JP3486937B2 - Figure transformation device - Google Patents

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a graphic transformation device capable of transforming an arbitrary line drawing in image processing.

[0002]

2. Description of the Related Art In computer image processing, a lot of processing is performed for transforming a line drawing drawn by a point drawing, a straight line, a curve function or the like for the purpose of performing animation processing.

However, conventionally, in order to deform a line drawing, the deformation information of each point forming the line drawing, the deformation information of the start point and the end point of each straight line, or the deformation information of each parameter of the curve function is required. Even a line drawing has a problem that a large amount of data is required to deform it.

An object of the present invention is to make it possible to transform an arbitrary line drawing with a small amount of transformation information and to facilitate the creation of the transformation information.

[0005]

The present invention firstly has graphic display means (display device 104) for displaying a line drawing graphic.

Next, the graphic display means has a frame determination means (step 202 in FIG. 2 executed by the CPU 101) for determining an arbitrary rectangular frame surrounding the line drawing figure on the display screen.

Next, on the display screen of the graphic display means, the rectangular frame determined by the frame determination means is divided into a plurality of triangular frames, and then the frame deformation means (executed by the CPU 101) for deforming each triangular frame. 2 of FIG. 2). This frame deforming means fixes one point in a rectangular frame
After determining the points, the rectangular frame is fixed
Is divided into a plurality of triangular frames each including one vertex. Alternatively, the frame deforming means determines one point in the rectangular frame as a fixed point, and then passes through the fixed point and each of the four corner points of the rectangular frame and the rectangular frame. A rectangular frame is divided into eight right triangle frames by two line segments parallel or perpendicular to the sides of.

Then, the frame transforming hand to be processed
The three that make up the triangular frame before being transformed in steps
The frame of the triangle after being deformed by the vertices and the frame deforming means.
Line drawing based on the positional relationship with the three vertices that make up the
Object to be processed in the figure before it is transformed by the frame transformation means
The operation of deforming the part inside the frame of the triangle is
Illustration to perform for each of multiple triangular frames
Shape transformation calculation means (FIG. 2 executed by the CPU 101)
Step 204).

[0009]

Since the graphic deformation is performed for each of the plurality of triangles that divide the rectangular frame determined by the frame determining means, the manner of dividing the frame can be specified in detail.

In this case, the deformation information of the line drawing figure is obtained only as the positional relationship between the three vertices forming the triangular frame before deformation and the three vertices forming the triangular frame after being deformed by the frame deforming means. Since it can be created, the processing amount of the graphic transformation processing is small.

Further, the transformation of the line drawing figure can be easily realized only by transforming the line drawing figure so that such positional relationship is preserved. Here, the rectangular frame is divided into a plurality of triangular frames each having a fixed point in the frame as one vertex, so that the triangular frame is deformed with one vertex of each triangular frame fixed. As a result, it is possible to reduce the calculation amount when the line drawing figure is deformed.

Further, a rectangular frame connects a fixed point in the frame and each of the four corner points of the frame, and
By dividing the frame into eight right-angled triangle frames by two line segments that pass through the fixed points and are parallel or perpendicular to the sides of the frame, it is possible to further reduce the calculation amount when the line drawing figure is deformed.

[0013]

Embodiments of the present invention will now be described in detail with reference to the drawings. FIG. 1 is a block diagram of an embodiment of a graphic transformation apparatus.

The CPU 101 operates while using the RAM 103 as a work memory according to a control program stored in the ROM 102, and controls all operations for graphic transformation.

The display device 104 is, for example, a CRT display for displaying a figure before transformation and a figure after transformation. In this case, a point function of a display position by a mouse or the like for enclosing a figure in a rectangular frame (described later) is also included.

FIG. 2 is an operation flowchart showing an outline of the graphic transformation process in the embodiment of FIG. First, in step 201, the user selects an original figure to be transformed on the display device 104. Specifically, the user
The original cursor is selected by moving the mouse cursor displayed on the display device 104 to the original figure (line drawing) to be selected and clicking the mouse button. Or
The user may enclose a range including a plurality of original figures (line drawings) with a box using a mouse. In response to this, the CPU 101 causes the coordinate values of the selected original graphic on the graphic data developed on the RAM 103,
Specifically, each coordinate value forming the selected line drawing is calculated. As a result of these processes, for example, as shown in FIG. 4A, a straight line figure 1 having both ends P1 and P2 is selected, the coordinate values of the points P1 and P2 are calculated, and the RAM 103
Held in.

Next, in step 202, the user determines, on the display device 104, a rectangular frame surrounding the original figure selected in step 201. In response to this, C
The PU 101 calculates the coordinates of the four points of the four corners of the rectangle forming the determined frame on the graphic data developed on the RAM 103, and stores the coordinates in the RAM 103.

Next, in step 203, the user first uses the mouse on the display device 104 to
The rectangular frame determined in step 202 is shown in FIG.
The frame is divided into a plurality of triangular frames in the form shown in (a), (b), or (c). Next, the user clicks the mouse button on an arbitrary intersection composed of a rectangular frame and a plurality of divided triangular frames, drags it to the position of the transformation destination, and then releases the mouse button. The rectangular frame and the triangular frames within the frame are deformed by repeating each arbitrary intersection. In response to this, C
The PU 101 calculates the coordinate value of an arbitrary intersection after deformation on the graphic data developed on the RAM 103, stores the coordinate value in the RAM 103, and displays the frame after deformation on the display device 104.

At step 204, the CPU 101 divides the rectangular frame before deformation into a plurality of triangular frames and divides the triangular vertices, which are held in the RAM 103 at step 202, into three vertices forming the triangular frame before deformation. For example, the coordinate values of points T1, T2, and T3 in FIG. 4A and the post-deformation triangular frame corresponding to the pre-deformation triangular frame to be processed, which is held in the RAM 103 in step 203, are configured. 3 vertices, for example, FIG.
Based on the positional relationship with the coordinate values of points T1 ', T2', and T3 'in (b), the original figure stored in the RAM 103 in step 201 is constructed, for example, the coordinates of points P1 and P2 in FIG. 4 (a). By transforming the values, points P1 'and P2' shown in FIG. 4 (b) are calculated.

In step 205, the CPU 101
Is, for example, the point P calculated in step 204 in FIG. 4 (b).
1 ′ and P2 ′ are the transformed figures l ′,
It is displayed on the display device 104.

Next, the specific type of frame division in step 203 and the specific processing of the graphic transformation operation in step 204 for each type will be described. First, FIG. 3A, FIG. 3B, and FIG. 3C show division types when the user divides a rectangular frame into a plurality of triangular frames in step 203 of FIG.

In the type 1 of FIG. 3A, the user can freely divide the rectangle. In the type 2 of FIG. 3B, the user can determine one point in the rectangle as a fixed point and then determine a plurality of triangular frames including the fixed point at one vertex.

In the type 3 of FIG. 3C, the user only performs the operation of determining one point in the rectangle as a fixed point. As a result, a rectangle that is divided by a line segment that connects the fixed point and each of the four corner points of the rectangular frame, and two line segments that pass through the fixed point and are parallel (or perpendicular) to the sides of the rectangular frame. Eight right-angled triangle frames within the frame are automatically determined.

Comparing the division types shown in FIGS. 3 (a), 3 (b) and 3 (c), the degree of freedom of division is (a)> (b).
＞ (c) is the order, but the calculation amount of figure transformation is (c) ＞
(b)> (a). Therefore, the user may select a desired division type in consideration of the balance between the degree of freedom of division and the calculation amount of the graphic transformation calculation.

In step 203 of FIG. 2, the user selects one of the division types shown in FIG. 3 (a), (b), or (c) to divide the rectangular frame into a plurality of triangular frames. After that, as described above, by moving the position for each vertex forming the frame of each triangle, the frame of each triangle is transformed, based on that,
In step 204 of FIG. 2, a graphic transformation operation is executed.

For example, when the user selects the division type shown in FIG. 3 (a) and transforms each triangular frame, the three vertices forming the triangular frame to be processed are shown in FIG. 4 (a), for example. If the points are T1, T2, and T3 as described above, the three vertices constituting the deformed triangular frame are represented by points T1 ′, T2 ′, and T3 ′ in FIG. 4B, for example.

A specific graphic transformation process in this case will be described below. First, in FIG. 4 (a), for each point P1 and P2 forming the straight line l that is the original figure, a straight line passing through each point and parallel to any side of a triangle having points T1, T2 and T3 as three vertices. Is calculated. In the example of FIG. 4 (a), the point P
For 1, the straight line W11-W12 parallel to the side T1-T2
Is calculated, and a straight line W21-W22 parallel to the sides T1-T3 is calculated for the point P2. Where W11 and W1
2, W21, and W22 are points where each parallel line intersects each side of the triangle. Since there are three ways of drawing a parallel line for each side of the triangle, as shown in FIG. 4A, for the point P2, a straight line (W21)-(W22 parallel to the sides T1-T2 is used. ) May be calculated.

Next, the three vertices T1, T2, T of the original triangle
When 3 is transformed into three vertices T1 ', T2', T3 ',
Parallel lines W11-W12 and W21-W22 are straight lines W1
It is transformed into 1'-W12 'and W21'-W22'. The limiting conditions in this case are straight lines W11'-W12 'and W2.
1'-W22 'are sides T1'-T2' and T1 ', respectively.
-Parallel to T3 '.

From these limiting conditions, the four points W1 after deformation are
1 ', W12', W21 ', and W22' are calculated by solving a simultaneous four-dimensional linear equation represented by the following equation.

[0030]

[Equation 1]

Based on this equation, the four points W11 ', W after deformation are
After 12 ′, W21 ′ and W22 ′ are calculated, the points P1 and P2 forming the straight line 1 which is the original figure are changed to points P1 ′ and P1.
It is transformed into 2 '. The limiting condition in this case is that, on the above-mentioned parallel line passing through the points forming the figure, a line segment whose two end points intersect the parallel line and the sides of the triangle is divided by the points forming the figure. That is, the division ratio of is equal before and after deformation.

According to this restriction condition, the points P1 'and P after deformation are changed.
2'is calculated by solving a simultaneous binary linear equation represented by the following equation.

[0033]

[Equation 2]

As described above, the graphic transformation operation for each frame of each triangle corresponding to the division type 1 in FIG. 3A is realized. Next, for example, when the user selects the division type of FIG. 3 (b) to deform the frame of each triangle,
If the three vertices forming the triangular frame to be processed are points T1, T2, and T3 as shown in FIG. 5, for example, the three vertices forming the modified triangular frame are, for example, point T1 in FIG. It is represented by ', T2', and T3. Here, the point T3 is one fixed point in the rectangular frame shown in FIG. 3 (b).

A specific graphic transformation process in this case will be described below. In FIG. 5, with respect to the point P constituting the original figure, one straight line passing through that point and parallel to any side of a triangle having points T1, T2 and T3 as three vertices is calculated. In the example of FIG. 5, a straight line parallel to the sides T1-T2 is calculated for the point P. Here, V1 and V2 are points at which the parallel line and the sides T1-T3 and T2-T3 of the triangle intersect.

Next, the two vertices T1 and T2 of the original triangle are 2
When transformed into vertices T1 'and T2', parallel lines V1-V
2 is transformed into a straight line V1'-V2 '. The limiting condition in this case is that the straight line V1'-V2 'is parallel to the side T1'-T2'.

From this restriction condition, two points V1 'after deformation,
V2 'is calculated by solving a simultaneous binary linear equation shown by the following equation.

[0038]

[Equation 3]

Based on this equation, the two points V1 ', V after deformation are transformed.
After 2 ′ is calculated, the point P that constitutes the original figure is changed to the point P ′.
Is transformed into. The limiting condition in this case is, as in the case of division type 1 in FIG. 3 (a), on the above-mentioned parallel line passing through the points forming the figure, the two points where the parallel line and the sides of the triangle intersect are the end points. That is, the division ratio when the line segment is divided by the points forming the figure is equal before and after the deformation.

Under this restriction condition, the deformed point P'is calculated by solving the linear equation shown by the following equation.

[0041]

[Equation 4]

As described above, the graphic transformation operation for each frame of each triangle corresponding to the division type 2 in FIG. 3B is realized. Next, for example, a case where the user selects the division type shown in FIG. 3C to deform the frame of each right triangle will be described.

Here, the user selects
When deforming each of the right-angled triangle frames of, or, if the three vertices forming the triangular frame to be processed are points T1, T2, and T3 as shown in FIG. The three vertices that make up the frame are represented by points T1 ', T2', T3 in FIG.

Further, the user selects ,, in FIG.
When deforming the frame of each right triangle of or,
If the three vertices forming the triangular frame to be processed are points T1, T2, and T3 as shown in FIG. 7, for example, the three vertices forming the modified triangular frame are, for example, point T1 in FIG. It is represented by ', T2', and T3.

First, a specific graphic transformation process in the case of FIG. 6 will be described below. In FIG. 6, as in the case of division type 2 in FIG. 3 (b), with respect to the point P which constitutes the original figure, the point P is formed on an arbitrary side of a right triangle having three vertices T1, T2 and T3. One parallel straight line is calculated. In the example of FIG. 6, for the point P, a straight line parallel to the sides T1-T2 is calculated. Here, V1 and V2 are points at which the parallel line and the sides T1-T3 and T2-T3 of the triangle intersect.

Next, the two vertices T1 and T2 of the original right triangle
Is transformed into two vertices T1 'and T2', the parallel line V1
-V2 is transformed into a straight line V1'-V2 '. The limiting condition in this case is that the straight line V1'-V2 'is parallel to the side T1'-T2', as in the case of the division type 2 in FIG. 3 (b).

This limiting condition and points T1, T2 and T3 are set to 3
From the condition that the triangle that is the vertex is a right triangle,
The following relationship holds.

[0048]

[Equation 5]

In the equation (5), it is assumed that the side T1-T3 is parallel to the x-axis on the xy coordinate axes and the side T1-T2 is parallel to the y-axis. The x coordinate and the y coordinate of the point P are Px and Py, and similarly, the x coordinate and the y coordinate of the point P ′ are P
Represented as x'and Py '. 2 vertices T
The x and y coordinates of 1 and T2 are T1x and T1y,
Similarly, T2x and T2y, as well as the x and y coordinates of the two vertices T1 'and T2' are T1x 'and T1y', T2x '.
And T2y '. Furthermore, points V1 and V
The x and y coordinates of 2 are V1x and V1y, V2x and V2y, as well as the x and y coordinates of points V1 ′ and V2 ′.
The coordinates are V1x 'and V1y', V2x 'and V2y'.
Is represented as.

Further, as in the case of the division type 1 in FIG. 3A and the division type 2 in FIG. 3B, the parallel line and the triangle are formed on the parallel line passing through the points forming the figure. A restriction condition is added that the division ratio in the case where a line segment whose two end points intersect with the edge is divided by the points forming the figure is equal before and after the deformation.

From this limiting condition and the equation (5), the x coordinate of the deformed point P'can be calculated by the following equation.

[0052]

[Equation 6]

Similarly, the y coordinate of the deformed point P'can be calculated by the following equation.

[0054]

[Equation 7]

As described above, the graphic transformation operation in the case of transforming the frame of each of the right triangles of, or in the division type 3 of FIG. 3B is realized. Next, a specific graphic transformation process in the case of FIG. 7 will be described below.

The operation in FIG. 7 is different from the operation in FIG. 6 in that the side T1-T3 is parallel to the y-axis instead of the x-axis on the xy coordinate axes, and the side T1-T2 is parallel to the y-axis instead of the x-axis. The only difference is that they are assumed to be.

Therefore, by considering in the same manner as in the case of FIG. 6, the relation of the following equation is established.

[0058]

[Equation 8]

Further, as in the case of FIG. 6, on a parallel line passing through the points forming the figure, a line segment having two points at which the parallel line and the sides of the triangle intersect as the end points constitutes the figure. The x-coordinate of the point P ′ after the deformation can be calculated by the following expression from the restriction condition that the division ratio in the case of division is the same before and after the deformation and the equation (8).

[0060]

[Equation 9]

Similarly, the y coordinate of the deformed point P'can be calculated by the following equation.

[0062]

[Equation 10]

In this way, the division type 3 of FIG.
In the case of deforming the frame of each right-angled triangle in ,, or, the graphic deformation operation is realized. By the graphic transformation processing described above, for example, as shown in FIG. 8, a line drawing figure surrounded by a rectangular frame can be variously transformed, and the manner of dividing the rectangular frame into a plurality of triangular frames is changed. As a result, it is possible to finely deform the figure.

[0064]

According to the present invention, since the graphic transformation is performed for each of a plurality of triangles that divide the rectangular frame determined by the frame determining means, the figure can be changed by changing the method of dividing the frame. It is possible to specify the deformation mode in detail.

Further, only the positional relationship between the three vertices forming the triangular frame before deformation determined by the frame determining means and the three vertices forming the triangular frame deformed by the frame deforming means is as follows. Since the deformation information of the line drawing figure can be created, there is an effect that the processing amount of the figure changing process is small.

Further, the user can transform the line drawing figure by a simple operation of moving each vertex.
Further, it is possible to easily realize the deformation of the line drawing figure only by changing the line drawing figure so that the positional relationship as described above is preserved.

Here, the rectangular frame is divided into a plurality of triangular frames each having a fixed point in the frame as one vertex, so that the triangular frame is fixed with one vertex of each triangular frame fixed. Is deformed, and as a result, it is possible to reduce the amount of calculation when the line drawing figure is deformed.

Further, a rectangular frame connects a fixed point in the frame and each of the four corner points of the frame, and
By dividing the frame into eight right-angled triangle frames by the two line segments that pass through the fixed points and are parallel or perpendicular to the sides of the frame, it is possible to further reduce the amount of calculation when transforming the line drawing figure.

[Brief description of drawings]

FIG. 1 is a configuration diagram of an embodiment of a graphic transformation device.

FIG. 2 is an operation flowchart showing a process of an embodiment of the graphic transformation device.

FIG. 3 is a diagram showing types of rectangular triangulation.

FIG. 4 is an explanatory diagram of type-1 graphic transformation processing for each triangle.

FIG. 5 is an explanatory diagram of a type 2 graphic transformation process for each triangle.

FIG. 6 is an explanatory diagram (No. 1) of the graphic transformation process for each right triangle in Type 3.

FIG. 7 is an explanatory diagram (No. 2) of the graphic transformation processing for each right triangle in the type 3;

FIG. 8 is a diagram showing an operation example of graphic transformation processing.

[Explanation of symbols]

101 CPU 102 ROM 103 RAM 104 display device

Claims (2)

(57) [Claims] 1. A graphic display means for displaying a line drawing graphic, a frame determining means for deciding an arbitrary rectangular frame surrounding the line drawing graphic on the display screen of the graphic display means, and a display screen for the graphic display means. Above, one point in the rectangular frame determined by the frame determination means is
After determining as a fixed point, move the rectangular frame
Divide into multiple triangular frames with fixed points at one vertex
After that, the frame deforming means for deforming each of the triangular frames, the three vertices constituting the triangular frame before being deformed by the frame deforming means which is the processing target, and the three points after being deformed by the frame deforming means Based on the positional relationship with the three vertices forming the triangular frame, the operation of deforming the portion of the line drawing figure in the triangular frame that is the processing target before being deformed by the frame deforming means is performed. A graphic transformation device, comprising: a graphic transformation calculation unit that executes each of the triangular frames. 2. A graphic display unit for displaying a line drawing graphic, and the line drawing graphic on a display screen of the graphic display unit.
Frame determination that determines the frame of any rectangle that surrounds
Means and the frame on the display screen of the graphic display means.
One point in the rectangular frame determined by the determination means
After determining the fixed point, the fixed point and the rectangular frame
The line segment connecting each of the four corner points of the ram and the fixed
2 which is parallel or perpendicular to the side of the rectangular frame passing through the point
The rectangular frame is divided into eight straight lines by
Divide it into rectangular triangular frames, and then
A frame deforming means for deforming the over arm, before being deformed by said frame deforming device to be processed
Three vertices forming a triangular frame and the frame
Construct a triangular frame after it has been deformed by the deformation means
Based on the positional relationship with the three vertices, among the line drawing figures
It is a processing target before being deformed by the frame deforming means.
The operation of deforming the part inside the triangular frame is
Shape to execute for each of a number of triangular frames
A graphic transformation device comprising: a transformation calculation means .