JP3087177B2 - Floating point calculation method and calculation processing device thereof - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Summary] The present invention relates to a floating-point calculation method for calculating an intersection between figures and a calculation processing device therefor, wherein the exponent is adjusted so that the exponent difference between coefficients of equations for calculating the intersection is minimized. In order to find the intersection stably irrespective of the combination of geometric shapes, an equation for calculating the intersection between given figures is set, and the maximum value and the minimum value of the exponent of each coefficient are approximately calculated. The conversion of the exponent of each coefficient is performed so as to be an intermediate exponent, and the intersection is calculated using an equation having the converted coefficient to calculate the intersection between the figures.

[Industrial applications]

The present invention relates to a floating-point calculation method for calculating an intersection between figures and a calculation processing device therefor.

[Problems to be solved by conventional technology and invention]

In the field of CAD, it is necessary to solve an algebraic equation when performing an intersection / intersection calculation between a line and a line, a line and a surface, a surface and a surface, and the like.

In this case, the coefficients of the equation for the intersection calculation usually vary greatly. In the process of solving the intersection calculation equation, it is necessary to divide each coefficient by the highest-order coefficient to normalize the coefficient, or to calculate the coefficient to the second to third power. For this reason, if the coefficient is too large or if there is too much variation, overflow occurs during the calculation,
There was a problem that the equation could not be solved and the intersection could not be found. These phenomena are particularly likely to occur when the figures are in contact with each other or when the figures are quite large, and when the user frequently uses them. It is desired.

An object of the present invention is to adjust an exponent so that an exponent difference between coefficients of an equation for calculating an intersection is minimized, and to stably find an intersection without depending on a combination of geometric shapes.

[Means to solve the problem]

 Means for solving the problem will be described with reference to FIG.

In FIG. 1, an intersection calculation module 1-1 sets up an equation for calculating an intersection between figures, and calculates each of the coefficients so that an index is substantially intermediate between the maximum value and the minimum value of the index of each coefficient. And requests the arithmetic unit 2 to find the intersection.

The calculation unit 2 calculates the intersection calculation equation notified from the intersection calculation module 1-1.

[Action]

According to the present invention, as shown in FIG. 1, the intersection calculation module 1-1 sets an equation for calculating an intersection between figures, and calculates an equation that is substantially intermediate between the maximum value and the minimum value of the index of each coefficient. The calculation unit 2 performs the calculation of the equation of the intersection calculation notified from the intersection calculation module 1-1, and notifies the result to the intersection calculation module 1-1 as a result. Output.

Therefore, after adjusting the exponent so that the index difference between the coefficients of the equation for calculating the intersection is minimized, by calculating the intersection, it is possible to obtain the intersection stably without depending on the combination of the geometric shapes. It becomes possible.

〔Example〕

Next, the configuration and operation of one embodiment of the present invention will be sequentially described in detail with reference to FIGS.

In FIG. 1, a data processing unit 1 includes an intersection calculation module 1-1, a geometric data access unit 1-2, and the like, and calculates an intersection.

The intersection calculation module 1-1 sets an equation for calculating an intersection between figures and converts the equation into an index approximately halfway between the maximum value and the minimum value of the index of each coefficient (for example, an integer multiple of hexadecimal). The conversion of the exponent of each coefficient is performed so that the calculation unit 2 requests the calculation unit 2 to obtain the intersection.

The calculation unit 2 calculates the intersection calculation equation notified from the intersection calculation module 1-1.

The display unit 3 is a display for displaying a geometric figure or the like.

The geometric data 4 is a file storing the geometric data.

Next, according to the order shown in the flowchart of FIG.
The operation of the diagram configuration will be described in detail.

In FIG. 2, EXTENT is taken. It takes double precision.

Makes an equation. This means that the geometric data of the figure requested by the user to calculate the intersection is extracted from the file, and an equation for performing the intersection calculation is established.

 Adjust the coefficient. This will be described in detail below.

Step 1: Calculate the hexadecimal ORDER (index) of each coefficient.

 Step 2: Find the maximum ORDER difference.

 Step 3: Find the optimal conversion ORDER.

The original intersection equation And t = s16 ^p , Where each coefficient at the time of conversion is a _i 16 ^pi (i = 0... K).
It is. The value p that minimizes the maximum difference between these ORDERs is determined.

Step 4: Adjust coefficients for optimal p and find new coefficients. The maximum q of the ORDER of the coefficients for the optimal p,
If the minimum is r, the new coefficients are:

bi = ai16 ^pi 16 ^{− (q + r) / 2} (3) where i = 0, 1,... k Further, the section for finding the solution is as follows.

t∈ [T ₁ , T ₂ ] → s∈ [T ₁ 16 ^-p , T ₂ 16 ^-p ] (4) calculates the intersection. In this case, the equations of the intersections where the respective coefficients are adjusted so as to obtain the optimum p in steps 1 to 4 are passed to the arithmetic unit 2 and the intersections are calculated. Then, the intersection is returned to the user.

As described above, after optimally adjusting the coefficients of the equation for calculating the intersection between two figures requested by the user, calculating and calculating the intersection, the influence of the combination of the geometric shapes of the figures is obtained. Therefore, the intersection can be reliably obtained.

FIG. 3 shows an example of calculating an intersection according to the present invention. This is an example of calculating the intersection between the spline and the circle, and the point E1
Suppose there is a request for the nearest intersection. The details will be sequentially described below.

An equation for finding the intersection between the second section of the spline and the circle is given by the following equation (5).

^{C (1) t 6 + C} (2) t 5 + C (3) t 4 + C (4) t 3 + C (5) t 2 + C (6) t + C (7) = 0 ··· (5) wherein each The coefficient is given by the following equation.

C (1) = 0.33484280685074295D-21 C (2) =-0.25663605759412337D-15 C (3) = 0.44144374389516779D-10 C (4) =-0.25216500766439103D-5 C (5) = 0.21871559152262257D + 1 C (6) = −0.21345202744064580D + 6 C (7) = − 0.17500000000000000D + 11 FIG. 3 (b) is a figure created with values of 10 ⁶ to 10 ⁷ , which is not a special case when designing by CAD.
As shown in the above equation (5), there is considerable variation in coefficients, overflow occurs during the calculation, and no intersection is obtained (only intersections with small circles in FIG. 3 (b) are obtained).

Therefore, in the present embodiment, the adjustment of the coefficients described above with reference to FIG. 2 is performed, and the coefficients are converted as shown below.
It is possible to obtain an intersection point provided with a circle having a small value.

C (1) = 0.617675956289821457D-2 C (2) = − 0.722366283344204468D−1 C (3) = 0.189598644305354530D + 0 C (4) = − 0.165258859422935306D + 0 C (5) = 0.218715591522622566D + 1 C (6) = − 0.325701946167977585D + 1 C (7) = − 0.407453626394271850D + 1 The above results were obtained as follows in accordance with FIG. 2 and the description thereof.

First, the ORDER (exponent) of each coefficient as hexadecimal is obtained in accordance with the description of step 1 in FIG. 2 and equation (2). The above formulas C (1) to C (7) are expressed in the form of formula (2), and the coefficient ai16 ^pi is changed within a certain range (for example, -100 to +100) to calculate ORDER. For example, in the case of p = 4, C (1) determined for the new coefficient C (1) = coefficient before conversion ^{C (1) × 16 4 ×} 6 = 0.098828153006371433 × 16 7 , and the index is 7.

Second, an optimal conversion ORDER is determined according to step 3 in FIG. In step 2, the value of p that minimizes the difference between the maximum and minimum values of ORDER is determined based on the result of trial calculation by changing the value of p within a certain range (for example, -100 to +100). For example, when p = 4 as described above, C
When trial calculation is performed for (1) to C (7), the maximum value of ORDER (index) is 9 (q = 9) and the minimum value is (r = 7), and the maximum difference of ORDER is minimum. Is obtained as 4.

Third, according to step 4 of FIG.
Find a new coefficient for. The new coefficient is given by equation (3)
The conversion is performed so as to be an intermediate value between the maximum value q and the minimum value r of the exponent as defined by. For example, if C (1), the new coefficient C (1) is the coefficient C (1) × 164 _{× 6} × 16− ^{(q + r) / 2} = C (1) × 164 _{4 × 6} × 16 before conversion. ^-8 required. This procedure is similarly repeated from C (2) to C (7).
By repeating this procedure, new coefficients having a small difference between the maximum value and the minimum value of the exponent of each coefficient, such as the new coefficients (C) 1 to C (7), are obtained.

FIG. 3 (a) shows the graphic data of FIG. 3 (b). The circle data and the spline data are shown.

 FIG. 3 (b) shows an example of calculating the intersection.

Is a schematic representation of the graphic data of FIG. 3 (a).

Indicates a point of intersection obtained in a state before the coefficient adjustment (conventional) by a small circle. In this case, the intersection closest to the point E1 shown in FIG. 3 (b) has not been found.

Indicates a point of intersection obtained in a state after adjusting the coefficient by a small circle. In this case, an intersection closest to the point E1 shown in FIG.

〔The invention's effect〕

As described above, according to the present invention, since the index is adjusted so that the index difference between the coefficients of the equation for calculating the intersection is minimized, and then the intersection is calculated, the geometrical configuration is adopted. Intersections can be obtained stably without depending on the combination of shapes.

[Brief description of the drawings]

FIG. 1 is a block diagram of one embodiment of the present invention, FIG. 2 is a flowchart for explaining the operation of the present invention, and FIG. 3 shows an example of calculating an intersection according to the present invention. In the figure, 1 is a data processing unit, 1-1 is an intersection calculation module, 1-2 is a geometric data access unit, 2 is an operation unit, 3 is a display unit, and 4 is geometric data.

Continuation of the front page (58) Field surveyed (Int.Cl. ⁷ , DB name) G06F 17/10 G06F 17/11 G06F 17/50

Claims (2)

(57) [Claims] 1. A computer which executes a calculation formula using a floating-point expression and overflows when the data length of the exponent exceeds the data length set by the computer during execution of the calculation. Extracting the exponent; converting the exponent to reduce the difference between the maximum value and the minimum value of the extracted exponent; converting each coefficient according to the converted exponent; Calculating according to a calculation formula composed of coefficients. 2. A computer which executes a calculation formula using a floating-point expression and overflows if the data length of the exponent exceeds the data length set by the computer during execution of the calculation. Extracting means for extracting the exponent; converting means for converting the exponent so as to reduce the difference between the maximum value and the minimum value of the exponent of each coefficient extracted by the extracting means; Calculating means for calculating in accordance with a calculation formula comprising an index and a coefficient converted by the means.