KR0147591B1 - 2-d graphic round drawing method - Google Patents

Abstract

The present invention relates to a round drawing method of two-dimensional graphics, and more particularly, to a round drawing method in two-dimensional graphics that round-draws edges formed in lines and lines when drawing shapes in two-dimensional graphics.

That is, the two-dimensional graphics round drawing method according to the present invention has an advantage of easy operation because it simply draws the corner portion with the desired arc of a radius by inputting only the radius of the arc to be drawn.

Description

2D Graphics Round Drawing Method

1 is an explanatory diagram showing an example of an actual round drawing method in graphics.

2 is an explanatory diagram that defines the starting point, length, and angle of two straight lines as preparation steps for round drawing the corners of two lines.

3 is an explanatory diagram showing the tangent direction vector at the end point of the first line and the start point of the second line defined in FIG.

4 is an explanatory diagram showing the direction of round drawing by the cross-product value of two tangent vectors obtained in FIG.

5 is an explanatory diagram for explaining a method for obtaining a starting point, a length, and an angle of a line moved when two lines are moved.

FIG. 6 is an explanatory diagram for explaining a method of performing round drawing around the intersection of two moving lines obtained in FIG. 5; FIG.

7 is a flowchart of a round drawing method according to the present invention.

8 is a block diagram of hardware for implementing the round drawing method of the present invention.

* Explanation of symbols for main parts of the drawings

1: Processor 2: ROM

3: RAM 4: CO-PROCESSOR

5: graphic display device 6: CRT

The present invention relates to a round drawing method of two-dimensional graphics, and more particularly, to a round drawing method in two-dimensional graphics that round-draws edges formed in lines and lines when drawing shapes in two-dimensional graphics.

When drawing shapes in general graphic fields, graphic software for CNC, CAD / CAM, etc., there are many cases where round drawing of lines and edges in line is carried out. This round drawing method is described in US Pat. No. 4,723,203.

As described above, when rounding the edges of lines and lines, the user inputs the radius of the arc to be drawn and the round drawing direction.

As described above, in performing the round drawing, there is a inconvenience in that two inputs, namely, the round drawing direction and the radius of the arc to be drawn must be input.

The present invention was devised to improve such inconvenience, and an object thereof is to provide a round drawing method of two-dimensional graphics that can execute round drawing with only one input, that is, only the radius of an arc to be round drawn.

In order to achieve the above object, a round drawing method of two-dimensional graphics according to the present invention includes a first straight line and a second straight line and a starting point, a length, and an angle respectively intersecting with each other. A radius input step of inputting a radius of an arc for rounding corners formed by intersections with each other,

Obtaining respective tangent direction vectors at the intersections of the two straight lines, wherein the tangent direction vector at the end point of the first straight line and the tangent direction vector at the start point of the second straight line are respectively obtained;

Obtaining a vector product of two direction vectors obtained in the step of obtaining a tangent direction vector at the intersection point;

A direction determining step of determining a direction of drawing an arc by determining a sign of the vector product obtained in the step of obtaining the vector product;

Moving the two straight lines to grasp the starting and ending points and the center point of the arc to be drawn;

Determining an intersection of the moved straight lines with a center point of the arc to be drawn;

And drawing an arc by using the intersection of the moved straight lines as the center of the arc to be drawn and using the intersections of the straight line and the non-moved straight line as the start and end points of the arc to be drawn, respectively.

The following describes the round drawing method of the two-dimensional graphics according to the present invention with reference to the drawings in the order introduced in the flowchart of the round drawing method according to the present invention shown in FIG.

First, the radius r of the circular arc to round the corner formed by two straight lines having a starting point, length and angle defined as a preparatory step for round drawing an edge between two straight lines as shown in FIG. Enter. In this case, the two straight lines are defined as follows.

First straight line: starting point Ls = (x1, y1), length len1, angle k1

Second straight line: starting point Le = (x21, y2), length len2, angle k2

Secondly, as shown in FIG. 3, the tangent direction vector at the end of the first straight line and the start of the second straight line. Obtain each of them. The tangent direction vectors are defined as follows, respectively.

= i cos (k1) + j sin (k1)

= i cog (k2) + j sin (k2)

Third, as shown in FIG. 4, the two tangent vectors Calculate the cross product CP. CP is defined as follows.

CP = cos (k1) * sin (k2)-sin (k1) * cog (k2)

Fourthly, as shown in Fig. 4, the direction of round drawing is determined according to the CP value. In case of CP0, arc is drawn counterclockwise. In case of CP0, arc is drawn clockwise.

Fifthly, as shown in FIG. 5, the two straight lines are moved to find the center point and the start point and the end point of the arc having the input radius r.

The starting point, length, and angle of two straight lines to be moved are as follows.

The shifted first straight line is obtained by starting point (x1 ', y1') = (Ls + v), length Len1, and angle k1. Since the normal point (n) = (sin (k1), -cos (k1)) of the first straight line,

If the round drawing direction is clockwise: v = (r * sin (k1), -r * cos (k1))

If the round drawing direction is counterclockwise, then v = (-r * sin (k1), r * cos (k1)).

The shifted second straight line is obtained by starting point P1 (x2 ', y2') = (Le + v), length Len2, and angle k2. Since the normal point of the second straight line (n) = (sin (k2),-cos (k2)),

If the round drawing direction is clockwise: v = (r * sin (k2), -r * cos (k2))

If the round drawing direction is counterclockwise, then v = (-r s sin (k2), r * cos (k2)).

Sixth, in order to find the center and start and end points of the arc to be drawn, the intersection of two moving straight lines as shown in FIG.

The first straight line to be moved

Starting point (x1 ', y1'),

Endpoint P2 (x1, y1) = (x1 '+ len1 * cos (k1)), y1' + len1 * sin (k1))

The equation of the first straight line is as follows.

y = A1 * x + B1 ‥‥ (1)

Where A1 = (y1'-y1 ') / (x1'-x1'), B1 = y1'- A1 * x1 '

The second straight line to be moved

Starting point P1 (x1 ', yl'),

Endpoint (x2, y2) = (x2'.len2 * cos (k2)), y2 '+ len2 * sin (k2))

The second straight line equation is:

y = A2 * x + B2 ‥‥‥‥‥‥‥‥ (2)

Where A2 = (y2'-y2 ') / (x2-x2'), B2 = y2'- A2 * x2 '

Therefore, the intersections of the two straight lines (Cx, Cy) are obtained by the simultaneous equations of the equations (1) and (2).

Seventh, as shown in FIG. 6, the arc of radius r is drawn by the intersections (Cx, Cy), P1, and P2 obtained so far. That is, the first straight line from the starting point (x1, y1) to the end point P1, the arc in the drawing direction obtained from the start point P1 and the end point P2 with the center point as the center point of the shifted intersections (Cx, Cy), and The second straight line draws from the starting point P2 to the ending point (x3, y3) the desired arc.

Where (x3, y3) is

(x3, y3) = (x2. len2 * cos (k2)), y2 + len2 * sin (k2))

8 is a block diagram of a CNC to which the round drawing method of the present invention is applied. Here, the ROM 2 stores a program, and the RAM 3 stores shape data. The operation is as follows.

First, two-dimensional data information (for example, lines or arcs constituting the shape) of the shape drawn on the screen is stored in the RAM 3.

Next, the radius of the arc entered by the user is stored in RAM (3), and the program in ROM (2) reads the value.

Next, the processor 1 uses three-dimensional shape data information of the RAM 3 to obtain three points (intersections, P1, P2) required for drawing an arc according to a program stored in the ROM 2.

Next, the processor 1 performs a linear black circular interpolation using the three points obtained above according to the program stored in the ROM 2, and stores the result in the video RAM of the graphic display device 5. Finally, the CRT 6 is displayed.

As described above, the two-dimensional graphics round drawing method according to the present invention has an advantage of easy operation because it simply draws the corner portion with the desired arc of a radius by inputting only the radius of the arc to be drawn.

Claims (3)

A radius input step of inputting a start point, a length and an angle of an intersecting first straight line and a second straight line, respectively, and a radius of an arc for rounding an edge formed by the intersection of the intersecting first and second straight lines; Obtaining respective tangent direction vectors at intersections of the two straight lines, wherein tangent direction vectors at the end points of the first straight line and tangent direction vectors at the start point of the second straight line are respectively obtained; and tangent directions at the intersection points Obtaining a vector product of the two direction vectors obtained in the step of obtaining the vector, determining a direction in which the arc is to be drawn by judging the sign of the vector product obtained in the step of obtaining the vector product, a starting point of the arc to be drawn, and Moving each of the two straight lines to establish an end point and a center point, and the center of the arc to be drawn. Determining an intersection point of the moved straight line with a point, making the intersection of the moved straight line a center of an arc to be drawn, and starting points of the arc to be drawn and the intersections of the straight line and the moved straight line, respectively; And a circular arc as an end point. The method of claim 1, wherein the determining of the direction in the step of determining the direction in which the arc is drawn comprises drawing clockwise or counterclockwise when the cross product value of the two vectors is positive, and counterclockwise or clockwise when negative. The round drawing method of the two-dimensional graphic characterized by the above-mentioned. The method of claim 1, wherein the starting point, the end point, and the center point of the arc to be drawn are obtained by moving the two straight lines through a predetermined method.