JPH08329245A - Method and device for graphic processing - Google Patents

Abstract

PURPOSE: To properly obtain the intersection between two geometrical elements even in the case of data of two geometrical elements including noise by providing a first discrimination process to discriminate graphics as an ellipse and a second discrimination process to discriminate graphics as a circle. CONSTITUTION: A central processing unit (CPU) 2, a read only memory (ROM) 3, and a random access memory (RAM) 4 are connected to a bus 1 (including a control line, a data line, and an address line), and an input device 6, a CRT 8, and an external storage device 10 are connected to the bus 1 through an input interface 5, a CRT interface 7, and an external storage device interface 9 respectively. The first discrimination process where a prescribed decision formula based on coefficients of an equation of graphics is calculated to discriminate graphics as an ellipse and the second discrimination process where graphics are discriminated as a circle in the case of the length difference between the minor axis and the major axis of graphics shorter than a prescribed value at the time when graphics are discriminated as an ellipse in the first discrimination process are provided to discriminate the graphics.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a graphic processing method and apparatus, and more particularly to a method of calculating a line of intersection of two graphics.

[0002]

2. Description of the Related Art Conventionally, when obtaining an intersection line, there has been a method of simply establishing simultaneous equations of two geometric elements and obtaining the equation of the intersection line algebraically and analytically. Also, when seeking the intersection line,
There has been a method of calculating the intersection line by previously determining the type of the intersection line using a discriminant or the like by utilizing the geometrical characteristics of the two geometric elements.

[0003]

However, according to the conventional method, when a numerical error due to a digit cancellation is included in the determination of the relationship between two geometric elements, the method is correct according to a unified and practical standard. There was a problem that it was not possible to make a judgment and the correct line of intersection could not be obtained in many cases. The present invention has been made in view of the above-mentioned conventional example, and provides a graphic processing method and an apparatus thereof for appropriately obtaining a line of intersection between two geometric elements even when data of the two geometric elements include noise. The purpose is to provide.

[0004]

In order to achieve the above object, a graphic processing method and apparatus of the present invention have the following configurations. That is, a predetermined discriminant based on the coefficient of the equation of the figure is calculated to determine the figure as an ellipse, and when the figure is determined as an ellipse in the first step, the figure is If the difference between the short axis length and the long axis length is less than or equal to a predetermined value, the second determination step of determining the figure as a circle is provided.

Another aspect of the present invention is to calculate a predetermined discriminant based on a coefficient of an equation of a figure to determine the figure as an ellipse, and to determine the figure by the first decision means. If it is determined that the figure is an ellipse and the difference between the short axis and the long axis of the figure is less than or equal to a predetermined value, the figure is determined to be a circle.
And the determination means of.

[0006]

In the above structure, a predetermined discriminant based on the coefficient of the equation of the figure is calculated, the figure is determined to be an ellipse, and when the figure is determined to be an ellipse in the first determining step, the figure If the difference between the length of the short axis and the length of the long axis is less than or equal to a predetermined value, the figure is determined to be a circle.

According to another aspect of the invention, the first determining means calculates a predetermined discriminant based on the coefficient of the equation of the figure and determines the figure as an ellipse, and the second determining means sets the When the figure is determined to be an ellipse by the determination unit 1 and the difference between the lengths of the short axis and the long axis of the figure is equal to or less than a predetermined value, the figure is determined to be a circle.

[0008]

First, one of the points of the graphic processing method of the embodiment according to the present invention is to obtain various discriminant determinants on the basis of the coefficient of the general equation of the intersecting line when obtaining the intersecting line of two figures. By performing a calculation, a so-called algebraic distinction is performed, which is to discriminate the types of rough intersecting lines, and then the intersecting lines roughly classified into each figure type are finally determined based on the plurality of geometric feature amounts. By having a configuration for performing so-called geometric classification processing of determining and adjusting the classification of intersection lines, it is possible to find appropriate intersection lines that are resistant to noise. (Embodiment 1) FIG. 1 is a block diagram of a graphic processing device according to one embodiment of the present invention. A bus 1 (including a control line, a data line and an address line) has a central processing unit (CPU).
2, read only memory (ROM) 3, random
Access memory (RAM) 4, input interface 5
An external storage device 10 such as a magnetic disk, a magnetic tape or the like via an input device 6, a CRT 8 via a CRT interface 7, and an external storage device interface 9 via
Is connected.

According to the program stored in the ROM 3,
The RAM 4 is used as a temporary storage device to perform various processes and controls, such as graphic input control, graphic display display, pick processing, hidden surface processing, and inside / outside determination. The input device 6 is provided with a keyboard, a tablet, a mouse, etc. and inputs graphic data, but this graphic data may be received from the host computer.

The CRT 8 has a plurality of bits, if necessary.
It includes maps and planes and displays graphics. Next, in order to facilitate understanding of the present embodiment, an example of a method of obtaining an intersection line between a cylinder and a plane as shown in FIG. 2, that is, an intersection line calculation method when the intersection line is an ellipse or a circle is taken as an example. Will be described below.

FIG. 3 is a flow chart for explaining the flow of graphic processing according to an embodiment of the present invention. Here, a processing program corresponding to the processing described below is stored in the ROM 3, and the CPU 2 reads this program, interprets it, and executes it. Hereinafter, before explaining the flowchart, terms necessary for the explanation will be defined. <Definition of Symbols and Terms for Planes and Cylindrical Surfaces> Symbols for planes and cylindrical surfaces are defined as shown in FIG.

P0: reference point on plane n0: normal vector of plane (unit vector) c0: reference point on axis of cylindrical surface r: radius of cylindrical surface n1: axis vector of cylindrical surface (unit vector) The following two are not shown in FIG. 4, but will be described in detail later.

EPS: Geometrical permissible length EPSA: Geometrical permissible angle << Term >> ・ Cylindrical reference plane: A plane that passes through c0 and is perpendicular to the axis of the cylindrical surface is referred to as the cylindrical reference surface.

Geometrical feature value: A value representing geometrical features such as the center, radius, major axis, and minor axis of a figure. Next, with reference to FIG. 3, a flow of graphic processing according to an embodiment of the present invention will be described. Although the above-mentioned variable names appear in the following description, those variable names are the random access memory 4
Be assigned to.

First, in step S6, the type and feature amount of the intersection line are calculated from the equation of the intersection line. Here, it is assumed that the data of the target plane and the cylindrical surface are already stored in advance in the external storage device or the random access memory, and the data of the target plane and the cylindrical surface are extracted from there. Also,
Coordinate conversion has already been applied to the target plane so that it becomes parallel to the predetermined xy plane, and the general form of a quadratic curve is expressed as a line of intersection: a · x ² + 2h · xy + b · y ² + 2g · x + 2f y + c =
0 where a, b, c, f and g are constants. It is assumed that the data has already been obtained in the form of, and the data is stored in the random access memory 4.

The above-mentioned coordinate conversion is performed by, for example, each coordinate of the target plane and a predetermined conversion matrix M (predetermined xy).
It can be realized by taking the product of the angle between the plane and the plane of interest in the original coordinate space). On the contrary,
The original target plane can be obtained by taking the product of each coordinate of the transformed plane and the inverse matrix M ′ of the transformation matrix M.

The details of the processing in this step will be described below. First, the determinant for determining the type of the above quadratic curve Is calculated and stored in the random access memory 4. Then, if D = 0, the above quadratic curve is classified as a straight line.

Next, another determinant for discriminating the type of the above quadratic curve Is calculated and stored in the random access memory 4. If Δ = 0, the above quadratic curve is classified as a parabola.

Next, x0 = (rfh-bg) / Δ y0 = (rhg-af) / Δ is calculated and stored in the random access memory 4. Then, X0 = (x0, y0) is calculated and stored in the random access memory 4.

Next, according to the relationship between a and b, the following equation θ = π / 4: (If a = b) θ = (1/2) atan (2h / (ab)) :( If a ≠ b), it is calculated and stored in the random access memory 4.

Next, t ² − (a + b) t + ab = 0 where a and b are constant solutions t1 and t2, which are stored in the random access memory 4.

Next, if h = 0, a and b are respectively a
2 and b2 are substituted, that is, a2 = a and b2 = b are substituted and stored in the random access memory 4.

If h> 0, then a2 = max (t1, t2) b2 = min (t1, t2) where max (x1, x2): The larger one of x1 and x2 is selected.
Function to do.

Min (x1, x2): A function for selecting the smaller one of x1 and x2. Is calculated and stored in the random access memory 4. If h <0, a2 = min (t1, t2) and b2 = max (t1, t2) are calculated and stored in the random access memory 4.

Next, if Δ> 0, the result (predetermined code for identifying the types) is stored in the random access memory 4 as being any one of a circle, an ellipse, a point ellipse, and an imaginary ellipse. Next, a / c is calculated. If a / c> 0, the result (a predetermined code for identifying the types) is stored in the random access memory 4 as a point or an imaginary ellipse.

If a / c> 0 is not established, the result (a predetermined code for identifying the types) is stored in the random access memory 4 as a circle or an ellipse. Next, r1 = √ (−c / a2) r2 = √ (−c / b2) where √ (x): a function for calculating the route of x. Is calculated and stored in the random access memory 4.

Here, if r1-r2 = 0, it is determined to be a circle, otherwise it is determined to be an ellipse, and the result (a predetermined code for identifying those types) is stored in the random access memory 4. If it is determined to be a circle in the above process, the radius rmin = r1 = r2. The center is X0
Is. These data are stored in the random access memory 4
To be stored.

When it is determined to be an ellipse in the above process and r1> r2, the long axis vector: (r1,0,0) is rotated by θ counterclockwise. The short axis vector: (0, r2,0) is rotated in the counterclockwise direction by θ and the data is stored in the random access memory 4 as the center: X0.

If the judgment conditions described above are not satisfied, that is, if the classification is not a circle or an ellipse, the process ends. On the other hand, if it is classified into a circle or an ellipse, step S7.
Go to. In step S7, it is checked whether the intersection line classified in step S6 is an ellipse, and if it is an ellipse, the process proceeds to step S8. Conversely, if it is a circle, the process proceeds to step S11.

In step S8, it is determined whether the length of the major axis or the minor axis is equal to or smaller than EPS, which is a predetermined geometrically allowable length. In this processing, the sizes (lengths) of the long axis and short axis vectors, which are the feature values of the ellipse obtained in step S6, are calculated, and the length of the long axis or the short axis is E.
It is determined whether it is PS or less. Then, if the length of the major axis or the minor axis is not more than EPS, the steps from step S13 are performed. Conversely, the length of the major axis or minor axis is E
If not less than PS, the processing from step S9 is performed.

In step S9, it is determined whether the difference between the lengths of the major axis and the minor axis is EPS or less. Here, if the difference is equal to or less than EPS, which is the geometrically allowable length, it is regarded as an approximate circle, and the processing from step S12 is performed. On the contrary, if the difference is not less than the geometrically allowable length EPS, it is regarded as an ellipse, and the processing from step S10 is performed. Step S
In 10, the intersection line is output as an ellipse. Specifically, the central coordinates, the long axis vector, and the short axis vector obtained in step S6 are inversely transformed into the original coordinate space, and the normal vector of the ellipse is made the same as the normal vector of the original plane. Are output as elliptic feature values, and the converted feature values are output to the random access memory 4 or the external storage device 10.
To be stored.

In step S11, it is determined whether the radius is less than EPS. Specifically, when it is determined that the intersection line is a circle and the radius thereof is minute, or due to a numerical error such as a digit loss, it is determined that the intersection line is less than or equal to the geometrical allowable error EPS. Performs the processing from step S13. On the contrary, when it is determined that it is EPS or more, step S1
Processing from 2 is performed.

In step S12, the line of intersection is output as a circle. Specifically, when it is determined that the line of intersection is a circle and the process proceeds from step S9 to this step, in other words, when it is determined to be an ellipse in the algebraic determination of step S6, there is a long axis and a short axis. , Here, the average of the sizes of the major axis and the minor axis is the radius of the circle. In addition, how to find the radius here is now
Although the average of the sizes of the major axis and the minor axis is used, either the major axis or the minor axis may be set as the radius of the circle.

Then, in order to transform the obtained circle parallel to the predetermined xy plane onto the original object plane, the product of the inverse matrix M'and each coordinate of the obtained circle is obtained. Convert coordinates. In this way, the feature values such as the center and radius of the circle having the same normal vector as the original target normal vector are output to the CRT 8. In step S13, it is determined that the intersection line degenerates to a point, and this determination state is output to the CRT 8 as a message.
The process ends without outputting to T8.

As described above, according to this embodiment,
Performs algebraic shape discrimination based on the coefficient of the general formula of the intersection line,
By using the result, the secondary shape determination is performed based on the geometric feature amount such as the short axis, the long axis, the radius, and the like, and the shape is adjusted, so that an appropriate intersecting line shape can be obtained. (Embodiment 2) The hardware configuration of the graphic processing apparatus of Embodiment 2 is the same as that of FIG. 1, but the method of calculating the line of intersection is different.

Hereinafter, with reference to the flowchart of FIG.
The intersection line calculation processing procedure in the second embodiment will be described. However, steps S6 to S13 of FIG. 4 are the same as the processing of steps S6 to S13 of the first embodiment, and a description thereof will be omitted. The terms used in the description are the same as in the first embodiment.

First, in step S1, the relationship between the flat surface and the cylindrical surface is determined. Specifically, the relationship between the normal vector of the plane and the axis of the cylinder is determined, and the type of intersection line is estimated.
Specifically, the correlation value based on the inner product between the plane normal vector n0 and the cylindrical axis vector n1 is calculated by the following formula. a = n0.n1 / (| n0 |. | n1 |) Then, the result a is stored in the random access memory 4. Next, it is determined whether or not the absolute value of the result a satisfies the following expression. When 1.0-EPSA ≦ | a | ≦ 1.0 + EPSA is satisfied, it is determined that the plane and the cylinder axis are vertical. When | a | ≦ EPSA is satisfied, it is determined that the plane and the cylinder axis are parallel to each other. Then, those results are stored in the random access memory 4
To be stored.

In step S2, the judgment result in step S1 is fetched from the random access memory, and if the plane and the circle are vertical, the process proceeds to step S14. On the contrary, if it is not vertical, the process proceeds to step S3. In step S14,
Calculate the intersection of the cylinder axis and the plane. In step S15,
The intersection line as a circle is output to the CRT 8. Specifically, the intersection obtained in step S14 is set to the random access memory 4
Then, the intersection is defined as the center of the circle, and the radius is defined as the intersection of the circle having the same radius as the radius r of the cylindrical surface. Output (see FIG. 2). Then, the process ends.

In step S3, it is determined whether the plane and the cylinder axis are parallel. Specifically, the determination result in step S1 is fetched from the random access memory 4, and it is checked whether or not the plane and the cylinder axis are parallel. If the plane and the cylinder axis are parallel, the process proceeds to step S16. If not, the process proceeds to step S4. Step S
In 16, it is assumed that the intersecting line is a straight line, and the calculation for obtaining the straight line is performed. Specifically, the intersecting line is 0 to 2 straight lines (see (b), (c), and (d) in FIG. 2), and the calculation is performed, and the data of the straight line is stored in the random access memory 4 Alternatively, it is output to the external storage device 10 or the CRT 8 (see FIG. 2). Then, the process ends.

In step S4, the plane and the cylindrical surface are coordinate-converted so that the plane is parallel to the xy plane. Specifically, coordinate conversion is performed on each feature value of the plane and the cylindrical surface so that the plane is parallel to the xy plane. In step S5, the Z coordinate value of the plane after conversion (the coordinate value of the plane in the Z axis direction with the axis orthogonal to the XY plane as the Z axis) Z0
Is substituted into the equation for the cylindrical surface, and the equation for the line of intersection is calculated. Specifically, the following processing is performed. That is, it is assumed that the equation of the plane becomes Z = Z0 as a result of the coordinate conversion in step S4. Moreover, it is each feature value of a plane and a cylindrical surface,
It is assumed that the reference point P0 on the plane, the reference point C0 on the axis of the cylindrical surface, and the axis vector n1 of the cylindrical surface are P0-> P01 C0-> C01 n1-> n11, respectively. At this time, the equation of the cylindrical surface of the converted, the (X-C01) · (X -C0) = {(X-C01) · n01} 2 + r 2 This equation, X = a (x, y, Z0) The substituted and expanded expression is obtained as the intersection line expression. Then, the parameters of the equation of the obtained intersection line are stored in the random access memory 4.

Next, even if the processing from step S6 onward described in the first embodiment is proceeded to, if it is determined that the line of intersection is an ellipse or a circle, it is C
If the result is output to the RT 8 or the like and is determined as a point, the effect is displayed on the CRT or the like, and the process ends. As described above, according to the present embodiment, first, the algebraic determination of the positional relationship between the plane and the cylindrical surface, more specifically, whether the plane and the cylinder are orthogonal or parallel is algebraically determined. If it is determined that the intersection line is a circle or a straight line, it is not necessary to perform the geometric processing in and after step S6 on them, and the graphic processing is executed at a higher speed. it can. In this way, by cleverly combining the above-mentioned algebraic processing and geometrical processing,
A proper intersecting line shape can be obtained. (Embodiment 3) In the present embodiment, when the axis of the cylindrical surface is determined to be parallel to the plane and the intersecting line is a straight line (FIGS. 4B, 4C, and 4D).
The method of calculating the line of intersection between the plane and the cylindrical surface in the reference) will be described.

A program corresponding to the following flow chart is stored in the ROM 3 in advance, and the CPU
2 refers to this program, interprets it, and executes it. Figure 5
Is a flowchart for explaining a method for calculating the intersection line between the plane and the cylindrical surface of the present embodiment, and the processing contents will be described for each step with reference to this flowchart. Here, terms and the like used in the description are the same as those in the first embodiment.

In step S100, the distance r2 between the axis of the cylindrical surface and the plane when the axis of the cylinder is parallel to the plane is calculated and stored in the random access memory 4. The calculation method may be to find the distance between any one point on the axis of the cylinder and the plane. In step S17, the shortest distance d between the cylindrical surface and the flat surface
(With a sign), that is, d = r2-r is obtained, and the result is stored in the random access memory 4.

In step S18, it is determined whether or not the shortest distance d between the cylindrical surface and the plane obtained in step S17 satisfies the following inequality d ≤ EPS. And if you are satisfied,
If not satisfied, go to step S22.
Process from.

In step S22, it is determined that the cylindrical surface and the flat surface are in contact with each other, and the determination result 4 is stored in the random access memory (see FIG. 2 (c)). In step S23, the contacting ridge lines are calculated as intersection lines. Specifically, when the point of the foot of the perpendicular line drawn from C0 to the plane is P3, it is calculated as a ridge line (intersection line) where a straight line passing through P3 and having the axial vector of the cylindrical surface as the direction vector is in contact. To do. Then, the result is displayed on the CRT 8 and the process ends.

In step S19, it is determined whether the shortest distance d between the cylindrical surface and the flat surface satisfies the following inequality d> EPS. Then, if satisfied, the process is performed from step S24, and if not satisfied, the process from step S20 is performed.

In step S24, it is determined that there is no line of intersection (see FIG. 4B), that is, it is determined that the plane and the cylindrical surface are distant from each other, the result is displayed on the CRT 8, and the process is terminated. In step S20, it is assumed that the two straight lines are intersecting lines, and these straight lines are obtained and stored in the random access memory 4 (see FIG. 4 (d)). Specifically, an intersection of a circle whose center is the reference point of the cylindrical surface and whose normal is a circle whose radius is the radius r of the cylindrical surface is the axial direction vector of the cylindrical surface and a plane,
Find P1 and P2. A straight line passing through P1 and P2 and having the axial direction vector of the cylindrical surface as the direction vector is defined as an intersection line.

In step S21, it is determined whether the distance between P1 and P2 is within EPS, and if it is within EPS, 2 is determined.
It is determined that the intersecting line distance of the book is within EPS, the result is stored in the random access memory 4, and the process proceeds to step S25. On the contrary, if it is not within EPS, the result is CRT8.
And is displayed. In step S25, a process of combining the two intersection lines into one is performed. Specifically, it is determined that the two intersection lines are approximately the same, and step S20 is performed.
A straight line that passes through either of the points P1 and P2 on the straight line obtained in step 3 and uses the axial direction vector of the cylindrical surface as the direction vector,
It is output to the random access memory 4, the external storage device 10 or the CRT 8 as the only line of intersection.

As described above, in the present embodiment, when it is determined that the axis of the cylindrical surface is parallel to the plane and the line of intersection is a straight line, the distance between the axis of the cylindrical surface and the plane and the predetermined threshold value are As shown in FIG. 2, it is possible to judge whether the cylindrical surface and the plane are separated from each other or are in contact with each other (have one intersection line) or have two intersection lines as shown in FIG. When it is determined that the lines of intersection have a distance of less than a predetermined threshold value, it is possible to obtain an appropriate line of intersection that is strong against noise by correcting the line into one straight line. (Embodiment 4) In this embodiment, a processing (see FIGS. 6 and 7) in which the intersection processing of FIG. 4 and the intersection processing when the intersection of FIG. 5 is a straight line are combined will be described. The point of the intersection line processing in this embodiment is that after the straight line as the intersection line is obtained in step S16 of FIG. 4, the processing from step S100 of FIG. 5 is performed to adjust the intersection line. , Provides a noise-resistant intersection line processing method.

The programs corresponding to the flowcharts shown in FIGS. 6 and 7 are stored in the ROM 3 in advance,
The CPU 2 refers to this program, interprets it, and executes it. FIG. 6 and FIG. 7 are flowcharts for explaining the intersection line calculation processing method between the plane and the cylindrical surface of the present embodiment, which is a combination of FIGS. 4 and 5. In this flow chart, each step number is the same as the step number in FIG. 4 and FIG.
This means that the processing contents in the corresponding steps of FIG. 4 and FIG. 5 are the same.

That is, steps S1 to S1 in FIGS.
Step S15 is step S1 to step S1 in FIG.
5 and steps S16 to S16 in FIG. 6 and FIG.
Step S25 is step S16 to step S2 in FIG.
This is the same as the process of 5. Therefore, the description of all steps is omitted. As described above, according to this embodiment,
By combining the intersecting line processing of FIG. 4 and the intersecting line processing of FIG. 5 when the intersecting line is a straight line to adjust the intersecting line, an intersecting line processing method resistant to noise is provided. (Other Embodiments) In the above, the intersection line calculation method has been described in relation to the plane and the cylinder. Needless to say.

The present invention may be applied to a system composed of a plurality of devices or an apparatus composed of one device. Further, it goes without saying that the present invention can be applied to the case where it is achieved by supplying a program to a system or an apparatus. As described above, in the embodiment according to the present invention, when the line of intersection of two geometric elements is obtained,
A special case such as a case where two geometric elements are in contact with each other is processed in advance by a geometrically meaningful error criterion, and the solution of the intersection line obtained by a general algebraic method is geometrically meaningful. By correcting using a certain error criterion, the solution of the intersection line can be stably obtained with a practical criterion, and it is also resistant to noise.

[0053]

As described above, according to the present invention, 2
Even if the geometric element data contains noise, the line of intersection between the two geometric elements can be properly obtained.

[Brief description of drawings]

FIG. 1 is a block diagram of a graphic processing device according to an embodiment of the present invention.

FIG. 2 is a diagram illustrating a state of a line of intersection corresponding to a positional relationship between a plane surface and a cylindrical surface.

FIG. 3 is a flow chart showing intersection line processing according to the first embodiment of this invention.

FIG. 4 is a flow chart showing intersection line processing according to the second embodiment of the present invention.

FIG. 5 is a flow chart showing intersection line processing according to a third embodiment of this invention.

FIG. 6 is a flow chart showing intersection line processing according to a fourth embodiment of the present invention.

FIG. 7 is a flow chart showing an intersection line process of a fourth embodiment of the present invention.

FIG. 8 is a diagram showing definitions of terms and the like for explaining processing in each embodiment.

Claims (40)

[Claims] 1. A first determination step of determining a figure as an ellipse by calculating a predetermined discriminant based on a coefficient of a figure equation, and a step of determining the figure as an ellipse in the first determination step. ,
A graphic processing method comprising: a second determination step of determining the graphic as a circle if the difference between the lengths of the short axis and the long axis of the graphic is not more than a predetermined value. 2. When the figure is determined to be a circle in the second determining step, an average value of the lengths of the major axis and the minor axis is set as a radius of the circle. Claim 1
The graphic processing method described in 1. 3. The graphic processing method according to claim 1, wherein when the graphic is determined to be a circle in the second determination step, the length of the major axis is set to the radius of the circle. . 4. The figure processing method according to claim 1, wherein when the figure is determined to be a circle in the second determination step, the length of the minor axis is set to the radius of the circle. 5. The equation of the figure is expressed by ax ² + 2hxy + by ² + 2gx + 2fy + c = 0 in which x and y are variables, and a, h, b, g, f and c are predetermined coefficients. The graphic processing method according to claim 1. 6. The first determination step is: ab-h ² > 0, a / c ≦ 0, and a solution t 1 of a quadratic equation t ² − (a + b) t + ab = 0 with t as a variable. , t2
Regarding a2 and b2, if h = 0, a2 = a, b2 = b h> 0, a2 = max (t1, t2), b2 = min (t1, t2) h <0, a2 = min (t1, t2), b2 = max (t1, t2), and the route calculation result of -c / a2 is r1, -c
When the route calculation result of / b2 is r2, r1≈r
If the figure is 2, the figure is determined to be an ellipse, and the figure processing method according to claim 5. 7. The graphic according to claim 1, further comprising a step of determining the graphic as a point if the length of either the short axis or the long axis of the graphic is not more than a predetermined value. Processing method. 8. When the figure is determined to be an ellipse in the first determining step and the difference between the short axis and the long axis of the figure is not less than a predetermined value, the figure is determined to be an ellipse. The graphic processing method according to claim 1, further comprising a determination step (3). 9. The graphic processing method according to claim 1, further comprising a step of displaying a graphic determined to be a circle in the second determination step. 10. The figure processing method according to claim 8, further comprising a step of displaying a figure determined to be an ellipse in the third determining step. 11. The graphic processing method according to claim 1, wherein the graphic is a graphic of an intersection of a predetermined plane and a predetermined cylindrical surface. 12. The graphic processing method according to claim 1, wherein the graphic is a graphic of an intersection of a predetermined plane and a predetermined conical surface. 13. The graphic processing method according to claim 1, wherein the graphic is a graphic of an intersection of a predetermined plane and a predetermined spherical surface. 14. Before the first determining step, a correlation coefficient based on an inner product of a radial vector of the plane and an axial vector of the cylindrical surface is obtained, and the correlation coefficient is within a predetermined range value. For example, a fourth determination step of determining the figure as a circle is provided, and if the figure is determined as a circle in the fourth determination step, the processing subsequent to the first determination step is not performed. The graphic processing method according to claim 8. 15. A correlation coefficient based on an inner product of a radial vector of the plane and an axial vector of the cylindrical surface is obtained before the first determining step, and the correlation coefficient is equal to or less than a predetermined threshold value. And a fifth determination step of determining the figure as a straight line, and if the figure is determined to be a straight line in the fifth determination step, the processing subsequent to the first determination step is not performed. The graphic processing method according to claim 8. 16. When the figure is determined to be a straight line in the fifth determining step and the distance between the plane and the cylindrical surface is within a predetermined range value, the plane and the cylindrical surface are in contact with each other. 16. The graphic processing method according to claim 15, further comprising a sixth determining step of determining that there is a ridge line that is in contact with the ridge line that is in contact with the ridge line. 17. When the figure is determined to be a straight line in the fifth determining step and the distance between the plane and the cylindrical surface is equal to or greater than a predetermined threshold, the plane and the cylindrical surface intersect with each other. The graphic processing method according to claim 15, further comprising a seventh determination step of determining that the graphic processing method does not have it. 18. When the figure is determined to be a straight line in the fifth determining step, the distance between the plane and the cylindrical surface is not within a predetermined range value, and the distance between the plane and the cylindrical surface is between. The graphic processing method according to claim 15, further comprising an eighth determination step of determining that the flat surface and the cylindrical surface have an intersection line of two straight lines unless the distance is equal to or larger than a predetermined threshold value. . 19. In the case where it is determined in the eighth determination step that the flat surface and the cylindrical surface have an intersection line of two straight lines, the distance between the two straight lines is smaller than a predetermined threshold value. The method according to claim 18, wherein the center line of the two straight lines is the only intersecting line. 20. When it is determined in the eighth determination step that the plane surface and the cylindrical surface have an intersection line of two straight lines, and the distance between the two straight lines is smaller than a predetermined threshold value. 19. The graphic processing method according to claim 18, wherein either one of the two straight lines is the only intersecting line. 21. A first discriminating means for discriminating the figure as an ellipse by calculating a predetermined discriminant based on the coefficient of the equation of the figure, and when the figure is discriminated as an ellipse by the first discriminating means. ,
A graphic processing apparatus comprising: a second determination means for determining the graphic as a circle if the difference between the short axis and the long axis of the graphic is less than or equal to a predetermined value. 22. When the figure is determined to be a circle by the second determining means, an average value of the length of the major axis and the length of the minor axis is set as the radius of the circle. The graphic processing device according to claim 21. 23. The graphic processing apparatus according to claim 21, wherein, when the graphic is judged to be a circle by the second judging means, the length of the major axis is set to the radius of the circle. . 24. The graphic processing apparatus according to claim 21, wherein when the graphic is judged to be a circle by the second judging means, the length of the minor axis is set to the radius of the circle. 25. The equation of the figure is ax ² + 2hxy + by ² + 2gx + 2fy + c = 0 where x and y are variables.
22. The graphic processing device according to claim 21, wherein a, h, b, g, f, and c are represented by a predetermined coefficient. 26. The first determining means is a solution t1 of a quadratic equation t ² − (a + b) t + ab = 0, where ab−h ² > 0, a / c ≦ 0, and t is a variable. , t2
Regarding a2 and b2, if h = 0, a2 = a, b2 = b h> 0, a2 = max (t1, t2), b2 = min (t1, t2) h <0, a2 = min (t1, t2), b2 = max (t1, t2), and the route calculation result of -c / a2 is r1, -c
When the route calculation result of / b2 is r2, r1≈r
26. The figure processing device according to claim 25, wherein if the figure is 2, the figure is determined to be an ellipse. 27. The graphic according to claim 21, further comprising means for determining the graphic as a point if the length of either the short axis or the long axis of the graphic is not more than a predetermined value. Processing equipment. 28. When the figure is determined to be an ellipse by the first determining means, and the difference between the short axis and the long axis of the figure is not less than a predetermined value, the figure is determined to be an ellipse. 22. The graphic processing apparatus according to claim 21, further comprising a determination unit of No. 3. 29. The graphic processing apparatus according to claim 21, further comprising means for displaying a graphic determined to be a circle by the second determination means. 30. The graphic processing apparatus according to claim 28, further comprising means for displaying a graphic determined to be an ellipse by the third determining means. 31. The graphic processing apparatus according to claim 21, wherein the graphic is a graphic of an intersection of a predetermined plane and a predetermined cylindrical surface. 32. The graphic processing apparatus according to claim 21, wherein the graphic is a graphic of an intersection of a predetermined plane and a predetermined conical surface. 33. The graphic processing apparatus according to claim 21, wherein the graphic is a graphic of an intersection of a predetermined plane and a predetermined spherical surface. 34. Before the first determining means, a correlation coefficient based on an inner product of a radial vector of the plane and an axial vector of the cylindrical surface is obtained, and the correlation coefficient is within a predetermined range value. For example, a fourth determination means for determining the figure as a circle is provided, and if the figure is determined as a circle by the fourth determination means, the processing subsequent to the first determination means is not performed. The graphic processing device according to claim 28. 35. Before the first determining means, a correlation coefficient based on an inner product of a radial vector of the plane and an axial vector of the cylindrical surface is obtained, and if the correlation coefficient is equal to or less than a predetermined threshold value. And a fifth determining means for determining the graphic as a straight line, and if the graphic is determined to be a straight line by the fifth determining means, the processing subsequent to the first determining means is not performed. 29. The graphic processing device according to claim 28. 36. When the fifth determination means determines that the figure is a straight line and the distance between the plane and the cylindrical surface is within a predetermined range value, the plane and the cylindrical surface are in contact with each other. 36. The graphic processing apparatus according to claim 35, further comprising a sixth determining unit that determines that the ridgelines that are in contact with each other are the intersection lines. 37. When the figure is determined to be a straight line by the fifth determining means, and the distance between the plane and the cylindrical surface is equal to or greater than a predetermined threshold value, the plane and the cylindrical surface intersect with each other. 36. The graphic processing apparatus according to claim 35, further comprising a seventh judging means for judging not to have. 38. When the figure is determined to be a straight line by the fifth determining means, the distance between the plane and the cylindrical surface is not within a predetermined range value, and the distance between the plane and the cylindrical surface is between. 36. The graphic processing apparatus according to claim 35, further comprising an eighth determination unit that determines that the flat surface and the cylindrical surface have an intersection line of two straight lines unless the distance is equal to or larger than a predetermined threshold value. . 39. When the eighth determination means determines that the flat surface and the cylindrical surface have an intersecting line of two straight lines, and the distance between the two straight lines is smaller than a predetermined threshold value. 39. The graphic processing apparatus according to claim 38, wherein, for example, the center lines of the two straight lines are the only intersecting lines. 40. When the eighth determination means determines that the flat surface and the cylindrical surface have an intersecting line of two straight lines, and the distance between the two straight lines is smaller than a predetermined threshold value. 39. The graphic processing apparatus according to claim 38, wherein either one of the two straight lines is the only intersecting line.