JPS63172382A - Relative position analyzing system for 2-dimensional coordinate space data - Google Patents

Abstract

PURPOSE:To increase a processing speed with the titled system by obtaining the relative position relation between two points in a 2-dimensional coordinate space from a monotonous increase function. CONSTITUTION:The relative position relation between at least two points A and B are obtained out of a group of data acquired in a 2-dimensional coordinate space. in this case, the position data on the point A are defined as AX and AY1 with the position data on the point B defined as BX and BY2 respectively. Then the distance R3 between both points A and B is calculated from an equation I. The comparison of values are carried out between said defined AX and BX as well as AY and BY respectively. Then the position of the point B relative to the point A is obtained from a function shown in a table based on the quadrant data obtained from said comparison of values as well as the data 3 on the distance R between both points.

Description

[Detailed Description of the Invention] [Summary] While analyzing a group of tracers obtained as data on a two-dimensional coordinate space, it is necessary to calculate a series of inverse trigonometric functions necessary to investigate the relative positional relationship between two points. In order to resolve the resulting deterioration in data processing performance, we have developed a method for determining the distance (■υ) between the two points, and the quadrant data of one of the two points with respect to the other point. By providing means for determining the relative positional relationship between the other point and one point based on the distance (R) between the two points and the quadrant data, ji ' as a key increasing function 6B
).

[Industrial application field]

The present invention relates to a method for analyzing the relative position of data on a two-dimensional coordinate space.

With the recent improvement in the performance of computer systems, graphics processing using these computer systems has come to be performed in various fields such as computer graphics.

During the graphic processing, an operator is required to extract one of the plurality of graphics displayed on the display 7 by, for example, using a cursor, and fill the graphic with a specific color. Sometimes.

When picking a specific shape from among these multiple shapes, it is necessary to determine whether or not the point indicated by the operator's cursor is within the shape. , is a process of determining the relative positional relationship with a specific point of the figure.

However, since the process of determining the relative position between the two points is only a pre-processing of the drawing process, it should be as simple as possible and an analysis process that does not affect the overall graphic process. Everything is needed.

[Prior art and problems to be solved by the invention] FIG. 3 is a diagram illustrating a conventional relative position analysis method for two-dimensional coordinate space data.

In the conventional method, as shown in (a) of this figure,
For example, the two points in the two-dimensional coordinate space A are the center point (0, 0) and the point (X, Y) of a coordinate system with the horizontal direction as the X axis and the vertical direction as the Y axis. The point (X,
By determining the angle θ of Y) with respect to the X axis, the relative positional relationship between the two points was analyzed.

In this case, sinθ−Y/(X2+Y2) ””= α
The angle θ can be determined as an arc sine. That is, θ= 5in-'α - α10 (l/2・3)α3 + ((1・3)/
(2・4 ・5)) α5+ ((l・3 ・5)
/ (2・4 ・6 ・7)) We will find the series function shown by α ゛゛---.

The above function is -1%) I as shown in figure (b)
It is a function of l to l correspondence from Q-π/2 to π/2.

Therefore, by carefully examining the values of X and Y in 1-1 and finding the quadrant,
The problem is that simply calculating the relative positional relationship between two points requires a large amount of time for the numerical calculation of the series function as described above. there were.

In view of the above-mentioned conventional drawbacks, the present invention provides
For example, it is an object of the present invention to provide a method for quickly determining the relative positional relationship between two points using simple processing.

[Means for solving problems]

FIG. 1 is a conceptual diagram of the configuration of a relative position analysis method for two-dimensional coordinate space data according to the present invention.

In the present invention, there is provided a method for analyzing the relative position of data existing in a two-dimensional coordinate space, the method comprising: analyzing the relative position of data existing in a two-dimensional coordinate space; When calculating the relative positional relationship between the two points, define AX, AM l as the position data of point A, BX, BY 2 as the position data of point B, and calculate the distance Alt between the two points. (R) 3, R= ((BX-AX)
``)(BY-AV)21'' To find the quadrant of point B with respect to point A, use the magnitude comparison 4 between AX and Bx and AV and BY defined above. Based on the quadrant data obtained by the size comparison means and the data 3 of the distance (R) between the two points, point B in the first quadrant is determined by -(BX-AX) /I? Point B in the second quadrant is −(
8Y-BY)/R+1.0 3rd quadrant (7) Point B -(A
X-BX)/R+2.0 The function is to indicate point B in the fourth quadrant as -(BY-8Y)/R+3.0, and is configured to determine the relative position of point B with respect to point A.

[Effect]

That is, according to the present invention, when analyzing a data group that is represented as data on a two-dimensional coordinate space, the calculation of a series of inverse trigonometric functions, which is necessary to examine the relative positional relationship between two points, is performed. In order to solve the decline in data processing performance, the above 2.
By providing means for determining the distance (I?) between points and means for determining the quadrant data of one of the two points with respect to the other point by comparing the magnitude of the coordinate data of the two points, the above-described method can be achieved. Since the relative positional relationship between the other point and one point can be obtained as a monotonically increasing function based on the distance (R) between the two points and the quadrant data, 2
This has the advantage that the relative positional relationship between two points on a dimensional coordinate space can be determined quickly using a monotonically increasing function.

〔Example〕

Embodiments of the present invention will be described in detail below with reference to the drawings.

The above-mentioned FIG. 1 is a conceptual diagram of the configuration of the relative position analysis method for two-dimensional coordinate space data of the present invention, and FIG. 2 is a diagram showing an embodiment of the present invention. and means 3 for determining the distance Am(R) between points.

Means for determining the quadrant of 13 points for point A by comparing the magnitude of the coordinates of the two points, and the distance iX'1f(R) between the two points.
Means for determining the educational system increasing function using the above and quadrant data is a necessary means for carrying out the present invention.

Note that the same reference numerals indicate the same objects throughout the figures.

Hereinafter, the relative position analysis method of two-dimensional coordinate space data of the present invention will be explained with reference to FIGS. 1 and 2.

In the present invention, a function is introduced that expresses the relative position of point B as seen from point A as a quantitative value different from the conventional angle θ.

For that purpose, first, as the position data of each point, point A: (
AX, AV) I B point: Define (IX, [) 2, (a) As shown in the figure, the position directly above point A is 0°, and ′ζ, for example, increases monotonically clockwise. Consider a function like Specifically, ■ First, the distance between point A and point B shown in figure (b)^1
1(R) 3, R= ((RX-AX)2+(IIY-AV)2)
Find with "".

(2) Next, find the quadrant of point B in the two-dimensional coordinate system centered on point A. Specifically, from the coordinates of the two points defined above, compare the sizes of AX and IIX, and AV and BY.
and find the quadrant based on Table 1.

Based on the quadrant data obtained in Table 1 ■ ■, calculate the following values. That is, 1st quadrant - (BX-Δx)/R 2nd quadrant - (AV-11Y)/R+ 1.0 3rd quadrant -
(AX-BX)/R+ 2.0 4th quadrant - (BY-AV
) /R13,0 The numerical value obtained by °ζ is 0
It can be seen that the numerical value is obtained as a monotonically increasing function up to 4.

FIG. 2 is a diagram showing an embodiment of the present invention, and is an example of picking up a fan shape with point P as the center and point Q and point R as end points.

In order to pick up this fan shape, when 8 points in the fan shape are given (for example, the point indicated by the cursor is
It is necessary to judge whether the eight points are points inside the fan shape and recognize that they are inside the fan shape.

The following two conditions are listed as conditions for the eight points to be inside the sector.

1) The distance between 1.5 points is shorter than the distance between PQs (or between PRs).

1i) When searching clockwise from point Q to point R, 8 points are searched.

Under the above conditions, there is no particular problem with i), but i)
In examining , we use the monotonically increasing function of the present invention. Specifically, centering on point P, Q, I+'.

5O) Calculate numerical values using the function of the present invention for the three points, and if the magnitude relationship of the three points is the value of Q < the value of S minus the value of R, then condition ii) above is satisfied. become.

In this way, the fan shape (P, u, R) is picked up, and image processing is performed to fill the fan shape with a specific color, for example.

In this way, the present invention analyzes the relative position of two points in a two-dimensional coordinate space, instead of finding the angle θ of the two points with respect to X (or Y) in the two-dimensional coordinate space. , said 2
Find the distance (R) on the coordinate system centered on one of the points and the quadrant data by comparing the magnitude of the coordinates of the two points, and calculate the distance (R).
R) and the numerical value of a monotonically increasing function calculated based on quadrant data.

〔Effect of the invention〕

As explained above in detail, the relative position analysis method for two-dimensional coordinate space data of the present invention examines the relative positional relationship between two points while analyzing a data group obtained as data on a two-dimensional coordinate space. In order to solve the deterioration in the performance of data processing due to the series calculation of inverse trigonometric functions required above, a means for calculating the distance (R) between the two points, and a means for calculating the distance (R) between the two points -
By providing means for obtaining quadrant data of one point with respect to the other point by comparing the magnitude of the coordinate data of the two points,
The relative positional relationship between the other point and one point can be obtained as a monotonically increasing function based on the distance (I?) between the two points and the quadrant data.
This has the advantage that the relative positional relationship between two points on a two-dimensional coordinate space can be determined quickly using a monotonically increasing function.

[Brief explanation of the drawing]

FIG. 1 is a conceptual diagram of the configuration of a relative position analysis method for two-dimensional coordinate space data according to the present invention. FIG. 2 is a diagram showing an embodiment of the present invention. FIG. 3 is a diagram illustrating a conventional relative position analysis method for two-dimensional coordinate space data. It is. In the drawing, 1.2 is the position data (coordinates) of two points. 3 is the distance (R) between two points, and 4 is the size comparison. are shown respectively. (λ) (b) Special 1 Figure

Claims (1)

[Claims] A method for analyzing the relative position of data existing in a two-dimensional coordinate space, comprising at least two points (point A, point A, When calculating the relative positional relationship between point B), define AX, AY (1) as the position data of point A, BX, BY (2) as the position data of point B, and calculate the two points. The distance between (R) (3), R = {(BX-AX)^
2+(BY-AY)^2^1^/^2 To find the quadrant of point B to point A, we need to use the above defined AX and BX and AY and BY. and a means for performing a size comparison (4) between the two points, and the point B in the first quadrant is determined based on the quadrant data obtained by the size comparison means and the data (3) of the distance (R) between the two points. ...(BX-AX)/R Point B in the second quadrant...(AY-BY)/R+1.0 Point B in the third quadrant...(AX-BX)/R+2.0 B in the fourth quadrant
The point is expressed as...(BY-AY)/R+3.0, and the A
2 characterized by finding the relative position of point B with respect to point
Relative position analysis method for dimensional coordinate space data.