JPH03250373A - Method and device for detecting 3-point designated circular arc - Google Patents

Abstract

PURPOSE:To quickly delete a 3-point designating circular arc which is not clearly detected out of the detection subjects and to attain the fast detection processing by deciding whether a rectangle including a circular arc crosses a detecting range or not. CONSTITUTION:A rectangle including a circular arc is calculated from the coordinate data on the start points X1 and Y1, the intermediate points X2 and Y2, and the end points X3 and Y3 which display a 3-point designating circular arc on a display device without calculating the center point of the circular arc. Then it is decided whether the rectangle crosses a detecting range or not. If not, no 3-point designating circular arc is detected, if so, the center point and the radius of the 3-point designating circular arc are calculated. Then the cross between the circular arc and the detecting range is decided. Thus it is possible to quickly delete the 3-point designating circular arc that is not clearly picked out of the picking subjects and to increase the detection processing.

Description

[Detailed description of the invention] [Table of contents] Overview Industrial application field (Figure 3.4 (a)) Prior art (Figures 4 (b), 19, 20, 21) Problems to be solved by the invention (Figs. 5, 19) Means for solving the problem (Figs. 1, 2) Effects (Figs. 1.2, 6, 7.8) Examples (Figs. 3.6.9 to 19) Invention Effect [Summary] 3 defined by the coordinate data of the starting point, intermediate point, and ending point.
A three-point designated arc that stores a point-designated arc as graphic data, displays an arc that passes through three points on a display device, and detects the three-point designated arc when it intersects a detection (pick) range defined as a rectangle. Regarding the detection method and device, the purpose of the present invention is to provide a method and device for detecting a 3-point specified arc that can perform detection processing at high speed, and to display the 3-point specified arc on a display device. Calculates a rectangle that encompasses the arc from the coordinate data of the point without calculating the center point of the arc, determines whether the rectangle intersects with the detection range, and if they do not intersect, detects the three-point specified arc. If the two points do not intersect, the center point and radius of the three-point designated arc are calculated, and then it is determined whether the arc intersects with the detection range.

[Industrial application field]

The present invention relates to a method and device for detecting a three-point designated arc, and in particular, stores a three-point designated arc defined by coordinate data of three points, a starting point, an intermediate point, and an end point, as graphic data, and detects a circular arc passing through the three points. The present invention relates to an arc detection method and apparatus for detecting a three-point specified arc displayed on a display device and intersecting a detection (pick) range defined as a rectangle.

A graphic processing system that displays graphics on a display device using a computer and processes the displayed graphics using an input device.
It relates to a figure detection (pick) method for interactively detecting a figure on the screen during the operation process of creating a figure using esign), etc., and editing the figure by moving, enlarging, reducing, etc. The present invention relates to a method and apparatus for detecting a three-point specified arc, which is composed of coordinate data of three points, a starting point, an intermediate point, and an ending point, as shown in FIG. 4(a) in a figure such as a circle, polygon, or character.

A graphic processing system has a configuration as shown in FIG. 3, for example, and a central processing unit (CPU) stores graphic data input from an input device, etc. in the main memory according to a program stored in the main memory. , and displays the graphic data on a display device (such as a CRT). Operators can perform their own edits (e.g.
Detect the shape you want to move (move, enlarge/reduce, change display color, delete, etc.). To perform this detection, use an input device such as a mouse, tablet, keyboard, joystick, light pen, etc. to move the cursor over the shape you want to detect, and enter a predetermined detection request operation in this shape processing system. on the device, such as pressing a button on a mouse or a stylus on a tablet.

Then, the central processing unit (CPU) determines the detection request operation of the input device and starts detecting the figure. Prior to detection, the central processing unit (CPU) determines a detection (pick) range that is a range for detecting a figure. The pick range is determined by the following method. In advance,
According to the size of the specified pick range, determine the coordinates where the pick range exists based on the size of the pick range centered on the position specified by the input device (the cursor position when performing the detection request operation on the input device). do.

Next, it is sequentially determined whether all the graphic data stored in the main storage device exists within this pick range. This determination method uses different methods depending on whether the graphic data is a line segment, a circle, a polygon, etc., depending on various types of graphic data. It is determined whether each type of graphic data exists within the pick range, and graphic data within the pick range is detected.

In the graphic processing system described above, even though the processing time for determining one piece of various graphic data is not that long, the detection process is performed for each graphic data one by one, so it is difficult to process dozens or more pieces of data such as CAD. A graphic processing system that handles graphic data has a drawback in that it takes a long time to detect a graphic.

Therefore, it is required to further speed up the detection time of various graphic data.

In particular, the detection processing time for a three-point specified arc is considerably slower than the detection time for a circle (a circle specified by the center and radius) because it is necessary to calculate the center point and radius from three points.
However, since it is used more frequently than yen, there is a need for faster speeds.

[Conventional technology]

Conventionally, there has been a method of detecting (picking) a three-point specified arc as shown in FIG.

The conventional method for detecting (picking) a three-point specified arc is step SAI, which detects three specified points (starting point, intermediate point, and ending point).
(XI, Yl), (X2.Y2).

From (X3.Y3), calculate the center and radius of the circle according to the following formula.

To find the center point (Cx, Cy) and radius r from the three specified points, it is necessary to solve the following simultaneous equations obtained by substituting the three specified points into the circle equation. .

(Xi-Cx)2+(Yl-Cy)2-r2(X2-C
x)2+(Y2-Cy)2=r2-formula (1)%formula%) Another method is to calculate the intersection of perpendicular lines that pass through the midpoint of the line segment connecting the starting point and the midpoint, and the midpoint and the end point, respectively. Calculate (Figure 20). This intersection is the center point of the three-point designated arc. Next, calculate the distance between the center point and one of the three points to find the radius.

The flow of this process is shown in FIG.

After finding the center point and radius as described above, proceed to step SA2 in FIG. 21, find the minimum square area that encompasses the circular arc from its center point (Cx, Cy) and radius r, and proceed to step SA3. This square (Cx-r, Cy-r), (
By determining whether or not the two points Cx+r and Cy+r) are the lower left and lower right vertices intersect with the pick range, circles that are clearly not to be picked are excluded from the pick target. Next, for arcs that could not be excluded, proceed to step SA4, approximate the arc to a polygon, and determine whether each side of the polygon intersects with the pick range, -
If there is an edge that intersects with the pick range in the book, the arc is picked in step SA5, and if the tree also does not intersect, it is not picked in step SA6. He was making pick decisions.

Or Horn″C1rcle Generator
s for DisplayDevices″COMP
UTERGRAPHIC3AND IMAGE PRO
CESSING 5. Generate points on the arc using the arc generation algorithm published in pp280-288, determine whether the generated points intersect with the pick range, and if there is a point that intersects with the pick range even at - points,
The arc was picked, and if the - points did not intersect, the arc was not picked.

(Problem to be Solved by the Invention) In the conventional example described above, when picking a three-point specified arc, the center and radius of the circle are determined from the three specified points before picking. there were.

However, in graphic processing systems, the size of the pick area is usually very small compared to the size of the coordinate system in which the graphic is defined (usually 1/10,000 or less in terms of area ratio).
The number of defined figures usually exceeds several dozen. Also, because the operator selects one of these shapes for editing, most of the shapes are not picked.

Therefore, calculations to find the center point and radius of a three-point specified arc are wasteful.

As in the example shown in FIG. 5, most of the three-point designated arcs in the figure clearly belong to the category that cannot be picked. Therefore,
In the conventional method, the center point and radius of these 3-point designated arcs that are clearly not picked are wasted.

Also, a 3-point specified arc is picked as a center point/radius specified arc after the center point and radius are determined, so no matter how you do it, the picking time for a 3-point specified arc will be the center point/radius specified. Compared to the arc pick time, it is slower by calculating the center point and radius. In particular, as shown in Figure 5, three-point designated arcs and center points, which are not clearly picked,
When comparing radius specified arcs, the center point/radius specified arc uses the square that encompasses this arc to first determine whether or not it will be picked, so in this case, at most 4
The process ends when the number of times is determined. On the other hand, for a 3-point designated arc, the center point and radius are calculated by the process shown in Figure 19, and then a square that encompasses the 3-point designated arc is found using this center point and radius. Determine whether or not it will be picked. Therefore, a three-point designated arc requires ten times more processing time than a center point/radius designated arc.

The present invention has been made by focusing on such conventional problems, and provides a method and apparatus for determining the center point and radius of a three-point designated arc that is not clearly picked without calculation, and increasing the picking speed. be.

(Means for Solving the Problems) In order to solve the above technical problems, the first invention provides three points defined by coordinate data of three points: a starting point, an intermediate point, and an ending point, as shown in FIG. Stores the specified arc as graphic data,
Displaying an arc passing through three points on a display device, and detecting the three-point specified arc when it intersects with a detection (pick) range defined as a rectangle (S5) In the arc detection method, displaying the three-point specified arc Calculate a rectangle that encompasses an arc from the coordinate data of three points, a start point, an intermediate point, and an end point generated on the device, without calculating the center point of the arc.si) Whether or not the rectangle intersects the detection range. (S2), and if they do not intersect, the three-point specified arc is not detected (S6); if they intersect, the center point and radius of the three-point specified arc are calculated (S3).
), and then it is determined whether the circular arc intersects with the detection range (S4).

On the other hand, the second invention, as shown in FIG. An instruction unit 8 that issues instructions such as detecting a designated arc, a display unit 2 that displays a figure based on instructions, and a center point and radius that calculates the center point and radius of an arc that passes through three points to be displayed based on the figure data. In a three-point designated arc detection device that includes a radius calculation unit 5 and an intersection determination unit 6 that determines whether or not a displayed circular arc intersects with a detection (pick) range defined as a rectangle, the display unit 2 The starting point of the three-point designated arc displayed above,
An inclusive rectangle calculation unit 4 calculates a rectangle that includes the arc from coordinate data of three points, an intermediate point and an end point, without calculating the center point of the arc, and whether or not the calculated rectangle intersects with the detection range. a center point/radius calculation unit 5 which calculates the center point and radius of the circular arc based on the graphic data when the determining unit 3 determines that the rectangles intersect. , if the inter-rectangle intersection determination unit 3 determines that the rectangles do not intersect, the arc is not detected, and if it is determined that the rectangles intersect, the intersection determination unit 6 further determines that the arc intersects. However, if it is determined that the arcs do not intersect, the arc detection section 7 does not perform the detection.

(effect) The operation of the first and second inventions will be explained.

When the instruction unit 8 instructs to detect a three-point designated arc, in step S1, the inclusive rectangle calculation unit 4 stores information regarding the three-point designated arc displayed on the display unit 2 in the graphic data storage unit 1. A rectangle that includes the arc is calculated based on the graphic data that has been created without calculating the center point of the arc.

Here, we will show an example where it is possible to calculate the center point of a circular arc without calculating it.

As shown in Fig. 6 (a), (b), (c), (d),
Starting point (Xi, Yl), intermediate point (X2.Y) of a 3-point specified arc
2) If the positional relationship of the end points (X3.Y3) satisfies the following conditions, you can easily find the rectangle that includes the 3-point specified arc without finding the center point and radius of the 3-point specified arc. can. By using this rectangle, three-point specified arcs that are clearly not picked can be quickly excluded from the pick targets, and the detection process becomes faster.

(Condition 1) When three points are translated in parallel as shown below so that the intermediate point (X2.Y2) becomes the origin, add the starting point (xi, yl), xl=X1-X2. yl-Yl-Y2 midpoint (0,0
) End point (x3.y3) However, x3=X3-X2. y3-Y3-Y2, and the starting point (x 1 , y 1 ) and the ending point (x3
．． When the position of y3) is located at a diagonal position, that is, when one of the following four conditions is satisfied.

■When the starting point is located in the 1st quadrant and the end point is located in the 3rd quadrant (Figure 6(a)) ■When the starting point is located in the 2nd quadrant and the ending point is located in the 4th quadrant (Figure 6(b)) ■Starting point When is located in the third quadrant and the end point is located in the first quadrant (Fig. 6 (C)) ■ When the starting point is located in the fourth quadrant and the end point is located in the second quadrant (Fig. 6 (d)) Here, Figure 7 shows each quadrant. Incidentally, a three-point designation arc that "does not satisfy the condition" is shown in FIG.

Next, a rectangle that includes the three-point designated arc can be found as follows.

(How to find a rectangle) For simplicity, assume that the three points are moved in parallel so that the midpoint is at the origin, and the midpoint is located at the origin. The actual rectangle can be found by translating the rectangle found below.

Under each condition, the arc portion (1) from the start point to the midpoint and the arc portion (2) from the midpoint to the end point are each encompassed by the following rectangles.

The maximum X coordinate and the maximum Y coordinate of the rectangle R1 that includes the arc portion (1) are Rlxmax, Rlymax, the minimum X coordinate,
The minimum Y coordinates are Rlxmin, Rlymin, and this rectangle R1 is (Rlxmin, Rlymin) - (Rlxma
x, Rlymax), and similarly, the rectangle R3 that includes the arc portion (2) is expressed as (R3xmin, R3ymin) - (R3xmax
, R3ymax), the rectangle R1 when the condition (1) is satisfied can be found using the coordinate components xi, yl of the starting point (x 1 , y 1 ).

If the thicker one of xl and yl is Ml, then R1xmin
= OR1ymin= ORlxmax = M I
Rlymax=M1. Also, R3 is as follows: If the larger of X3 and -y3 is M3, then R3x+ntn = -M 3 R3ymin =
-M3R3xmax=OR3ymax=0.

■When the conditions are met, the rectangle R1 is at the starting point (xi, yl)
It can be determined using the coordinate components xi and yl of .

If the larger of Xl and yl is Ml, then R1xmi
n=-MI R1ymin=OR1xmax=O
Rlymin=M1. Also, rectangle R3 is as follows: If the larger of X3 and -y3 is M3, then R3xmin= OR3ymin= -M 3R3xm
ax=M3R3ymax=0.

■When the conditions are met, the rectangle R1 is at the starting point (xi, yl)
It can be determined using the coordinate components xi and yl of .

If the larger of -xi and -y1 is Ml, then R1xmin=-MI R1ymin=-MIR1
xmax=0. Rlymax-0. In addition, rectangle R3 is defined as R3xmi, where M3 is the larger of x3 and y3.
n= OR3ymin= OR3xmax = M 3
R3ymax=M3.

■When the conditions are met, the rectangle R1 is at the starting point (xi, yl)
It can be determined using the coordinate components xi and yl of .

If the larger of xi and -y1 is Ml, then R1xm
in= OR1ymin= -M IR1xmax=
M I R1ymax=0. In addition, rectangle R3 is defined as R3xmi, where M3 is the larger of X3 and y3.
n= −M 3 R3ymin= OR3xmax
=OR3ymax=M3.

Here, we will try to prove how the above rectangle can encompass the circular arc when the above conditions are met, using the above circular arc part (1) of ■.Other cases can be easily applied similarly. Can be done.

The equation of a circle passing through the center (Cx, Cy) and having radius r is: It can be expressed as (x-Cx)2+(y-Cy)2-r2.

Since the midpoint of the arc passes through the origin, that is, x=y=
Since o satisfies the above formula, there is a relationship of "Cx2+Cy2mr".

Therefore, the equation of the circle is (x-Cx) 2+(y-Cy) 2=Cx2+Cy2
Since the condition of formula (2) (■) is satisfied, the equation of this circle is that at points other than the origin, X≦0. It passes through a point where y≦0.

To satisfy this, Cx≧o, cy≦0 or C
x≦o, cy≧0 (however, Cx,
Cy is not 0 at the same time).

This is because, for example, if Cx≧o, cy≧0, then
If ≧o, y≧0, (x-Cx) 2+ (y-Cy) 2<=Cx2+C
y2, which satisfies the equality sign only when x=y=0, and does not pass through any point other than the origin where X≧o and y≦0.

Solving equation (2) for y, y=cyf Prove the case ≦0.

When Cx≧0・cy≦0, the equation expressing the circular arc part (1) is: y=Cyx+Cy−x−Cx) Also, X≧o, y≧0 Equation (3) Maximum value of y is x=
When cX, y=cy+rτi7T℃7τ ≦Cy+1TC1: 1 ton T (because Cx>Cy) =Cy+Cx-Cy =Cx Therefore, if X≧Cx, for a point (x + y) on the arc, If y≦X holds true and 0≦x<Cx, y in equation (3) is monotonically increasing, so the larger value of X and y can be used.

According to the above, the arc portion (1) when the condition (■) is satisfied is the coordinate component X of the point (x, y) on the arc.

If the larger one of y is Ml, then 0≦X, y≦M1. (End of proof) (Condition 2) Also, as shown in Figure 8, if the starting point and end point of a 3-point designated arc match, the line segment connecting the starting point and the midpoint becomes the diameter of the 3-point designated arc. Therefore, the center point can be calculated using the following simple calculation.

Cx=xl÷2 cy=y2÷2 Find a rectangle that includes the three-point designated arc from this center point and radius r.

The radius can be determined by the following calculation, but R = 10 balls 7 - [ji7τ Since it involves square root calculation, the calculation process is slow. Therefore, approximate the radius using the following formula and find a rectangle from the center and radius.

r=lcxl+Icy The rectangles are (Cx-r, Cy-r) and (Cx+r).

It becomes a rectangle with two points (Cy+r) as diagonal corners.

As explained above, when a rectangle is calculated by the inclusive rectangle calculating section 4 in step S1 of the flowchart of FIG. Determine whether or not.

If it is determined that the three-point arc does not intersect, the process proceeds to step S6, and the arc detection section 7 does not detect the three-point arc; if it is determined that the three-point arc intersects, the process proceeds to step S3, and the center point/radius calculation section 5 The center point and radius of the three-point arc are calculated.

After the center point and radius of the arc are calculated, step S4
In step S5 or S6, the intersection determining unit 6 determines whether the arc intersects with the detection range, and in step S5 or S6, the arc detecting unit 7 determines whether or not the arc is detected based on the determination result. A judgment will be made.

(Example〕 An example of this embodiment will be described below.

FIG. 3 shows a graphic processing system that implements the three-point designated arc detection method and apparatus of the graphic processing system according to this embodiment.

The three-point designated arc detection device according to this embodiment includes a starting point, an intermediate point,
A part of the main storage device 32 serves as a figure data storage unit 1 that stores a three-point designation arc defined by the coordinate data of three end points as figure data, and a display unit 2 that serves as a display unit 2 that displays figures according to instructions. A frame memory 34 that stores image data corresponding to the display device 35 and the screen, and a CPU as a center point/radius calculation unit 5 that calculates the center point and radius of an arc passing through three points to be displayed based on the graphic data.
31 and the main storage device 32 as an intersection determination unit 6 that determines whether or not the program stored in the main storage device 32 intersects with the displayed circular arc and a detection (pick) range defined as a rectangle. 32 and the coordinate data of the starting point, middle point, and end point of the 3-point designated arc displayed on the display device 35 to create a rectangle that encompasses the arc without calculating the center point of the arc. A CPU 31 as the inclusive rectangle calculation unit 3 to calculate and a program stored in the main storage device 32, and an input device as the instruction unit 8 to issue various instructions such as detecting a three-point designated arc and inputting data to the system. 36 and a bus 33.

In order to display a graphic using this system, information regarding graphic data is input to the graphic processing system using the input device 36. Then, the CPU (central processing unit) 31 of the graphic processing system operates according to the program of the graphic processing system stored in the main storage device 32, and creates graphic data from the input information. C.P.
U31 adds the created graphic data to the graphic data list on the main storage device 32 and displays this graphic data on the display device 35. For example, when displaying a three-point designated arc, first instruct the CPU 31 to input the three-point designated arc, and then input the three points: a starting point, an intermediate point, and an end point. Then, the CPU 31 creates graphic data representing a three-point designated arc as shown in FIG. 10, adds it to the graphic data list, and displays it on the display device 35.

Next, the detection process when the operator performs an operation to select a figure will be described. Here, the order of the starting point, intermediate point, and end point in the graphic data representing the three-point designated arc may be in any order as long as it is uniquely determined by the graphic processing system.

In order for the operator to select a figure on the display device 35, as shown in FIG. Move to. Next, the input device 36 is operated to notify the graphic processing system that a graphic is to be selected.

This is usually done by pressing down on a mouse button.

When the CPU 31 receives a graphic detection request operation from the input device 36, it calculates the pick range as shown in FIG.

The method of determining the pick range will be explained according to the flowchart of FIG. 12.

The CPU 31 uses the input device 36 to take in the coordinate values (Px, Py) of the cursor when a detection request operation (for example, pressing down a mouse button) is performed, and stores them in a register. Next, the coordinates where the pick range exists are calculated from the width W and height H of the pick range stored in the main storage device 32 according to the following formula.

Pxmin =Px-W Pymin =Py-H Pxmax =Px+W Pymax =Py+H Using the pick range determined in this way, the following is done.
The detection process begins, but the method of specifying the pick range is not limited to the method described above; for example, the input device 3
There is also a method of specifying two points from 6 and setting a rectangle with diagonal corners of those two points as the pick range. In any case,
The CPU 31 determines the maximum coordinates of the pick range (Pxmax,
Pymax ) and minimum coordinates (Pxmin , Pymi
n ) and store it in a register.

Next, the CPU 31 searches the graphic data list for graphic data existing within this pick range. This process will be explained based on the flow chart of FIG.

The CPU 31 sequentially extracts graphic data from the top of the graphic data list and determines whether the extracted graphic data exists within the coordinates of the pick range. This determination process differs depending on the type of graphic data (eg, line segment, polygon, character string, circle, arc, ellipse, elliptical arc, etc.). For example, in the case of a circle (consisting of center point and radius data), it is determined whether it exists within the pick range as follows.

The smallest square area that encompasses the arc is defined as its center point (Cx,
Cy) and radius r, and calculate this square ((Cx-r, C
By determining whether or not the two points y-r)+ (Cx+r, Cy+r) are the lower left and upper right vertices intersect with the pick range, circles that are clearly not to be picked are excluded from the pick target. For circles that could not be picked, approximate the circle as a polygon and determine whether each side of the polygon intersects with the pick range. If even one is picked, it is detected, and if no books are picked, it is not detected. The circle pick judgment is performed using the following method. The present invention relates to a detection process for determining whether or not a three-point designated arc exists within a pick range, among the determination processes for each type of graphic data. The detection process for this three-point designated arc is [
The three-point designated arc detection process will be described in detail later.

As described above, the detection process is sequentially performed for each piece of graphic data, and ends when the graphic data existing within the pick range is found. If it doesn't exist,
The process ends after processing up to the last graphic data in the graphic data list.

[3-Point Designated Arc Detection Process] The process of determining whether the 3-point designated arc intersects the pick range will be described below along the flowchart of FIG. 14.

To determine whether an arc actually intersects the pick range, it is necessary to determine whether a point on the arc exists within the pick range. However, only one figure among dozens of figures is picked, and most of the figures are located far away from the pick range. Therefore, in order to speed up the picking process, the shape is expanded into points or line segments, and before determining whether each point or line segment intersects with the pick range, a rectangle that includes the shape is found, and this rectangle and the pick Determine whether a shape can intersect the pick range by determining whether the ranges intersect. In other words, if the rectangle does not intersect with the pick range, the shape will not intersect with the pick range. Determining whether a rectangle intersects the pick range requires only four comparisons, which is much faster than determining whether the rectangle intersects the pick range by expanding the shape into points or line segments.

Therefore, even in the case of a figure called a three-point designated arc, a rectangle that includes the three-point designated arc is found, and it is determined whether this rectangle intersects with the pick range. If the rectangle does not intersect with the pick range, the three-point specified arc will not intersect with the pick range. If the rectangle intersects with the pick range, the three-point designated arc is developed into points or line segments on the arc to determine whether the rectangle intersects with the pick range.

Conventionally, to find a rectangle that includes this three-point specified arc,
There was no way to do this without finding the center point and radius of the three-point specified arc. In other words, after calculating the center point (Cx, Cy) and radius r of the 3-point designated arc, calculate the rectangle xmin= Cx -r ymin= Cy -r xmax= Cx + r ymax= Cy + r, and then I was using a rectangle.

However, since the process of calculating the center point and radius from the three points of a 3-point arc is very complex, the processing speed of excluding 3-point arcs that are unlikely to be picked using a rectangle is faster. I can't. For this purpose, a method is needed to find a rectangle that includes a circular arc without finding the center point and radius from three points.

The method is as follows.

[Find a rectangle that includes the three-point specified arc] (Figures 15 and 16) First, in order to simplify the calculations below, the three specified points are parallelized so that the midpoint becomes the origin. Moving.

The three specified points are respectively the starting point (Xi, Yl), the intermediate point (X2.Y2), and the ending point (X3.Y3), and the three points after moving the intermediate point parallel to the origin are the starting point (x
i, yl), intermediate point (x2.y2), end point (x3, ys
), then xl=X1-X2 yl = Y1-Y2 x2=0 y2=O x3=X3-X2 y3=Y3-Y2.

Next, a rectangle that includes the three-point specified arc is obtained using the three points after parallel translation. In particular, if these three points satisfy the following conditions, there is no need to perform the process of determining the center point from the three points as shown in FIG. 19, and the rectangle can be determined with less processing, resulting in high speed.

[Conditions ■ When the starting point is located in the 1st quadrant and the ending point is in the 3rd quadrant.In other words, when xi>=O and yt>=o and x3<=O and ysku=0 ■The starting point is in the 2nd quadrant and the ending point If is located in the fourth quadrant, that is, if xi<=0 and yl>=0 and x3>=0 or ys<=o ■If the starting point is located in the third quadrant and the end point is located in the first quadrant In other words, When xi<=O and yl<=O and x3>=0 or ys>=o ■When the starting point is located in the fourth quadrant and the end point is located in the second quadrant In other words, xi>=0 and y+<=o and x 3 <=
When O and y3>=0 (2) The coordinates of the starting point and the ending point are the same. In this case, the three-point designated arc becomes a perfect circle.In other words, if x 1 = x3 and y1 = y3, (1) ■
In the case of the condition, the three-point designated arc that satisfies this condition is the arc shown in No. 61J(a).

The maximum X coordinate and maximum Y coordinate of rectangle R1 that includes the arc of the first quadrant are Rlxmax and Rlymax, and the minimum coordinate and minimum Y coordinate are Rlxmin and Rlymin,
Let's define the rectangle R1 as (Rlxmin, Rlymin) - (Rlxmax
, Rlymax).

Then, when the condition ■ is satisfied, the rectangle R1 has the starting point (xi
, yl) using the coordinate components xi, yl.

If the larger of Xl and yl is Ml, then R1xmi
n= OR1ymin= ORlxmax= M I
R1ymax=M1.

Similarly, a rectangle R3 that includes the arc of the third quadrant
, (R3xmin, R3ymin) −(R3xmax
, R3max).

If the larger of x3-y3 is M3, then R3xmi
n = -M3R3ymin = -M3R
3xmax=OR3ymax=0.

Using the two rectangles R1 and R3 obtained here, it is determined whether there is a possibility that the three-point designated arc intersects with the pick range. In this embodiment, the R1 and R3 rectangles are determined as one rectangle R, but the R1 and R3 rectangles may be separately compared and determined with the pick range.

A rectangle R is obtained from the R1 and R3 rectangles as follows.

Rxm1n =R3xmin Rymin ==R3ymin Rxmax =R1xmax Rymax =R1ymax Similarly, rectangles R including the three-point designated arcs that satisfy the condition ■■■ are determined as follows.

(2) In the case of condition (2), the three-point designation arc that satisfies this condition is an arc as shown in FIG. 6(b).

The maximum coordinates of a rectangle R1 that includes the arc of the second quadrant,
The maximum Y coordinate is Rlxmax, Rlymax, the minimum X coordinate, and the minimum Y coordinate are Rlxmin, Rlymin,
This rectangle R1 is defined as (Rlxmin, Rlymin) - (Rlxma
x, Rlymax).

Then, when the condition ■ is satisfied, the rectangle R1 has the starting point (xi
, yl) using the coordinate components xi, yl.

If the larger of xl and yl is Ml, then R1xmi
n= −M I R1ymin= ORlxmax
=OR1ymax=M1.

Similarly, a rectangle R3 that includes the arc of the fourth quadrant
(R3xmin, R3ymin) −(R3xmax
, R3ymax).

If the larger of X3 and -y3 is M3, then R3xm
in= OR3ymin= −M 3R3xmax=
M3R3ymax=0.

Using the two rectangles R1 and R3 obtained here, it is determined whether there is a possibility that the three-point specified arc intersects with the pick range. In this example, R1°R3 is determined by assuming that the rectangles are one rectangle R, but the rectangles R1 and R3 may be determined by separately comparing them with the pick range.

A rectangle R is found from the rectangles R1 and R3 as follows.

Rxm1n =R1xmin Rymin =R3ymin Rxmax =R3xmax Rymax =R1ymax (3) In the case of condition (2), the three-point designation arc that satisfies this condition is an arc as shown in FIG. 6(c).

The maximum X coordinate and the maximum Y coordinate of the rectangle R1 that includes the arc of the third quadrant are Rlxmax, Rlymax, and the minimum X
Coordinates, the minimum Y coordinates are Rlxmin, Rlymin, and this rectangle R1 is (Rlxmin, Rlymin) - (Rlxmax
, Rlymax).

Then, when the condition ■ is satisfied, the rectangle R1 has the starting point (xi
, yl) using the coordinate components xi, yl.

If the larger of xi and -y1 is Ml, then R1xmin=-MI RIymin=-MIR1
xmax=OR1ymax=0.

Similarly, a rectangle R3 that includes the arc of the third quadrant
, (R3xmin, R3ymin) −(R3xmax
, R3ymax).

If the larger of X3 and y3 is M3, then R3xmi
n= OR3ymin= OR3xmax = M 3
R3ymax=M3.

Using the two rectangles R1 and R3 obtained here, it is determined whether there is a possibility that the three-point specified arc intersects with the pick range. In this embodiment, the rectangles R1 and R3 are determined as one rectangle R, but the rectangles R1 and R3 may be separately compared with the pick range for determination.

Rxm1n =R1xmin Rymin =R1ymin Rxmax =R3xmax Rymax =R3ymax (4) In the case of condition (2), the three-point designation arc that satisfies this condition is an arc as shown in FIG. 6(d).

The maximum X coordinate and the maximum Y coordinate of the rectangle R1 that includes the arc of the fourth quadrant are Rlxmax, Rlymax, and the minimum X
Coordinates, the minimum Y coordinates are Rlxmin, Rlymin, and this rectangle R1 is (Rlxmin, Rlymin) - (Rlxmax
, Rlymax).

Then, when the condition ■ is satisfied, the rectangle R1 has the starting point (x
1, y1) using the coordinate components xi, yl.

If the larger of Xl and -y1 is Ml, then R1xm
in= OR1ymin= -M IR1xmax=
M I R1ymax=0.

Similarly, a rectangle R that includes the arc of the second quadrant,
3 as (R3xmin, R3ymin) −(R3xmax
, R3ymax).

If the larger of X3 and y-3 is M3, then R3xm
in=-M3 R3ymin=OR3xmax=
OR3ymax=M3.

Using the two rectangles R1 and R3 obtained here, it is determined whether there is a possibility that the three-point designated arc intersects with the pick range. In this embodiment, the rectangles R1 and R3 are determined as one rectangle R, but the rectangles R1 and R3 may be determined by comparing them separately with the pick range.

A rectangle R is found from the rectangles R1 and R3 as follows.

Rxm1n = R3xmin Rymin = R1ymin Rxmax = R1xmax Rymax = R3ymax (5) Next, when condition (2) is satisfied, the three-point designated arc becomes a perfect circle. A three-point designation arc that satisfies this condition is an arc as shown in FIG. Since the starting point and the ending point coincide, the line segment connecting the intermediate point and the starting point becomes the diameter of the three-point designated arc. Therefore, the center of the circle is the midpoint of the line segment connecting the midpoint and the starting point.

The center point (Cx, Cy) is as follows: Cx=x l÷2 cy=y+÷2 Only when the circle is a perfect circle, the center point of the circle can be determined by simple calculation.

After that, by finding the radius r, you can find a rectangle that encompasses the circle.

The radius can be determined by the following calculation, but it is slow because it involves calculating the square root of r= Find the rectangle R from.

r=lcxl+lcy Rxmin=Cx-r Rymin=Cy-r Rxmax=Cx+r Rymax=Cy+r (6) If the above conditions do not satisfy ■~■ (Figure 9)
As in the conventional method, the center point and radius are determined according to the flowcharts in FIGS. 17 and 19, and the rectangle R is determined from the center and radius in the same manner as above.

[Detection of intersection between rectangle and pick range (Figure 18) Since the rectangle R obtained here is a rectangle whose origin is at the midpoint,
Now move in parallel in the opposite direction so that the midpoint is at the original position.

Xm1n = Rxm1n + X 2Ymin = R
ymin + Y 2 Xmax = Rxmax 10X 2 Ymax = Rymax + Y 2 This rectangle (Xmin, Ymin) - (Xmax, Ym
ax) is the pick range (Pxmin, Pymin)
- Determine whether it intersects with (Pxmax, Pymax).

Xmax<　Pxmin or Xm1n>Pxmax or Ymax<Pymin or Ym　in　＞　Pymax If , this rectangle does not intersect the pick range.

If all of the above conditions are not met, this rectangle intersects the pick range.

If the rectangle R does not intersect with the pick range, this three-point designated arc does not intersect with the pick range and is not picked. If rectangle R intersects the pick range, this 3-point specified arc may intersect with the pick range, so find the center point and radius of the 3-point specified arc (in the case of (5) and (6) (If the center point has already been found, only the radius is calculated.) As with the traditional method, expand the arc into points or line segments to determine whether it intersects the pick range. .

If even one of them intersects, this three-point designated arc is picked. If none intersect, it will not be picked.

〔Effect of the invention〕

According to the present invention, it is possible to obtain a rectangle that includes a three-point specified arc without calculating the center point of the three-point specified circular arc.

Therefore, it becomes possible to quickly exclude three-point specified arcs that are not clearly detected from detection targets, and as a result, the detection process is speeded up.

[Brief explanation of drawings]

Fig. 1 is a principle flowchart of the first invention, Fig. 2 is a principle block diagram of the second invention, Fig. 3 is a block diagram showing a graphic processing system according to an embodiment, and Fig. 4 is a starting point and an intermediate point. FIG. 5 is a diagram showing a 3-point designated arc detection test screen, FIG. 6 is a diagram showing a 3-point designated arc that “satisfies the conditions” according to the example, and FIG. 7 is a diagram showing each quadrant. Figure 8 is a diagram showing the case where the starting point and end point match according to the example, Figure 9 is a diagram showing a three-point designated arc that "does not satisfy the condition" according to the example, and Figure 10 is a diagram showing the case where the starting point and end point match according to the example. FIG. 11 is a diagram showing the screen of the display device according to the example. FIG. 12 is a process flowchart for determining the pick range according to the example. FIG. 13 is a diagram showing the graphic data list according to the example. Data search processing flowchart, FIG. 14 is a flowchart of a three-point specified arc detection process according to the embodiment, FIGS. 15 and 16 are processing flowcharts for finding a rectangle that includes a three-point specified arc according to the embodiment, and FIG. 17 is a circular arc Processing flowchart for finding the center point and radius (same as before), No. 18
The figure is a process flowchart for determining the intersection between a rectangle and a pick range according to the embodiment, Figure 19 is a process flowchart for determining the center point and radius of an arc (same as before), and Figure 20 is an explanation for determining the radius and center point of an arc. 21 and 21 are flowcharts according to the conventional example.

Claims (1)

[Claims] 1) A three-point designated arc defined by the coordinate data of three points, a starting point, an intermediate point, and an end point, is stored as graphic data, and the arc passing through the three points is displayed on a display device and defined as a rectangle. detected (
(S5) In the arc detection method, the three-point specified arc is detected when it intersects with the range, the starting point, intermediate point, and
A rectangle that includes the arc is calculated from the coordinate data of the three end points without calculating the center point of the arc (S1), and it is determined whether the rectangle intersects the detection range (S2
), if they do not intersect, the three-point specified arc is not detected (S6)
, If they intersect, calculate the center point and radius of the three-point designated arc (S3), and then determine whether the arc intersects with the detection range (S3).
4) A three-point designated arc detection method. 2) A graphic data storage unit (1) that stores, as graphic data, a 3-point specified arc defined by the coordinate data of the 3 points of the starting point, intermediate point, and end point, and performs various instructions such as detecting the 3-point specified arc. An instruction section (8), a display section (2) that displays a figure according to instructions, and a center point/radius calculation section (5) that calculates the center point and radius of an arc passing through the three points to be displayed based on the figure data. ) and an intersection determination unit (6) that determines whether or not the displayed arc intersects with a detection (pick) range defined as a rectangle. ) An inclusive rectangle calculation unit that calculates a rectangle that encompasses the arc from the coordinate data of the starting point, middle point, and end point of the three-point designated arc without calculating the center point of the arc (
4), an inter-rectangle intersection determination unit (3) that determines whether or not the calculated rectangle and the detection range intersect, and when the determination unit (3) determines that they intersect, the graphic data a center point/radius calculation unit (5) that calculates the center point and radius of the circular arc based on the above, and a rectangular intersection determination unit (3) that does not detect the circular arc if it is determined that the rectangles do not intersect. , if it is determined that the arc intersects, the intersection determination section (6) detects the arc when it is further determined that the arc intersects; however, if it is determined that the arc does not intersect, the arc is not detected; (
7) A three-point designation arc detection device comprising: