JPH02240776A - Straight line picking system and curve generating system - Google Patents

Abstract

PURPOSE:To attain a straight line picking process at a high speed and with high accuracy by deciding an area to a straight line connecting two points which are shifted in the two directions vertical to the straight line and opposite to each other from a picking point by a picking range. CONSTITUTION:The coordinate data Q0, Q1 on a curve are produced from the control data which prescribes the curve, and both data Q0 and Q1 are connected to each other with a straight line 10 for production of pseudo curve. At the same time, the tilt of the line 10 is obtained from both end points of the line 10. Then two points P1 and P2 are decided by moving along the direction vertical to the line 10 from a point set on the curve formed between both ends of the line 10 into the two directions opposite to each other by an extent equal to an allowable error. Then a curve interpolation is carried out to decide an allowable error for three points P0, P1 and P2 via a straight line picking process which decides an area to the line 10. As a result, the set value for decision of the allowable error is never changed by the tilt of the line 10 and an error can be decided with high accuracy with no application of a distance calculation. Then a curve interpolation is attained at a high speed and with high accuracy.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to straight line picking processing in the field of computer graphics, that is, to pick a straight line by two points generated from a specified point in a direction perpendicular to the straight line. Concerning the straight line pick method for extracting .

[Conventional technology]

In the conventional pick process of picking shapes, the specified 1
A pick frame is constructed from points, a figure to be picked is drawn, and when a figure to be drawn within the pick frame is found, this figure is extracted as a picked figure and pick processing is performed. However, with this method, the pick processing takes time, and a high-speed pick processing method has been desired.

Therefore, a pick processing method as shown in FIG. 5 and described in Japanese Unexamined Patent Publication No. 143675/1983 was proposed.

In this pick method, first, pick point 2P is selected.

Four corner points 20P to P4 are generated from (χP, 1. Pa).

Next, at all four corner points 20, straight lines 10a, z
+b+c = Assign the coordinate values of each point to the left side of O and check the sign.

As a result of the judgment, if even one of Pyu to P4 is zero.

Straight lines are pink. Also, if even one equation has a different sign, a straight line is picked. If all have the same sign, no straight line is picked.

Straight line pick processing is performed based on the above three condition determinations.

[Problem to be solved by the invention]

These four corner points are generated, and area judgment (
In the straight line pick method, which performs determination of whether an object is on a straight line, a negative area, or a positive area, pick processing can be performed faster than pick processing using a pick frame. However, when it is desired to perform pick processing with high precision, the distance from the pick point (the center point of the four corner points) varies depending on the slope of the straight line that is the pick target. (Q-work and bag shown in Figure 5) Also, the direction of the straight line with respect to the pick point is
It is unidirectional, and area determination of three or two of the four corner points results in unnecessary processing.

Therefore, one object of the present invention is to improve the accuracy of the pick process by performing the pick process in the same pick range for straight lines in all directions.

An object of the present invention is to speed up the pick process.

[Means to solve the problem]

According to the present invention, in a method in which one designated point (pick point) constitutes a pick frame and one straight line is picked, the slope of the straight line is determined from two points on the straight line, the direction perpendicular to the straight line is determined,
A straight line pick method is provided in which both end points are generated by moving the pick range amount in two opposite directions from the pick point along that direction, and the area of the straight line between the pick point and both end points is judged based on a discriminant and the pick processing is performed. .

Furthermore, only the sign of the slope of the straight line to be picked is determined, and both end points are generated by moving the pick range amount in the opposite direction from the pick point in the fixed pick range expansion direction.
A straight line pick method is provided which performs pick processing by determining the area of a straight line between a pick point and both end points using a discriminant.

Further, according to the present invention, in a curve interpolation method in which one designated point (pick point) picks one straight line, coordinate data on the curve is generated from control data that defines the curve, and By connecting the data with straight lines,
When generating a pseudo curve, find the slope of the straight line from both end points, determine the perpendicular direction to the straight line, and then calculate the opposite two points along that direction from the points on the curve between the end points of the straight line.
Generate two points that have moved by an amount of tolerance in the direction, and use the discriminant to determine the area for the point on the curve between the two end points of the straight line and the straight line between the two points, and determine the tolerance based on whether or not the straight line has been picked. A curve interpolation method is provided that generates a curve while performing.

Furthermore, in a curve interpolation method that picks a straight line with one pick point, only the sign of the slope of the straight line is determined from both end points of the straight line, a fixed pick range expansion direction is determined, and along that direction, Furthermore, we generate two points that are moved by the amount of tolerance in two opposite directions from the point on the curve between the two end points of the straight line, and use the discriminant to calculate the points on the curve between the two end points of the straight line and the two points While determining the area and determining the tolerance based on whether or not a straight line was picked, curves,
& A curve interpolation method for generating is provided.

[Effect]

According to the present invention, in the method of picking a straight line with one pick point, the conventional method performs area determination for each of the four corner points of the pick frame for the straight line to be picked, and performs pick processing based on the determination result. Whereas I was going
Since pick processing is performed using only two points, two points moved by the pick range amount in two opposing directions perpendicular to the straight line from the pick point and the pick point, or the pick process is performed using only two points, the same pick value can be obtained for straight lines in all directions. Accurate, high-speed pick processing can be achieved within a certain range.

Also, from only the sign of the slope of the straight line to be picked,
By determining a fixed pick range expansion direction and performing the above pick processing, even faster pick processing can be achieved.

According to the present invention, coordinate data on a curve is generated from control data that defines one curve in a linear interpolation method in which pick points pick one straight line, and the generated coordinate data are connected with a straight line.

Find the slope of the straight line, determine the direction perpendicular to the straight line, and along that direction, generate two points that are moved by an amount of tolerance in two opposite directions from the point on the curve between the two end points of the straight line, and calculate. 3
For points, since curve interpolation is performed to determine tolerance by straight line pick processing, which performs region determination for straight lines, the set value for tolerance determination does not change depending on the slope of the straight line.
Highly accurate error determination can be achieved without using distance calculations, and highly accurate and high speed curve interpolation is possible.

Further, since the fixed pick range expansion direction is determined only from the sign of the slope of the straight line to be picked, and the above-mentioned allowable error determination is performed, even faster curve interpolation is possible.

〔Example〕

An embodiment of the present invention will be described below with reference to FIG. 1st
In the figure, 1 is both end points of a straight line to be picked, and 2 is a pick point representing a point position for picking the straight line. 3 is a pick determination section. The pick determination section 3 is formed into an ellipse including a pick two point generation means 4, a discriminant generation means 5, and a pick determination means 6. 7 is a determination result as to whether or not the straight line to be picked has been picked.

Next, the operation will be explained. FIG. 2 is a diagram showing how a straight line to be picked by the ellipse shown in FIG. 1 is picked by pick point 2.

First, the coordinate value Q of both end points 1 of the straight line that is also the target of picking
0 (2-0, n.), Q (2-8, n.), and the coordinate value P o (Z POt > pa) of the pick point 2 are input to the pick determination section 3 .

c to the input endpoints IQ,. ,hmm. ), Q□ (Power!

71) and the pick point 2 (Y Pa pn Pa) are input to the pick 2 point generating means 4. There, the distance between the two end points Q and Q of the straight line in the two-axis direction and the n-axis direction is Δ2,8
．． Calculate Δr9 from the following formula.

Also, the slope m of the straight line 10 that is the target of picking = Δri/Δ
seek meaning.

Furthermore, a direction that passes through pick point 2 and is perpendicular to straight line 10, that is, a straight line direction that passes through pick point 2 and has an inclination of (-7rL), is determined, and a pick range gfiQ 11 is perpendicular to straight line 10 from pick point 2. Move in two contradictory directions and create two new points Px (Zp□, Ripi) 12- Pg(χt
q t > pg ) 13 is generated as a determination point.

At this time, the force axis direction, the direction of movement in the >axis direction, and the ratio of the amount of movement d, ;e 14/ d, > 15 and the straight line 10
There is a relationship as shown below between the slope m (Δri/Δ2−).

i) If the slope m(Δ>/Δ2−) is a positive value, the slope m(
If ΔR/ΔF) is a negative value, ctF/-7=ΔR/Δ2
(2) At this time, the pick point P m (j
2 directions parallel to the straight line 10 (areas of the 1st and 3rd quadrants when pick point 2 is considered as the origin), that is, there is no straight line that is the target of the pick Since there is no pick range in the direction, the pick determination process can be reduced.

Next, in the discriminant generating means 5, both end points of the straight line IQ0
(尤., ん.), Q工 (尤□, ＞,), the discriminant can be found by the following equation.

C5 2 Laz Pa 3 yo 2 a'-""7-x->
E・(3)1 1 II Mountain b c Discriminant D = Mountain z + b + C Next, the discriminant D = obtained by the 1 discriminant generating means 5
From a, +b>+c, the pick determining means 6 draws a straight line 1.
Determine whether 0 is picked.

First, pick point 2P0 (KaPa + npo)
Substitute into the discriminant.

a, r, p,, +b>p, +c Substituted value (mountain; c pg + bp,, +c) = O
If so.

The pick point P,2 is on the straight line 10 and immediately moves to the straight line lO
is picked.

a,, tp, +b Pa + c) If O, then Po
is a positive region with respect to the straight line, o-zp0+bnp0+c
<O, it exists in the negative region. Therefore, remember the area where Po exists.

Next, the P work 12 generated by the pick two point generating means 4.
Similar determination is made for P and 13 as well.

As shown in Fig. 2, pick point 2 P O (2-Pa
Pa) is the discriminant D=a, zp, +bp,, +
a Pi (zpxy
> p ) 12 is the discriminant D = mountain zp1 + b Pi + c
< Exists in the negative region from O. Pi(Epz+ >p
a) 13 exists in the positive region. In this case, pick point P
For 02, 2 points P work 12. P.

13 is determined to exist in a different area, and the straight line 10 has been picked. Further, if both are in the same area, the pick determination means 6 outputs a 1 determination result 7 such that the direct 1/lAl0 is not picked and is greater than or equal to 0.

Using the method described above, first, pick judgment is performed at pick points P, 2, and 2 points P□12. Since pick determination is performed using only three points, P and 13, it is possible to reduce the scale of calculations based only on multiplication and addition, and it is possible to perform high-speed straight line pick processing. Second, since the pick range R11 equal to 1 can be arbitrarily set in two directions perpendicular to any straight line depending on the slope m to be picked, highly accurate straight line pick processing is possible.

In addition, only the sign of the slope of the straight line to be picked is determined, and the pick range expansion direction (self-z
= d, n), even faster pick processing can be achieved.

Another embodiment in which the present invention is applied to curve generation will be described with reference to FIG. Figure 3 shows control coordinate data C0 (16 peaks), CI (16b), C2 (1
6c), From C3 (16d,), by calculating the coordinate data Q (t08) on the curve 17 expressed by the cubic Bezuer curve equation, plotting them, and connecting them with a straight line, we can obtain the Bezuer curve 19. This is a diagram in which the pseudo-Bezuer curve interpolation is generated in a pseudo manner.
The pseudo curve 1 is determined while determining the error (flatness) between the pseudo curve 19 and the ideal curve 17.
There is a method for generating 9. In this method, a Bezuer curve interpolation method using the straight line pick method of the present invention will be described.

First, coordinate data Q on the curve is calculated using the Bezuer curve equation.
Calculate (1/2). With the second Q (1/2) as the pick point P02, the allowable error range between the pseudo curve and the ideal curve for the straight line Q(0)Q(1) is the pick range + 2
Pick processing is performed as 11. At this time, the straight line Q(0)
Q(1) is not picked, that is, Q (1/2) is outside the allowable error range from the straight line Q(0)Q(1).

In this case, to get closer to the ideal curve, further coordinate data Q
Since it is necessary to generate , coordinate data Q (1/4) and Q (3/4) on one curve are calculated next. Similarly, Q (1/4) performs straight line pick processing. At this time, the straight line Q(0)Q(1/)2) and the straight line Q(1/2)Q
None of (1) is picked t・), and Q (1/4) and Q (3/4) are straight lines Q (
0) Q(1/2) and Q(1/2)Q(1) are outside the allowable error range.

Similarly, Q (1/8), Q (3/8), Q (5
/8), Q (7/8), and perform pick processing.

For the first time, the straight line Q(0)Q(1/4).

Q (3/g)s Q (5/8) and Q (7/8) are clearly within the allowable error range.

So, in this case, Q (1/8), Q (3/8).

Q (5/8) and Q (7/8) are not generated as data points on the curve, but rather, quantitatively, at the starting point Q (0).

c;) (1/4) , Q (1/2) , Q (
3/4), a pseudo Bezuer curve connecting the end point Q(1) with a straight line can be generated, and the error between the pseudo curve and the ideal curve is within the allowable error range.

In conventional curve interpolation, this error determination was done by actual distance calculation, which took a long time to process.
With this method, the pick range can be set in the vertical direction for any straight line, so highly accurate error determination can be made without using route calculations, and processing time can be further shortened.

FIG. 4 is a diagram showing another embodiment of the present invention.

In FIG. 2, the pick range 1111Q is taken as the minimum unit. Therefore, the pick determination unit 3 performs pick processing on the straight line 10 to be picked. At this time, the straight line m1
If 0 is not picked, pick range 11Ω by 2*
2, pick processing is performed in the same manner.

This operation is repeated n times until the straight line 10 is picked.

From the above, since the pick range expansion direction is perpendicular to the picked straight line, the pick point P 62 (
2-Pay) PG) and two points Qo(
The distance between the pick point and the straight line can be measured without using route calculations from only the information of :catn o) and Q-technique (2-0, ri,)1.

〔Effect of the invention〕

As explained above, according to the present invention, in a straight line to be picked, there are two opposing directions perpendicular to the straight line from the pick point.
By performing pick processing by area determination for two straight lines that have been moved by the pick range amount in the direction, highly accurate and high-speed straight line pick processing can be realized.

Furthermore, according to the present invention, in a curve interpolation method in which a straight line is picked with one pick point, the tolerance judgment between a curve made of pseudo-generated straight lines and an ideal curve can be performed in any way possible. Since the pick process is performed by picking the same amount of pick range even for straight lines with angles, highly accurate and high-speed curve interpolation process can be realized.

[Brief explanation of drawings]

FIG. 1 is a straight line pick processing block diagram showing an embodiment of the present invention. FIG. 2 is a diagram showing how a straight line to be picked is picked by pick points. FIG. 3 is a diagram showing Bezuer curve interpolation using pick processing for error determination, showing another embodiment. FIG. 4 is a diagram showing distance measurement between a point and a straight line using pick processing, showing another embodiment. FIG. 5 is an explanatory diagram of a pick process in which a straight line is picked from four corner points, showing a method of the prior art. 1...Both end points of a straight line to be picked, 2...Pick point, 3...Pick determination unit. 4... Pick 2 point generation means, 5... Discriminant generation means, 6... Pick determination means,
7... Judgment result. Country 2 Entaku 7 4th national talent

Claims (1)

[Claims] 1. In a straight line pick method in which straight line picking is determined by determining whether a straight line is within a certain area from a specified point, A judgment point is generated that has moved a predetermined distance from the specified point, and it is determined whether the judgment point and the specified point are in the positive or negative area of the straight line, and one point is in the positive area and the other point is in the positive area. A straight line pick method that determines that it has been picked if it exists in the negative area. 2. In claim 1, two points Q_0(X_0,
Y_0), Q_1(X_1, Y_1), the discriminant D=(
Y_1-Y_0)X-(X_1-X_0)Y-(X_0
Y_1-X_1Y_0), and calculate the coordinate value P of the specified point.
_0 (X_0, Y_0) and the coordinate value P_1 of the determination point
A straight line pick method characterized in that (X_1, Y_1) is substituted into the discriminant and area determination is performed based on the sign of the discriminant. 3. The straight line pick method according to claim 1, wherein the determination points are generated at two points symmetrical to the specified point. 4. A straight line pick method according to claim 1, characterized in that the slope of the straight line is determined from at least two points on the straight line, a direction perpendicular to the straight line is determined from the determined slope, and the determination point is generated. . 5. In a curve generation method that generates a pseudo-curve by connecting multiple points on an ideal curve with a straight line, from the specified point generated on the ideal curve AB connecting two adjacent points A and B on the ideal curve A judgment point is generated that is moved by a tolerance distance L from the specified point in a direction perpendicular to the straight line A-B connecting the two points A and B, and the judgment point and the specified point are either positive or negative of the straight line A-B. A curve generation method characterized in that it is determined whether a point exists in a region, and if one point exists in a positive region and the other point exists in a negative region, it is determined that the point is within an allowable error range. 6. Connect two points on the ideal curve with a straight line, determine the distance between the ideal curve and the generated straight line, and successively generate new points between the two points until the distance is within the tolerance range. In a curve generation method that brings a pseudo-curve closer to an ideal curve by Generate a determination point that has moved by a distance, determine whether the determination point and the designated point are in the positive or negative region of the straight line, and one point exists in the positive region and the other point exists in the negative region. A curve generation method characterized by determining that the two points are within an allowable error range and stopping the generation of new points between those two points.