WO2013102955A1

WO2013102955A1 - Drawing device and drawing method

Info

Publication number: WO2013102955A1
Application number: PCT/JP2012/000057
Authority: WO
Inventors: 博康根岸
Original assignee: 三菱電機株式会社
Priority date: 2012-01-06
Filing date: 2012-01-06
Publication date: 2013-07-11

Abstract

The present invention is provided with a triangle extractor (22) and an operation unit (23). The triangle extractor (22) extracts, on the basis of a drawing order for vertices of a polygon, a plurality of triangles having each of a second vertex and a third vertex changed with reference to a draw-start vertex; extracts a draw-start triangle in which the draw-start vertex is connected to two vertices for which the drawing order is contiguous from the draw-start vertex; and stores the draw-start triangle in a polygon storage unit (24). The operation unit (23) performs a logical operation based on the drawing order of the vertices of the triangle that is the result of an [MV1] operation or the draw-start triangle stored in the polygon storage unit (24), and the drawing order of the vertices of a triangle in which the second vertex and the third vertex are changed with reference to a draw-start point, the triangle not being the draw-start triangle.

Description

Drawing apparatus and drawing method

The present invention relates to a drawing apparatus and a drawing method for creating drawing data representing a graphic to be displayed.

Conventionally, in computer graphics processing for drawing a figure with basic drawing primitives of points, lines, and triangles, a mask image of the figure is created as a method of drawing a figure including a self-intersecting polygon, and the mask image The method of filling the inside of was used.
In the drawing processing apparatus disclosed in Patent Document 1, a plurality of triangles obtained by selecting three points from points defining the outline of a closed region graphic are extracted, and the vertices constituting the extracted plurality of triangles are the first. Mask image using the result of rendering with triangles arranged in the rotation direction enabled, and mask using the result of drawing with the triangles constituting the extracted triangles arranged in the second rotation direction enabled A mask buffer is configured using the image, and a mask image configuring the mask buffer is drawn according to the non-zero winding rule. In the image processing apparatus of Patent Document 1, it is necessary to mount a three-dimensional graphics hardware accelerator in order to create a mask image.

On the other hand, in the drawing apparatus disclosed in Patent Document 2, a linear contour and a curved contour are analyzed for graphic data without mounting the above-described three-dimensional graphics hardware accelerator, Triangulate to generate triangle data, generate a mask image based on the drawing order of the vertices of the generated triangle data, refer to the pixel value of the generated mask image, and rasterize the place where the pixel value is a predetermined value Drawing data is generated.

JP 2011-165062 A JP 2007-304871 A

However, in the above-described conventional technique, a mask image is generated, and drawing processing is performed with reference to the generated mask image. Therefore, in addition to a frame buffer memory for image display, a mask image memory is required. There was a problem. As the size of the memory for creating the mask image, since there is a possibility that the entire screen of the display device is drawn, the same resolution as that for the screen display is required. For this reason, there is a problem that it is difficult to draw a graphic including a self-intersecting polygon in an environment where there are few memory resources and hardware dedicated for graphic drawing is not installed.

The present invention has been made to solve the above-described problems. A graphic including a self-intersecting polygon without using a mask image memory and without mounting dedicated graphic drawing hardware. An object of the present invention is to provide a drawing apparatus that enables drawing.

The drawing apparatus according to the present invention acquires polygon data of a polygon to be drawn, detects vertices that specify a polygon from the acquired polygon data, and acquires vertex data that gives a drawing order to the detected vertices And a triangle extracting unit for extracting a plurality of triangles obtained by changing the second vertex and the third vertex from the polygon based on the drawing start vertex based on the drawing order given by the vertex data obtaining unit, and a triangle An arithmetic unit that performs a logical operation using a plurality of triangles extracted by the extraction unit, a polygon storage unit that stores a polygon that is a set of triangles as a calculation result of the arithmetic unit, and a polygon storage unit A drawing unit for drawing a polygon, and the triangle extraction unit extracts a drawing start vertex and a drawing start triangle connecting two vertices whose drawing order is continuous from the drawing start vertex and stores the drawing start triangle in the polygon storage unit. , The arithmetic unit is The drawing start triangle stored in the square storage unit or the drawing order of the vertices of the triangle that is the operation result, and the second vertex and the third vertex are changed based on the drawing start point except for the drawing start triangle When the logical operation is performed on all triangles extracted by the triangle extraction unit in the operation unit, the logical operation is performed based on the drawing order of the respective vertices of the triangles, and stored in the storage unit. It draws a polygon.

According to the present invention, it is possible to draw a graphic including a self-intersecting polygon without creating a mask image and without installing hardware dedicated to graphic drawing.

1 is a block diagram illustrating a configuration of a drawing apparatus according to Embodiment 1. FIG. 3 is a flowchart illustrating an operation of the drawing apparatus according to the first embodiment. FIG. 6 is an explanatory diagram illustrating processing of the drawing apparatus according to the first embodiment. FIG. 6 is an explanatory diagram illustrating processing of the drawing apparatus according to the first embodiment. FIG. 6 is an explanatory diagram illustrating processing of the drawing apparatus according to the first embodiment.

Hereinafter, in order to explain the present invention in more detail, modes for carrying out the present invention will be described with reference to the accompanying drawings.
Embodiment 1 FIG.
FIG. 1 is a block diagram illustrating a configuration of a drawing apparatus according to the first embodiment.
The drawing apparatus 1 includes a drawing processing unit 2 configured by an arithmetic processor represented by a CPU (Central Processing Unit) and the like, and a memory 3 that holds instruction codes and data of the drawing processing unit 2. The drawing device 1 is connected to a storage device 5 and a display device 6 via an I / O interface 4. The storage device 5 stores a plurality of polygon data for specifying polygons to be drawn. The display device 6 displays the polygon drawn by the drawing device 1 on a screen or the like.

The drawing processing unit 2 includes a vertex data acquisition unit 21, a triangle extraction unit 22, a calculation unit 23, a polygon storage unit 24, a drawing unit 25, and a display control unit 26.
The vertex data acquisition unit 21 reads polygon data from the storage device 5 via the I / O interface 4, detects each vertex specifying the polygon from the read polygon data, and sets the drawing order to each detected vertex. Numbers shown (for example, V1, V2, V3,..., Vn) are assigned.

The triangle extraction unit 22 refers to the number of each vertex assigned by the vertex data acquisition unit 21, selects one vertex (for example, the vertex V1) as the start vertex, and then continues to the second vertex (for example, the vertex V2) and A third vertex (for example, vertex V3) is selected to extract a triangle. Further, with reference to the extracted triangle vertex numbers, it is determined whether the vertex arrangement direction is clockwise or counterclockwise. For the apex arrangement direction (clockwise or counterclockwise), for example, in the case of the triangle V1-V2-V3, the cross product of the vector V1-V2 and the vector V2-V3 is calculated, and the sign of the Z component in the depth direction of the calculated cross product Determined by. The triangle (drawing start triangle) extracted first by the triangle extraction unit 22 and data indicating the arrangement direction of the vertices of the triangle are stored in a polygon storage unit 24 described later.

The calculation unit 23 acquires data indicating the arrangement direction of the triangles and vertices stored in the polygon storage unit 24, and data indicating the arrangement direction of the triangles and vertices most recently extracted by the triangle extraction unit 22, and obtains two triangles. Perform logical operation. When the two triangles are arranged in different directions, an operation based on a logical difference is performed. When the two triangles are arranged in the same direction, an operation based on a logical sum is performed. The polygon storage unit 24 stores polygons that are aggregates of triangles that are the calculation results of the calculation unit 23. Further, the triangle extraction unit 22 stores data indicating the triangle (drawing start triangle) extracted first and the arrangement direction of the vertices. The drawing unit 25 fills a polygon to be drawn using the calculation result stored in the polygon storage unit 24. The display processing unit 26 performs display processing on the polygonal drawing data painted in the drawing unit 25.

Next, the operation of the drawing apparatus 1 will be described. FIG. 2 is a flowchart showing the operation of the drawing apparatus according to the first embodiment.
When execution of the program in the memory 3 is started in the drawing device 1, the vertex data acquisition unit 21 of the drawing processing unit 2 reads and acquires the necessary number of polygon data from the storage device 5 (step ST1). In this operation description, it is assumed that one piece of polygon data is acquired. Furthermore, the vertex data acquisition unit 21 reads out each vertex of the polygon to be drawn based on the acquired square data, and stores each vertex with a number indicating the drawing order (step ST2).

The triangle extraction unit 22 refers to the vertex data stored in the vertex data acquisition unit 21, selects the vertex having the smallest number from the numbers assigned in step ST2 as the drawing start vertex, and continues from the start vertex. Extract the triangles that connect the two vertices as the second vertex and the third vertex in ascending order of numbers, refer to the extracted triangle vertex numbers, and the vertex alignment direction is clockwise or counterclockwise Is determined (step ST3). The arrangement direction of the triangles and vertices extracted in step ST3 is stored in the polygon storage unit 24 (step ST4). Further, the triangle extraction unit 22 extracts the triangle connected with the last vertex of the previously extracted triangle as the second vertex and the next vertex continuous with the second vertex as the third vertex, It is determined whether the vertex arrangement direction is clockwise or counterclockwise (step ST5).
The vertex arrangement direction is determined by calculating the outer product of the vector from the drawing start vertex to the second vertex and the vector from the drawing start vertex to the third vertex as described above, and using the Z component code in the depth direction. .

The calculation unit 23 acquires the arrangement direction of the triangles and vertices stored in the polygon storage unit 24 and the arrangement direction of the triangles and vertices extracted by the triangle extraction unit 22, and the arrangement direction of the vertices of the two triangles is the same. Is determined (step ST6). When the arrangement directions of the vertices of the two triangles are the same (step ST6; YES), one or more triangles are obtained by performing an operation by logical sum (step ST7). On the other hand, if the arrangement directions of the vertices of the two triangles are not the same (step ST6; NO), one or more triangles are obtained by performing a calculation based on a logical difference (step ST8). The triangle acquired in step ST7 or step ST8 is overwritten and stored in the polygon storage unit 24 (step ST9).

The calculation unit 23 determines whether or not the last vertex of the polygon is included in the two triangles used in the calculation process (step ST10). When it is determined that the last vertex is not included (step ST10). NO), returning to the process of step ST5 described above, extracting the next triangle and repeating the process described above.

On the other hand, when it is determined that the last vertex is included (step ST10; YES), the drawing unit 25 reads out the triangle stored in the polygon storage unit 24, fills it, and draws the polygon to be drawn. Is performed (step ST11). The display processing unit 26 performs display processing on the polygonal drawing data drawn in step ST11, and outputs it to the display device 6 via the I / O interface 4 (step ST12), and ends the processing. Note that various polygons can be obtained as the calculation method of the logical operation depending on the algorithm.

Next, the drawing process of the self-intersecting polygon shown in FIG. 3 will be described along the flowchart shown in FIG.
In step ST1, the vertex data acquisition unit 21 reads polygon data relating to the polygon A, and in step ST2, assigns numbers a1, a2, a3, a4, a5 to the vertices of the polygon A in the drawing order and stores them. . As step ST3, the triangle extraction unit 22 selects the vertex a1 as the drawing start vertex, and extracts the triangle a1-a2-a3 (drawing start triangle) having the vertex a2 as the second vertex and the vertex a3 as the third vertex. Then, the arrangement direction Q1 of the vertices a1, a2, and a3 is determined to be counterclockwise by the sign of the Z component in the depth direction of the outer product of the vector a1-a2 and the vector a1-a3 of the extracted triangle a1-a2-a3. To do. In step ST4, the extracted triangle a1-a2-a3 and vertex arrangement direction Q1 are stored in the polygon storage unit 24.
Note that the vertex arrangement directions Q2, Q3, Q4, and Q5 shown in the following description are also determined by the sign of the Z component in the depth direction of the outer product of two vectors.

Next, in step ST5, the triangle extraction unit 22 extracts a triangle a1-a3-a4 having the last vertex a3 of the previously extracted triangle a1-a2-a3 as the second vertex and the vertex a4 as the third vertex. Then, it is determined that the vertex arrangement direction Q2 of the extracted triangles a1-a3-a4 is clockwise.

As step ST6, the operation unit 23 compares the triangle a1-a2-a3 stored in the polygon storage unit 24 with the triangle a1-a3-a4 extracted by the triangle extraction unit 22, and arranges the apex directions Q1, It is determined that Q2 is not the same, and in step ST8, calculation is performed using a logical difference using the triangle a1-a2-a3 and the triangle a1-a3-a4, and the triangle a1-a4-a6 and the triangle a6-a2-a3 (FIG. 3 ( e) See). At the same time, the alignment directions Q4 and Q5 of the vertices of the triangle a1-a4-a6 and the triangle a6-a2-a3 are also acquired. As step ST9, the calculation unit 23 overwrites and stores the acquired triangle a1-a4-a6 and vertex arrangement direction Q4 and triangle a6-a2-a3 and vertex arrangement direction Q5 in the polygon storage unit 24.

Further, in step ST10, the calculation unit 23 determines that the triangle a1-a2-a3 and the triangle a1-a3-a4 used for the calculation do not include the last vertex a5 of the polygon, and the process of step ST5 Returning to FIG. 3, the triangle extraction unit 22 extracts the next triangle a1-a4-a5, and determines that the arrangement direction Q3 of the vertices of the extracted triangle a1-a4-a5 is counterclockwise.

As step ST6, the calculation unit 23 compares the triangle a1-a4-a6 stored in the polygon storage unit 24 with the triangle a1-a4-a5 extracted by the triangle extraction unit 22, and arranges the apex direction Q4 of each triangle. It is determined that Q3 is not the same, similarly, the triangle a6-a2-a3 and the triangle a1-a4-a5Q5, Q3 are compared to determine that the arrangement direction of the vertices of each triangle is the same, and in step ST7, the triangle a1 -A4-a6 and a triangle a1-a4-a5 are used to perform an arithmetic operation, the triangle a6-a2-a3 and a triangle a1-a4-a5 are used to perform an arithmetic operation, and a triangle a1-a6-a9 , Triangle a4-a10-a6, triangle a6-a2-a3, and triangle a8-a5-a7 (see FIG. 3 (f)). Note that various polygons can be obtained as the calculation method of the logical operation depending on the algorithm. As step ST9, the computing unit 23 overwrites and stores the acquired triangle a1-a6-a9, triangle a4-a10-a6, triangle a6-a2-a3, and triangle a8-a5-a7 in the polygon storage unit 24.

In step ST10, the calculation unit 23 determines that the triangle a1-a4-a5 used for the calculation includes the last vertex a5 of the polygon, and in step ST11, the drawing unit 25 sets the polygon storage unit 24. The triangles a1-a6-a9, triangles a4-a10-a6, triangles a6-a2-a3 and triangles a8-a5-a7 stored in FIG. As step ST12, the display processing unit 26 performs display processing on the drawing data of the polygon A, outputs it to the display device 6 via the I / O interface 4, and ends the processing.

Next, the non-self-intersecting concave polygon drawing process shown in FIG. 4 will be described with reference to the flowchart shown in FIG.
In step ST1, the vertex data acquisition unit 21 reads polygon data relating to the polygon B, and stores the vertexes of the polygon A with numbers b1, b2, b3, b4, and b5 in step ST2. As step ST3, the triangle extraction unit 22 selects the vertex b1 as the drawing start vertex, and extracts the triangle b1-b2-b3 (drawing start triangle) having the vertex b2 as the second vertex and the vertex b3 as the third vertex. Then, the arrangement direction R1 of the vertices b1, b2, and b3 is determined to be clockwise by the sign of the Z component in the depth direction of the outer product of the vector b1-b2 and the vector b1-b3 of the extracted triangle b1-b2-b3. . In step ST4, the extracted triangle b1-b2-b3 and vertex arrangement direction R1 are stored in the polygon storage unit 24.
Note that the vertex arrangement directions R2, R3, and R4 shown in the following description are also determined by the sign of the Z component in the depth direction of the outer product of two vectors, as described above.

Next, as step ST5, the triangle extraction unit 22 extracts a triangle b1-b3-b4 having the last vertex b3 of the previously extracted triangle b1-b2-b3 as the second vertex and the vertex b4 as the third vertex. Then, it is determined that the vertex arrangement direction R2 of the extracted triangles b1-b3-b4 is counterclockwise.

As step ST6, the calculation unit 23 compares the triangle b1-b2-b3 stored in the polygon storage unit 24 with the triangle b1-b3-b4 extracted by the triangle extraction unit 22, and arranges the apex alignment directions R1, R1 of the triangles. It is determined that R2 is not the same, and in step ST8, an operation based on a logical difference is performed using the triangle b1-b2-b3 and the triangle b1-b3-b4 to obtain the triangle b2-a3-a4 (see FIG. 4 (e)). . In step ST9, the calculation unit 23 overwrites and stores the acquired triangle b2-b3-b4 in the polygon storage unit 24.

Further, in step ST10, the calculation unit 23 determines that the triangle b1-b2-b3 and the triangle b1-b3-ab used in the calculation do not include the last vertex b5 of the polygon, and the process of step ST5 Returning to, the next triangle b1-b4-b5 is extracted, and it is determined that the vertex arrangement direction R3 of the extracted triangle b1-b4-b5 is counterclockwise.

As step ST6, the calculation unit 23 compares the triangle b2-b3-b4 stored in the polygon storage unit 24 with the triangle b1-b4-b5 extracted by the triangle extraction unit 22, and arranges the apex alignment directions R4, R4 of the triangles. It is determined that R3 is the same, and in step ST7, an arithmetic operation is performed using the triangle b2-b3-b4 and the triangle b1-b4-b5, and the triangle b2-b3-b4 and the triangle b1-b4-b5 (FIG. 4 (f)). As step ST9, the calculation unit 23 overwrites and stores the acquired triangle b2-b3-b4 and triangle b1-b4-b5 in the polygon storage unit 24.

In step ST10, the calculation unit 23 determines that the triangle b1-b4-b5 used for the calculation includes the last vertex b5 of the polygon, and in step ST11, the drawing unit 25 sets the polygon storage unit 24. The triangles b2-b3-b4 and triangles b1-b4-b5 stored in the above are read out and painted, and the polygon B to be drawn is drawn. As step ST12, the display processing unit 26 performs a display process on the drawing data of the polygon B, outputs it to the display device 6 via the I / O interface 4, and ends the process.

Furthermore, the drawing apparatus 1 of the first embodiment can also draw a non-self-intersecting convex polygon shown in FIG. In the case of a convex polygon, the triangle c1-c2-c3 (drawing start triangle), the triangle c1-c3-c4, and the triangle c1-c4-c5 extracted sequentially from the drawing start vertex c1 do not overlap each other, Furthermore, since the arrangement directions of the vertices are the same (counterclockwise in the example of FIG. 5), the extracted triangles c1-c2-c3, triangles c1-c3-c4, and triangles c1-c4-c5 are all subjected to a logical OR operation. Do. As a result, the polygon drawn by the drawing unit 25 is the same as the polygon C divided by three triangles (see FIG. 5B).

As described above, according to the first embodiment, the vertex data acquisition unit 21 that detects a vertex of a polygon and assigns the drawing order, and the triangle extraction unit that extracts a plurality of triangles based on the drawing order of the polygon 22, a calculation unit 23 that performs a logical sum operation or a logical difference calculation based on the arrangement direction of the triangles stored in the polygon storage unit 24 and the triangle vertices extracted by the triangle extraction unit 22, and the calculation result of the calculation unit 23 Since it is configured to include a polygon storage unit 24 that stores polygons that are aggregates of triangles and a drawing unit 25 that draws polygons stored in the polygon storage unit 24, mask data is created. Thus, it is possible to draw a graphic including a self-intersecting polygon without mounting hardware dedicated to graphic drawing.

Further, according to the first embodiment, the vertex arrangement direction determined by the sign of the outer product of the two vectors constituting the triangle is calculated, and the calculation unit 23 performs logic based on the arrangement direction of the two triangle vertices. Since the sum operation or the logical difference operation is performed, it is possible to draw a graphic including a self-intersecting polygon without creating mask data.

In the above-described first embodiment, the configuration in which the triangles are extracted in ascending order of the numbers assigned to the vertices is shown, but the extraction order is not limited to this.

In the present invention, any component of the embodiment can be modified or any component of the embodiment can be omitted within the scope of the invention.

As described above, drawing of polygons including self-intersecting figures by the drawing apparatus and drawing method according to the present invention may include a device that cannot secure a memory capacity for creating mask data or special hardware. Suitable for mounting on devices that cannot.

1 drawing device, 2 drawing processing unit, 3 memory, 4 I / O interface, 5 storage device, 6 display device, 21 vertex data acquisition unit, 22 triangle extraction unit, 23 operation unit, 24 polygon storage unit, 25 drawing unit , 26 Display processing unit.

Claims

A vertex data acquisition unit that acquires polygon data of a polygon to be drawn, detects a vertex that identifies the polygon from the acquired polygon data, and assigns a drawing order to the detected vertex;
Based on the drawing order given by the vertex data acquisition unit, a triangle extraction unit that extracts a plurality of triangles, each of which changes the second vertex and the third vertex based on the drawing start vertex from the polygon,
An arithmetic unit that performs a logical operation using a plurality of triangles extracted by the triangle extraction unit;
A polygon storage unit that stores polygons that are aggregates of triangles that are calculation results of the calculation unit;
A drawing device comprising a drawing unit for drawing a polygon stored in the polygon storage unit,
The triangle extraction unit extracts a drawing start triangle connecting the drawing start vertex and two vertices whose drawing order is continuous from the drawing start vertex, and stores the drawing start triangle in the polygon storage unit,
The calculation unit is the drawing start triangle stored in the polygon storage unit or the drawing order of each vertex of the triangle as the calculation result, and other than the drawing start triangle, and based on the drawing start point Perform a logical operation based on the drawing order of each vertex of the triangle with each of the 2 vertices and the 3rd vertex changed,
The drawing unit draws a polygon stored in the polygon storage unit when a logical operation is performed on all the triangles extracted by the triangle extraction unit in the calculation unit. Drawing device.
The calculation unit is other than the drawing start triangle stored in the polygon storage unit or the calculation result triangle and the drawing start triangle, and the second vertex and the third are based on the drawing start point. For each of the triangles whose vertices are respectively changed, the drawing direction indicating the drawing order when drawing the other two vertices from the base point is obtained from the predetermined vertex, and the drawing directions of the obtained two triangles 2. The drawing apparatus according to claim 1, wherein a logical sum operation is performed when the two are the same, and a logical difference operation is performed when the drawing directions of the two triangles are not the same.
The triangle extraction unit is configured to change the second vertex and the third vertex other than the drawing start triangle and the drawing start triangle and changing the second vertex and the third vertex respectively with reference to the drawing start point, and the other two from the base point. The drawing apparatus according to claim 2, wherein the drawing direction is determined using a sign of an outer product of two vectors extending toward the vertex.
The said calculating part determines the said drawing direction using the code | symbol of the outer product of two vectors extended toward the other two vertexes from the said base point about the triangle which is the said calculation result. Drawing device.
A vertex data acquisition unit acquires polygon data of a polygon to be drawn, detects a vertex specifying the polygon from the acquired polygon data, and assigns a drawing order to the detected vertex;
A step of extracting a plurality of triangles in which the second vertex and the third vertex are respectively changed from the polygon based on the drawing start vertex based on the drawing order given by the vertex data obtaining unit; When,
A calculation unit performing a logical operation using a plurality of triangles extracted by the triangle extraction unit;
A step of storing a polygon which is an aggregate of triangles as a result of the operation of the operation unit;
A drawing unit comprising a step of drawing a polygon stored in the polygon storage unit,
The triangle extraction unit extracts the drawing start vertex and a drawing start triangle connecting two vertices whose drawing order is continuous from the drawing start vertex, and stores the drawing start triangle in the polygon storage unit;
The calculation unit is other than the drawing start triangle stored in the polygon storage unit or the calculation result triangle, and the drawing start triangle, and the second vertex and the third based on the drawing start point Performing a logical operation using triangles with different vertices of
The drawing unit includes a step of drawing a polygon stored in the polygon storage unit when a logical operation is performed on all the triangles extracted by the triangle extraction unit in the calculation unit. A drawing method characterized by that.
The calculation unit is other than the drawing start triangle stored in the polygon storage unit or the calculation result triangle, and the drawing start triangle, and the second vertex and the third based on the drawing start point Obtaining a drawing direction indicating a drawing order when drawing the other two vertices from the base point with respect to each of the triangles each having the vertex of each changed as a base point; and 6. The drawing method according to claim 5, further comprising a step of performing a logical sum operation when the drawing directions are the same and a step of performing a logical difference operation when the drawing directions of the two triangles are not the same.
The triangle extraction unit, for the triangles other than the drawing start triangle and the drawing start triangle and changing the second vertex and the third vertex based on the drawing start point, respectively, from the base point to the other two The drawing method according to claim 6, further comprising the step of determining the drawing direction using a sign of an outer product of two vectors extending toward the vertex.
The calculation unit includes a step of determining the drawing direction with respect to a triangle as the calculation result by using a sign of an outer product of two vectors extending from the base point toward the other two vertices. Item 7. The drawing method according to Item 6.