The expression is unified, and there is an effect that the existing rasterizing process can be used without being changed.

  According to the configuration of the second aspect, the one-time differential value of x with respect to y in the xy orthogonal coordinate system at the position where the parameter value of the divided Bezier curve is 0 and 1 respectively. And an approximate expression for the pre-division Bezier curve of the divided Bezier curve so that the differential values thereof coincide with those at the corresponding points of the pre-division Bezier curve. There is an effect that the equation of the curve can be obtained efficiently.

  According to the configuration of the third aspect, the parameter value of the divided Bezier curve is 0, 0.5, and 1 at each of the positions, and x relative to y in the xy orthogonal coordinate system at the position. Since an approximate expression for the Bezier curve before the division of the divided Bezier music is determined so that the differential value of one time coincides with those at corresponding points of the Bezier curve before the division, the division is performed in the same manner as described above. There is an effect that the equation of the Bezier curve thus obtained can be obtained efficiently.

  According to the configuration of the fourth aspect, after directing the boundary line of the graphic, there is an effect that it is possible to obtain graphic parts that do not overlap with each other by the simple process.

  According to the configuration of the fifth aspect, after the orientation of the boundary line of the graphic is performed, there is an effect that it is possible to obtain graphic parts to be superimposed on each other by the simple process.

  Other objects, characteristic configurations and effects of the present invention will become apparent from the following description read in connection with the appended claims and the drawings.

1 is a schematic diagram of an image forming system according to a first embodiment to which the present invention is applied. FIG. 2 is a schematic block diagram mainly showing a hardware configuration of an image forming apparatus. It is a schematic flowchart which shows the superimposition figure division | segmentation process before rasterizing the vector object contained in PDL data. (A) and (B) are both explanatory diagrams of closed curve trace direction determination. It is a detailed flowchart of step S1 of FIG. It is explanatory drawing of two figures of a process target. It is explanatory drawing with the clockwise direction of each line segment of the figure of FIG. FIG. 4 is an explanatory diagram for determining a larger closed curve in step S <b> 17 of FIG. 3. (A)-(C) is an exceptional process explanatory drawing in case two figures have an inclusion relation, respectively. It is processing object explanatory drawing in case the intersection of two figures is four. It is explanatory drawing with the clockwise direction of each line segment of the figure of FIG.

  FIG. 1 is a schematic diagram of an image forming system according to a first embodiment to which the present invention is applied.

  In this system, an image forming apparatus 10 and a PC (Personal Computer) 20 are connected by a network 30. When a user activates an application on the PC 20 to create a document and gives an instruction to start printing, the application converts the document into PDL (Page Description Language) data via a printer driver. It is sent to the printer via the spooler function and communication function of the Operating System.

  FIG. 2 is a schematic block diagram mainly showing a hardware configuration of the image forming apparatus 10.

  In the image forming apparatus 10, a CPU 11 is coupled to a PROM 13, a DRAM 14, an auxiliary storage device 15, a network interface 16, an operation panel 17, a scanner 18, a printer 19, and a fax modem 1 </ b> A through an interface 12. In FIG. 5, a plurality of types of interfaces are represented by one block 12 for the sake of simplicity.

  The PROM 13 is, for example, a flash memory, and stores a basic input / output system (BIOS), an OS, various drivers, and various applications for functioning as an image forming apparatus.

  This application includes a print processing program that rasterizes PDL data, converts it into bitmap data on the DRAM 14, and supplies the data to the printer 19 to transfer the image onto a sheet.

  The DRAM 14 is used as a main storage device. The auxiliary storage device 15 stores printing data, image data read by the scanner 18, and facsimile reception data. The network interface 16 is coupled to the network 30 and is used for transmitting PDL data. The operation panel 17 includes an input unit and a display unit. The scanner 18 is used for generating an image file, and this file is used for printing, facsimile transmission, or file transmission. The printer 19 includes a print engine, a paper feed unit, a conveyance unit, and a paper discharge unit. The bitmap data generated in the DRAM 14 is supplied, and an electrostatic latent image is formed on the photosensitive drum based on the data. This image is developed with toner, and the toner image is transferred and fixed on paper, and discharged.

  FIG. 3 is a schematic flowchart showing a superimposed graphic division process before rasterizing a vector object included in PDL data as print data in the print processing program. In the following, the step identification codes in the figure are shown in parentheses.

  (S0) Since the trace direction of the closed curve is used later, the orientation of each figure boundary line is made one direction, for example, clockwise.

  For example, for a figure 40 having a straight line P1P2 and a curve P2P1 as a boundary line as shown in FIG. 4A, a circumscribed rectangle R1 determined from the definition area and the value area of the XY orthogonal coordinate system is obtained, and the coordinate origin O is defined as ( The midpoint of the definition area of the rectangle R1 and the midpoint of the range of the rectangle R1). Describe the quadrant value (values 1 to 4 in the first to fourth quadrants) of one of the contact points, for example, the point of contact sequence (P1, P2, P8, P7) that passes around the figure 40 in one direction from the point P1. As a result, (3, 2, 4, 4) is obtained, and it can be determined that this is a clockwise pattern.

  In this case, the straight line P1P2 is directed clockwise from the end point P1 to the end point P2, and the curved line P2P1 is directed to the line segment of the boundary line when the direction from the end point P2 to the end point P1 is clockwise. . If it is determined that the pattern is in the counterclockwise direction from the quadrant value order pattern, the line segment is directed in the opposite direction.

  This orientation may be performed as shown in FIG. That is, for the rectangle R2 inscribed by the triangle P1P2P9 of the three points that are not on the same straight line on the figure 40, for example, the points P1, P2, and P9, the coordinate origin O of the XY orthogonal coordinate system is set to (the rectangle R2 The midpoint of the definition area and the midpoint of the range of the rectangle R2). Describe the quadrant value of one of the triangles P1P2P9, for example, the point (P1, P2, P9) that passes from the point P1 to the figure 40 in one direction and passes in order, it becomes (3, 2, 1). It can be determined that the pattern is clockwise, and the line segment is oriented as described above.

  (S1) Intersection processing between one graphic and the other graphic is performed. FIG. 5 is a detailed flowchart of this intersection processing.

  The intersection process includes a process for obtaining intersection coordinates and a process for obtaining an expression representing each divided line segment by dividing the line segment at the intersection. The former is performed in steps S31 to S37 below, and the latter is performed as follows. The steps S39 to S44 are performed. The result of the orientation is considered in the latter steps S42 and S43. It is assumed that the line segment is a cubic Bezier curve or a straight line.

  (S30) The initial value 0 is substituted into the intersection counter Ncp.

  The following processing from step S31 to step S37 is performed for each line segment of one figure. For example, in FIG. 6, if the graphic 40 is one graphic, the following processing is performed for each of the straight line P1P2 and the curve P2P1 that are line segments of the graphic 40.

  (S31) One line segment of the one figure is selected.

  The following steps S32 to S36 are performed for each line segment of the other graphic. For example, the following processing is performed for each of the straight line P3P4 and the curve P4P3 of the graphic 41 in FIG.

  (S32) One line segment of the other graphic is selected.

  (S33) If an intersection exists between the line segments selected in step S31 and step S32, the process proceeds to step S34, and if not, the process proceeds to step S36. In the case of FIG. 6, since there is no intersection between the straight line P1P2 and each of the straight line P3P4 and the curve P4P3, a negative determination is made in step S33, and between the curve P2P1, the straight line P3P4, and the curve P4P3, respectively. Since there is an intersection, the process proceeds to step S34.

  (S34) The coordinates of the intersection of the selected line segment are obtained by solving the equation by, for example, a bisection method.

  (S35) The intersection counter Ncp is incremented by one.

  (S36) If there is an unselected line segment for the other graphic, the process returns to step S32; otherwise, the process proceeds to step S37.

  (S37) If there is an unselected line segment for the one figure, the process returns to step S31, and if not, the process proceeds to step S38.

  (S38) If the intersection counter Ncp is positive, the process proceeds to step S39; otherwise, the process of FIG. 5 is terminated.

  Thereafter, the processes of steps S39 to S44 are performed for each line segment of each figure.

  (S39) One line segment is selected.

  (S40) If the intersection coordinates obtained in step S34 exist on this line segment, the process proceeds to step S41, and if not, the process proceeds to step S44.

  (S41) If this line segment is a Bezier curve, the process proceeds to step S42, and if it is a straight line, the process proceeds to step S43.

  (S42) The Bezier curve is divided at the intersections, and an approximate expression of each divided Bezier curve is obtained.

  For example, with respect to the curve P2P1 in FIG. 6, there are intersections P5 and P6. Therefore, the expression of the Bezier curve P2P5 where the area of the parameter t is [0, 1] and the Bezier curve P5P6 where the area of the parameter t is [0, 1]. And a Bezier curve P6P1 with a parameter t of [0, 1].

More specifically, the coordinates of an arbitrary point on the curve P2P1 in the xy orthogonal coordinate system are (f (t), g (t)), and the coordinates of the control point Qi of the curve P2P1 are (xi, yi). , I is an integer in the range of 1-4,
f (t) = (1-t) ³ x1 + 3 (1-t) ² tx2 + 3 (1-t) t ² x3 + t ³ x4 (1)
g (t) = (1-t) ³ y1 + 3 (1-t) ² ty2 + 3 (1-t) t ² y3 + t ³ y4 (2)
It is expressed. Here, the area of the parameter t is [0, 1]. When t = 0, the start point P2 = Q1 = (x1, y1), and when t = 1, the end point P1 = Q5 = (x4, y4). The value of t at the intersection P5 is represented as t1.

U and v of coordinates (u (t), v (t)) of an arbitrary point on the Bezier curve P2P5 whose parameter t is [0, 1],
u (t) = a1 · t ³ + b1 · t ² + c1 · t + d1 (3)
v (t) = a2 · t ³ + b2 · t ² + c2 · t + d2 (4)
The eight unknowns a1, b1, c1, d1, a2, b2, c2, and d2 are obtained as solutions of simultaneous equations that are the following eight conditional expressions to determine the expression of the Bezier curve P2P5.

(A) Since the coordinates of the start point P2 and the intersection point P5 are equal in both curves,
(F (0), g (0)) = (u (0), v (0))
(F (t1), g (t1)) = (u (1), v (1))
The following four conditional expressions are obtained.

  (B) The condition that the slopes at the start point P2 and the intersection point P5 are equal in both curves is given. If 'is the differential symbol at t, then this condition is that f' (t) / g '(t) at t = 0 and u' (t) / v '(t) at t = 0. The values of f ′ (t) / g ′ (t) at t = t1 and the values of u ′ (t) / v ′ (t) at t = 1 are equal to each other. And two more conditional expressions are obtained.

  (C) Further, a condition is given that the rate of change in slope at the start point P2 and the intersection point P5 is the same for both curves. The condition is that the value of (f ′ (t) / g ′ (t)) ′ / g ′ (t) at t = 0 and (u ′ (t) / v ′ (t) at t = 0. ) ′ / V ′ (t) and the values of (f ′ (t) / g ′ (t)) ′ / g ′ (t) at t = t1 and t = 1 (U ′ (t) / v ′ (t)) ′ / v ′ (t) is expressed by an equation that the values are equal to each other, and two conditional expressions are obtained.

  The eight unknowns are determined by the above eight conditional expressions.

  By such processing, since the Bezier curve can be obtained without determining the control points of the divided Bezier curve, the divided Bezier curve formula can be obtained efficiently.

  Instead of the condition (c), the following conditions may be given for approximation. That is, the Bezier curve P2P1 is determined so as to pass through the coordinates (u (0.5), v (0.5)) at the parameter midpoint t = 0.5 on the Bezier curve P2P5. That is, the constraint conditions of f (t2) = u (0.5) and g (t2) = v (0.5) are given. Since a new unknown t2 has been introduced, a condition is given that both slopes at this coordinate are equal to each other. That is, the value of (f ′ (t) / g ′ (t)) ′ / g ′ (t) at t = t2, and (u ′ (t) / v ′ (t) at t = 0.5. ) The condition that the values of '/ v' (t) are equal to each other is given.

  In this case, the same effect as described above can be obtained.

  The above equations (3) and (4) are transformed into equations (1) and (2) and expressed by control points, so that a Bezier curve is represented by the coordinate sequence of the control points and is passed to the rasterizer. It may be.

  Next, each Bezier curve divided at the intersection is oriented in the same direction (clockwise direction) as the Bezier curve P2P1 before the division as shown in FIG. This orientation is performed by adding direction information to the line segment. For example, when the coordinates are moved in the clockwise direction when the parameter t changes from 0 to 1, this direction information is added to the parameter t. When the coordinate moves in the counterclockwise direction when the parameter t changes from 0 to 1, the coordinate moves in the clockwise direction when the parameter t changes from 0 to 1 by performing a linear transformation on the parameter. Like that. The direction information may be a flag indicating whether the coordinate moves in the clockwise direction when the parameter t changes from 0 to 1 or from 1 to 0.

  Next, the process proceeds to step S44.

  (S33) The straight lines are divided at the intersections to obtain the divided domains, and the formulas of the respective straight lines are the same as those before the division. Each straight line is oriented in the same direction as the straight line before the division as shown in FIG. For the straight line P3P4 in FIG. 6, there is an intersection point P5. Therefore, the straight line P3P4 is divided into a line segment P3P5 and a line segment P5P4 to obtain respective definition areas, and the respective line segments are shown in FIG. In the same direction as the straight line P3P4 before division.

  It should be noted that straight lines are also expressed using the parameter t, and each straight line is expressed in the same manner as in the case of a Bezier curve so that the area of t is [0, 1]. You may be able to do it uniformly.

  (S34) If there is an unselected line segment for all figures, the process returns to step S39, and if not, the process proceeds to step S2 in FIG.

  (S2) If the intersection counter Ncp is positive, the process proceeds to step S3, and if not, the process proceeds to step S19.

  Thereafter, for each intersection obtained in step S1, the graphic division / registration process for the non-overlapping portion in steps S3 to S9 is performed.

  (S3) One of the intersection points is selected.

  (S4) One clockwise line segment starting from this intersection is selected, and the moving direction is determined as the clockwise direction.

  (S5) Move on this line segment in the determined direction and move to the next intersection. For “move”, it is only necessary to follow the end point of the line segment (the same applies hereinafter).

  In FIG. 7, for example, when the intersection point P5 is selected in step S3 and the line segment P5P4 is selected in step S4, the point P4 moves to the point P6 of the curve P4P6.

  (S6) If this intersection is not the start point, the process proceeds to step S7, and if it is the start point, the process proceeds to step S8.

  (S7) Move from this intersection to the same point on the other graphic. The moving direction is determined to be the reverse direction before moving, and the process returns to step S5.

  In the above case, the point P6 of the curve P4P6 of the figure 41 moves to the point P6 of the curve P5P6 of the figure 40, and the moving direction is determined to be counterclockwise. Next, in step S5, the curve P5P6 moves from the intersection point P6 to the intersection point P5. In step S6, the intersection point P5 is determined to be the starting point, and the process proceeds to step S8.

  (S8) The closed curve returned to the start point is registered as a divided closed curve. Since the color attribute of this divided closed curve is not a graphic overlapping portion, it is made the same as the color attribute of the graphic before division including the divided closed curve.

  (S9) If there is an unselected intersection, the process returns to step S3, and if not, the process proceeds to step S10.

  If the intersection point P6 of FIG. 7 is selected in step S3 and the curve P6P1 is selected in step S4, the point P1 is moved from P1 to P2 and P5 in step S5, a negative determination is made in step S6, and the process proceeds to step S7. It moves from the intersection P5 of 40 to the points P5, P3, P6 of the figure 41, affirmative determination is made in step S6, closed curve P6P1P2P5P3P6 is registered in step S8, and its color attribute is determined in the same manner as described above.

  In the following steps S10 to S17, the figure logical product and the graphic logical sum are found and registered, and the figure logical product is superimposed by determining which one is the graphic logical sum and deleting it. This is a process for obtaining a divided figure.

  (S10) One of the intersection points is selected.

  (S11) One line segment in the clockwise direction starting from this intersection is selected, and the moving direction is determined as the clockwise direction.

  (S12) This line segment is moved in this direction and moved to the next intersection.

  In FIG. 7, for example, when the intersection point P5 is selected in step S10 and the curve P5P6 is selected in step S11, the movement is made from the intersection point P5 to the intersection point P6 of the curve P5P6.

  (S13) If this intersection is not the start point, the process proceeds to step S14, and if it is the start point, the process proceeds to step S15.

  (S14) From this intersection, it moves to the same point in the clockwise line segment of the other graphic, determines the moving direction as the same clockwise direction as the previous time, and returns to step S12.

  In the above case, the process moves from the intersection P6 of the curve P5P6 of the graphic 40 to the intersection P6 of the curve P6P3 of the graphic 41. Next, in step S12, it moves from the intersection point P6 to the point P3 and the intersection point P5. In step S13, it is determined that the intersection point P5 is the start point, and the process proceeds to step S15.

  (S15) The closed curve returned to the start point is registered as a divided closed curve.

  (S16) If there is an unselected clockwise line segment at the start point, the process returns to step S11, and if not, the process proceeds to step S17.

  If the curve P5P4 in FIG. 7 is selected in step S11, the point moves from the intersection point P5 to the points P4 and P6 in step S12, and a negative determination is made in step S13 to proceed to step S14. It moves to intersection point P6, points P1, P2, and P5, affirmative determination is made in step S13, and closed curve P5P4P6P1P2P5 is registered in step S15.

  (S17) Of the two closed curves registered in step S15, the larger one (closed curve of figure logical sum) is deleted. Which is larger is determined on the basis of the inclusion relation by obtaining circumscribed rectangles R3 and R4 determined from the definition range and the value range for each of the two closed curves, for example, as indicated by dotted rectangles in FIG.

  (S18) Of the two closed curves registered in step S15, the smaller one (closed curve of the figure logical product) is the overlapping part of the two figures before the division, and the color attribute is assigned to each color attribute of the two figures. This is determined based on a preset blend mode.

  For example, in FIG. 8, when the figure 41 overlaps the figure 40 and the color attribute of the figure 41 has transparency, for the closed curve P5P6P3P5, the paint color that is the color attribute of the figure 40 and the paint attribute that is the color attribute of the figure 41 The blend color is determined based on the color and transparency and a default value or a blend mode set by the user. If the transparency is 0 (opaque), the paint color that is the color attribute of the graphic 41 is determined as the color attribute of the closed curve.

  Thus, the process of FIG. 3 is completed.

  (S19) As shown in FIG. 9A, if the relationship between the graphic 40 and the graphic 41A is an inclusion relationship, that is, one graphic contains the other graphic, the process proceeds to step S20. Otherwise, the process proceeds to step S22.

  Whether or not there is an inclusion relationship is determined by whether or not an arbitrary point in the graphic 41A, for example, an arbitrary straight line passing through the point P3, for example, a horizontal straight line intersects the graphic 40 on both sides of the point P3. can do.

  (S20) Dividing into an inner closed curve and an outer closed curve hollowed out on the inner side, and registering each as a divided closed curve.

  (S21) For the inner closed curve, the blend color is determined in the same manner as in step S18, and the processing in FIG. 3 is terminated.

  (S22) The respective closed curves 40 and 41 are registered, and the processing of FIG.

  9B, one side of the figure 41B overlaps the side of the figure 40 and does not have an intersection (intersection), or one point P4 of the figure 41C is the figure 41 as shown in FIG. 9C. If there is no intersection point, the inclusion relation is determined in the same manner as described with reference to FIG. 8, and the same processing as in FIG.

  FIG. 10 shows a case where the figure 40 and the figure 41 overlap to have four intersections.

  In this case, the directional line segment as shown in FIG. 11 is obtained by the process of FIG. In addition, the closed curve P5P4P6P5, the closed curve P6P7P6, the closed curve P7P8P7, and the closed curve P8P1P2P5P3P8 that do not overlap are obtained by repeating the processes of steps S3 to S9 in FIG. 3, the graphic logical OR closed curve P5P4P6P7P8P1P2P5 and the graphic AND closed curve P5P6P7P8P3P5 are obtained.

  According to the first embodiment, when an intersection exists on a cubic Bezier curve that is a part of the boundary line between the two figures 40 and 41, the cubic Bezier curve is represented at each end point and the position at the intersection. Since each divided line segment is approximated by a cubic Bezier curve whose parameter area is [0, 1], and this is used to describe the closed curve of the divided parts of the two figures 40 and 41, The graphic representation is unified before and after the division, and the existing rasterization process can be used without being changed.

  Further, after the orientation of the figure boundary line is performed in step S0 in FIG. 3, it is possible to obtain the parts of the figure that do not overlap each other with the simple processing in steps S3 to S9.

  Furthermore, after performing this orientation, there is an effect that it is possible to obtain graphic parts to be superimposed on each other by simple processing of steps S10 to S18.

  In the above, preferred embodiments of the present invention have been described. However, the present invention includes various modifications, and other configurations that realize the functions of the respective components described in the above embodiments are used. However, other configurations that would be conceived by those skilled in the art from these configurations or functions are also included in the present invention.

  For example, one direction in steps S11 and S14 in FIG. 3 may be a direction opposite to the direction indicated by the direction information.

  In step S42, an approximation error (the difference between the two y coordinates) at the corresponding point (the x coordinate is the same point) of the Bezier curve before division at t = 0.5 of each divided Bezier curve. If the absolute value) is a threshold value, for example, one pixel or more, the approximation accuracy may be improved by further dividing the Bezier curve at this point. This two-part dividing process may be continued for each of both sides of the dividing point until the error becomes less than the threshold value.

  Furthermore, if there are more than three figures, the first two figures are taken out from the lower layer and the processing described in the above embodiment is performed, then the third figure is taken out, and this is divided into the registered divided figures. The processing described in the above embodiment may be performed in order for each, and thereafter the fourth and subsequent figures may be processed in the same manner. By applying the present invention to at least two figures, the above effect can be obtained.

10 Image forming apparatus 11 CPU
12 Interface 13 PROM
14 DRAM
15 Auxiliary storage device 16 Network interface 17 Operation panel 18 Scanner 19 Printer 1A Fax modem 20 PC
30 network 40, 41, 41A-41C figure P1-P4 point P5-P8 intersection

Claims (5)

A processor and storage means for storing a program, the program superimposing a second graphic having transparency as a color attribute on top of the first graphic having a color attribute to the processor; And print data in which the second graphic is described by a vector object.
(A) dividing the first graphic and the second graphic into a portion that overlaps each other and a portion that does not overlap each other;
(B) The color attribute of the superimposed portion is determined based on at least the color attributes of both figures,
(C) Bitmap development is performed for each of the overlapped portion and the other portions to form an image.
In the image forming apparatus, each boundary line of the first graphic and the second graphic is represented by a cubic Bézier curve or a straight line, and the program further includes a step (a) for the processor.
If there is an intersection on the cubic Bezier curve, the cubic Bezier curve is divided at each end point and the position at the intersection, and each divided line segment has a parameter area of [0, 1] 3 Approximated by a second-order Bezier curve, and if the line segment of the closed curve of the divided portion is the third-order Bezier curve divided, this is described by the approximated third-order Bezier curve.
An image forming apparatus. The program is further sent to the processor in step (a),
The first and second differential values of x with respect to y in the position where the parameter value of the divided Bezier curve is 0 and 1, respectively, in the xy orthogonal coordinate system at the position are the values before the division. Let the approximate expression of the divided Bezier curve to the Bezier curve before the division be determined so as to match those at corresponding points of the Bezier curve.
The image forming apparatus according to claim 1. The program is further sent to the processor in step (a),
The parameter value of the divided Bezier curve is 0, 0.5, and 1 at each position, and the first differential value of x with respect to y in the xy orthogonal coordinate system at the position is the Bezier before division. Let the approximate expression of the divided Bezier curve to the Bezier curve before the division be determined so as to match those at corresponding points of the curve.
The image forming apparatus according to claim 1. The program is further sent to the processor in step (a),
(A1) For each of the first graphic and the second graphic, direction information is added to the boundary line so as to turn in one direction on the boundary line,
(A2) When dividing the line segment of the boundary line at the intersection, the direction information of the line segment after the division is matched with the direction information of the line segment before the division,
(A3) For each intersection, select one line segment having direction information whose starting point is the direction in which the one direction is away from the starting end, and determine the moving direction as the one direction.
(A4) logically move on the line segment to the next intersection in the determined direction;
(A5) If the intersection after movement is not the start point, the intersection is moved to the corresponding point of the other figure, the movement direction is determined to be opposite to the direction in step (a4), and then step (a4) If it is the start point, it is determined that the closed curves that have made one round are the closed curves that do not overlap each other.
The image forming apparatus according to claim 1, wherein the image forming apparatus is an image forming apparatus. The program for the processor in step (a) for one intersection and one direction,
(A6) One line segment in the one direction starting from the intersection is selected,
(A7) Move on the line segment in the one direction logically to the next intersection,
(A8) If the intersection after movement is not the start point, move to the corresponding point of the other figure at the intersection, and then return to step (a7). If there is one closed curve stored by the processing of steps (a6) to (a8), the process returns to step (a6). If there are two closed curves, the other closed curves included in one of both closed curves are superimposed on each other. The closed curve of the part to be
5. The image forming apparatus according to claim 1, wherein the one direction is one of a direction indicated by direction information of a line segment and a direction opposite thereto.

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