JP2641877B2 - Information processing system - Google Patents

Description

Detailed Description of the Invention [Table of Contents] Overview Industrial application field Conventional technology (Fig. 8) Problems to be solved by the invention Means for solving the problems (Fig. 1) Action embodiment (a) (2) Description of one embodiment (FIGS. 2 and 3) (b) Description of area calculation method (FIGS. 4, 5, and 6)
(FIG. 7) (c) Description of Another Embodiment Effect of the Invention [Overview] An information processing system that is used in analysis processing of a CAD system or the like and obtains the area of a two-dimensional closed area including an automatically designed arc is described. A memory for storing contour data of a closed region including a circular arc, and an area of the closed region including the circular arc from the contour line data, for the purpose of simplifying the logic, reducing the program size, and shortening the processing time. And a processing unit for calculating the area of the closed area excluding the arc from the contour data, and searching for the arc along the closed area, the contour data of the arc , The area of the arc is calculated, a code is added according to the direction of the arc with respect to the search direction, and the area is added to the area of the region excluding the arc.

[Industrial applications]

The present invention relates to an information processing system which is used for analysis processing of a CAD system or the like and calculates an area of a two-dimensional closed region including an automatically designed arc.

CAD (Computer Ai) for automatic design by computer
ded Design) system is widely used.

In a mechanical part designed using such a CAD system, its area needs to be calculated in order to calculate strength, obtain weight, and the like.

In such an area calculation, a polygon or the like can be calculated relatively easily, but a closed region partially including a circular arc is not easy, and a technique capable of performing calculation easily and in a short time is required.

[Conventional technology]

 FIG. 8 is an explanatory diagram of the prior art.

As shown in FIG. 8 (A), arcs l ₂ ,
To calculate the area of the closed area provided with l ₅ and l ₈ ,
The area can be calculated by the processing flow of FIG.

First, the closed area ignoring the arcs l ₂ , l ₅ , l ₈ , in this case, the pentagonal area Sa shown by the solid line in FIG. 8 (B) is defined as the contour data l ₁ , l ₃ , l ₄ , l _6, is calculated from l _7, l _9.

Next, it is checked whether the arc portions l ₂ , l ₅ and l ₈ are convex or concave with respect to the pentagon.

Therefore, it is determined by logic whether an arbitrary point (xn, ym) on the arc segment is included in the figure (pentagon) ignoring the arc, and if it is included, it is determined as a concave and the arc area Sc
Is subtracted from Sa, and if it is not included, it is regarded as convex, and this arc area Sc is added to Sa.

[Problems to be solved by the invention]

However, in such a conventional area calculation method, it is necessary to check the positional relationship between a point on the arc line and the figure by calculating the unevenness of the figure in the arc portion by calculation, and the processing logic is complicated and the program size is large. In addition, there is a problem that the processing time becomes longer.

SUMMARY OF THE INVENTION An object of the present invention is to provide a method for calculating the area of a closed region including a circular arc, which has a simple processing logic, a small program size, and a short processing time.

[Means for solving the problem]

 FIG. 1 is a diagram illustrating the principle of the present invention.

In the figure, reference numeral 1 denotes a memory in which contour data of a closed region including an arc is stored, and 2 denotes a processing unit which calculates the area of the closed region in which the contour data in the memory 1 includes an arc. It is.

In order to achieve the above object, the present invention provides an information processing system for processing graphic information indicating a graphic including an arc,
Storage means for storing graphic information of a graphic and information indicating a displacement direction of each arc; first calculating means for calculating an area of a closed region excluding an arc based on the graphic information; The second calculating means for calculating the area of the arc, the sign determining means for determining the sign of the area of the arc based on the displacement direction information of each arc, and the corresponding second calculating means to which the sign is assigned are calculated. Third calculation means is provided for adding the area of the arc to the area of the closed region excluding the arc calculated by the first calculation means to calculate the area of the figure including the arc.

In the present invention, as shown in FIG. 1 (B), the area Sa of the region excluding the arc from the contour data is calculated, and the area calculation of the arc is performed as follows.

When counterclockwise as the search direction of the arc first diagram (C) ~ (E), counter so-clockwise (counterclockwise), the area of arc l ₂ as in the first diagram arc l ₂ (C) Add a positive sign to Sc ₁ .

Similarly since the arc l ₅ is clockwise as the first diagram (D) (clockwise), given the negative sign area Sc ₂ arc l _5, arc l
Since ₈ is a counterclockwise direction as shown in FIG. 1 (E), given the positive sign in an area Sc ₃ arc l _8.

Then, by adding this, the area A is obtained.

[Action]

The present invention does not judge the unevenness of the circular arc portion in the closed region, but uses the shape of the arc as it is without being conscious of the unevenness.

That is, by examining the direction of the circular arc with respect to the search direction of the circular arc, it can be determined whether it is concave or convex, and it is possible to identify addition or subtraction simultaneously with the area calculation.

Therefore, since it is sufficient to simply check the direction of the arc, the processing logic is simple, the program size is small, and the processing time is short.

〔Example〕

(A) Description of one embodiment FIG. 2 is a block diagram of one embodiment of the present invention, showing an engineering workstation as an example.

In the figure, the same components as those shown in FIG. 1 are indicated by the same symbols, 3a is a display unit, which is constituted by a high-precision graphic display, 3b is an input unit, a keyboard, coordinates It includes an input device and the like.

The processing unit 2 includes a main control processor, a graphic and a processor, and shares graphic processing and other processing.

The contour data is stored in the memory 1, and a line segment type (straight line "1", circular arc "2") corresponding to the number of the corner contour data (straight line or arc), straight line start point Coordinates (xn, y
n) or the center coordinates (xr, yr) of the arc, the unit direction vector of the straight line or the start point angle (start angle) and end point angle (end angle) of the arc, and the length of the straight line or the radius of the arc.

FIG. 3 is an explanatory diagram of a target closed region according to an embodiment of the present invention, and the contour line data will be specifically described with reference to FIG.

The closed area in FIG. 3 is the same as that shown in FIG. 8 (A), in which three arcs l ₂ , l ₅ and l ₈ are provided in a pentagon.

Here, it is assumed that the contour data is taken counterclockwise (counterclockwise) in ascending order.

Data of the contour line l ₁ is the type from a straight line "1", a straight line starting coordinates P ₁ (x _1, y _1), the unit direction vector of the straight line, x-direction positive "1", y-direction Is "0" and the length is L1.

Data of the contour line l ₂ is the type since an arc "2", the center of the arc is _{0 1 (x 1 ', y} 1'), the starting point of the arc P ₂ (Fig coordinates
The angle of x ₂ , y ₁ ) is -x direction from 0 ₁ to P ₂ ,
Similarly, since the angle of π and the end point P ₃ is from ₋₁ to P ₃ in the −x direction, the radius is r ₁ .

Hereinafter, a similar contour line l ₃ as denoted in FIG. 2 to l ₉
Data.

After all, a straight line is represented by start point coordinates, a unit direction vector and a length of the straight line, and an arc is represented by center coordinates and angles and radii of the start point and end point of the arc.

The angles of the starting point and the ending point are defined as follows: when a line segment is drawn from the center of the arc to the starting point and the ending point, a line parallel to the x axis is used as a reference. In radians.

(B) Description of Area Calculation Method FIG. 4 is a processing flowchart of an embodiment of the present invention, and FIGS. 5 to 7 are explanatory diagrams of an embodiment of the present invention.

In this area calculation method, the area of the line segment and the area of the X axis (or Y axis) are sequentially obtained and added to obtain the area of the entire closed region.

Then, the contour line of the closed region is processed clockwise or counterclockwise, and only the object whose value changes on the X axis and the arc are processed.

 The area calculation processing will be described with reference to FIG.

First, the processing unit (hereinafter referred to as CPU) 2 resets the content A of the area accumulation area in its own memory to zero.

Next, the CPU 2 reads out the contour data of the closed area of the memory 1 sequentially from the top and starts the processing, and determines whether the data to be read is completed.

If not finished, the contour line data in the memory 1 is read out, and the CPU 2 checks the unit direction vector field of the data and checks whether there is a change in the value of the x-axis.

If the unit direction vector of the x-axis is other than “0”, it is determined that the straight line has a change in the value of the x-axis.

On the other hand, in the case of a circular arc, the circular arc is ignored, the starting point and the ending point are obtained from the center position and the radius, and it is checked whether there is a change in the X-axis value between the starting point and the ending point.

 If there is no change in the value of the X axis, the process proceeds to the step.

If there is a change in the value on the X-axis, then it is checked whether there is a change in the value on the Y-axis.

In the case of a straight line, if the unit direction vector of the Y-axis is other than "0", it is determined that there is a change in the value of the Y-axis. In the case of an arc, it is checked whether the value of the Y-axis has changed between the start point and the end point.

If there is a change in the value of the Y-axis, the portion between the contour and the X-axis is divided into a triangular portion and a quadrangular portion as described later with reference to FIG. Calculate the area.

On the other hand, if there is no change in the value of the Y-axis, the outline is parallel to the X-axis. Therefore, the area of the square portion between the outline and the X-axis is calculated as described later with reference to FIG. .

Next, the CPU 2 determines whether or not the arc is an arc based on the line segment type of the contour data thus read out.
Calculate the area of the arc from the radius, start angle and end angle.

If it is not a circular arc, or after the end of the step, the area calculated in the step is added to the accumulated content A, updated, and the process returns to the step.

When the CPU 2 completes the processing of all data in the memory 1 in this way, it calculates the absolute value | A | of the accumulated content A, sets this as the area of the closed area, and ends the processing.

The above processing will be described with reference to FIGS. 5 to 7 by taking the figure of FIG. 3 as an example.

(I) First, when the contour (l ₁ ) data No. 1 in the memory 1 is examined, since the data is only the change in the value of the X axis in the step, as shown in FIG. calculating the area S ₁ of the rectangle.

That, y coordinates y ₁ the height of the starting point P _1, a line segment of length L ₁ as _{width, L 1 = (x 2 -x} 6) calculated by S ₁ = L ₁ · y _1. This becomes A = S _1.

(Ii) Next, the contour (l ₂ ) data No. 2 is a circular arc, but the circular arc is ignored and the line segment P _{2 as} shown in FIG.
Considered as P _3.

At this time, since the slope between the start point and the end point is the X-axis “1”, it is set as a calculation target, and the area of the square S ₂ is determined by the step.
Ask for.

The area S ₂ is obtained from the y coordinate y ₁ of the center coordinate and the radius r ₁ as S ₂ =
(X ₃ −x ₂ ) · y ₁

Further, since the step is a circular arc, the area of the circular arc is determined.

At this time, the area around the end points P ₂ and P ₃ of the arc is determined to be counterclockwise from the start angle and the end angle, so the area S ₃ is set to “minus” as shown in FIG. 5 (C).

In the following figures, the hatched portion from right to left indicates the area of “plus”, and the hatched portion from left to right indicates the area of “minus”.

S ₃ is obtained example by π · r ₁ ^2/2, when added in step, as shown in FIG. 5 _{(D), A = S 1} + S 2 + (- S 3)
Becomes

(Iii) Next, for the contour (l ₃ ) data No. 3, the area S ₄ = L ₂ · y ₁ is obtained by the same method as the contour data No. 1 shown in step (i) ( L ₂ = x ₄ −x ₃ )
As shown in FIG. 5 (E), A = S ₁ + S ₂ + (− S ₃ ) + S ₄ .

(Iv) Next, for the contour line data (l ₄ ) No. 4, since the inclination of the X axis is “−1”, the area S ₅ of the square is S ₅ = It is obtained by L ₃ · y ₃ and has a “minus” area. Because L ₃ = x ₅ −x ₄ and x ₅ is
x ₄ smaller. Therefore L ₃ is because the "minus".

When this is added to the area A in FIG. 5 (E), as shown in FIG. 5 (B), A = S ₁ + S ₂ + (− S ₃ ) + S ₄ + (−
The S _5).

(V) Next, with respect to the contour (l ₅ ) data No. 5, in the same manner as the arc contour data No. 2 shown in step (ii), as shown in FIG. Line segments that ignore arcs
Considering P ₅ P ₆ , the square area S ₆ is S ₆ = y ₃ · (x ₆ −x ₅ )
Find more.

At this time, when comparing the coordinates of the end points P ₆ and P _5, x-coordinate of P ₆ is
For less than the x-coordinate of P _5, the area is "negative".

Further, the area of the arc is determined. Since the direction around the end point P ₅ P ₆ of the arc l ₂ is clockwise in the same judgment as in step (ii),
Area ^{_{S 7 = π · r 2 2}} /2 is "positive".

When these are added to the area A in FIG.
As shown in FIG. (D), A = S ₁ + S ₂ + (− S ₃ ) + S ₄ + (− S ₅ )
+ (− S ₆ ) + S ₇ .

(Vi) Next, the contour (l ₆ ) data No. 6 is the same as the steps (i) and (iv), and the square surface application S ₈ = y ₃ · y ₄
(L ₄ = x ₇ −x ₆ ), and the area is “minus” in the same manner as in the step (iv). When the area is added to the area A in FIG. 6 (D), as shown in FIG. 7 (A) , A = S ₁ + S ₂ + (−
_{S 3) + S 4 + (} - S 5) + (- S 6) + S 7 + (- a S _8).

(Vii) Further, regarding the contour (l ₇ ) data No. 7,
Figure as (B), because of the oblique line segment, decomposes shapes to S ₁₀ of S ₉ and a square triangle. The area S ₁₀ of the square is y ₃ (x ₈ −
x ₇ ), which is the same as step (iv) and has a “minus” area.

On the other hand, the area S ₉ of the triangle, because of this triangle right triangle, the start point P ₇ of the line segment l _7, the coordinates of the end point _{P 8, S 9 = (x} 8 -
x ₇ ) · (y ₄ −y ₃ ) / 2, which is a “plus” area.

When this is added to the area A in FIG. 7 (A), as shown in FIG. 7 (C), A = S ₁ + S ₂ + (− S ₃ ) + S ₄ + (− S ₅ ) +
(−S ₆ ) + S ₇ + (− S ₈ ) + S ₉ + (− S ₁₀ ).

(Viii) Next, the outline (l ₈ ) data No. 8 is basically the same as the arc processing in step (ii).

In this case, since a diagonal line when ignoring the arc l _8, as FIG. 7 (D), similarly to the above Dzu Figure 7 (B), the area of the rectangle S ₁₁ (the area of the "negative"), the triangle Area S
₁₂ (the area of “plus”) and then the area S _{13 of the} arc l ₈
Is obtained in the same manner as in step (ii). Arc l ₈ is so counterclockwise area S ₁₃ is the area of the "minus".

When this is added to the area A in FIG. 7 (C), as shown in FIG. 7 (E), A = S ₁ + S ₂ + (− S ₃ ) + S ₄ + (− S ₅ ) +
(−S ₆ ) + S ₇ + (− S ₈ ) + S ₉ + (− S ₁₀ ) + (− S ₁₁ ) +
S ₁₂ + (− S ₁₃ ).

(Ix) Finally, for the contour (l ₉ ) data No. 9, similarly to the diagonal line l _{7 in} the step (vii), the “minus” square area S ₁₄ and the “plus” triangle area S ₁₅ are calculated. And the seventh
In addition to the area A in FIG. (E), as shown in FIG. 7 (F), A = S ₁ + S ₂ + (− S ₃ ) + S ₄ + (− S ₅ ) + (− S ₆ ) + S ₇ + ( −S ₈ ) + S ₉ + (− S ₁₀ ) + (− S ₁₁ ) + S ₁₂ + S ₁₃ + (S ₁₄ ) + S ₁₅ (1), and the total area of the closed region is obtained.

In this example, since the figure element is calculated counterclockwise, the area A is “minus”.

Accordingly, the absolute value of the value A obtained in the step of FIG. 4 is taken, and the sign is made positive.

In this embodiment, after all, from the equation (1), A = (S ₁ + S ₂ + S ₄ −S ₅ −S ₆ −S ₈ + S ₉ −S ₁₀ + S ₁₁ + S ₁₂ −S ₁₄ + S ₁₅ ) + (− S _{3 + S 7 + S 13)} ...... (2) , and the former is the area of a closed region of the first view which ignores an arc (B), the latter is the area of all arcs.

Therefore, the area ignoring the arc and the area of all the arcs are obtained.

Since the contours are processed in order, the area of each graphic element is calculated in the order described above.

Since this method only needs to process contours in order, the processing is simple and the processing time is short. In addition, the area of each graphic element is determined only by the relationship with the X axis without referring to other contour data. And the processing can be further simplified.

(C) Description of Another Embodiment In the above-described embodiment, the graphic element is calculated counterclockwise.
The calculation may be performed clockwise. In this case, the area A obtained is “plus”, and the area may be calculated based on the Y axis instead of the X axis.

Alternatively, the area of all the circular arcs may be obtained after calculating the area ignoring the circular arc as in Equation (2), and the method of obtaining the area of the closed region ignoring the circular arc may be another method.

Further, the arc is not limited to a semicircle, but can be applied to a partial circle, and various shapes of the closed region can be used, and the figure in the first quadrant has been described. The figure can be calculated with the same radius.

Although the present invention has been described with reference to the embodiments, the present invention can be variously modified in accordance with the gist of the present invention, and these are not excluded from the present invention.

〔The invention's effect〕

As described above, according to the present invention, it is possible to determine whether to add to or subtract from a closed region based on the shape (direction) of the arc, without being aware of the unevenness of the arc portion, and to obtain the effect that the area can be calculated. Therefore, the processing logic of the area calculation can be simplified, the program size can be reduced, and the processing time can be reduced.

[Brief description of the drawings]

FIG. 1 is a diagram for explaining the principle of the present invention, FIG. 2 is a block diagram of an embodiment of the present invention, FIG. 3 is an explanatory diagram of a closed region to be subjected to an embodiment of the present invention, and FIG. FIGS. 5 to 7 are explanatory diagrams of an embodiment of the present invention, and FIG. 8 is an explanatory diagram of a conventional technique. In the figure, 1... Memory, 2... Processing unit, l _{1 to} l ₉ .

Claims (1)

(57) [Claims] 1. An information processing system for processing graphic information indicating a graphic including an arc, comprising: storage means for storing graphic information of the graphic and information indicating a direction of displacement of each arc; First calculating means for calculating the area of the closed area, second calculating means for calculating the area of each arc based on the graphic information, and determining the sign of the area of the arc based on the displacement direction information of each arc. Sign determining means, and adding the area of the arc calculated by the corresponding second calculating means with the sign to the area of the closed region excluding the arc calculated by the first calculating means, including the arc An information processing system, comprising: third calculation means for calculating the area of a figure.