JP2006202066A - Apparatus for creating model of curve or curved surface using three-dimensional computer graphics and its system - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an apparatus for creating models of curves or curved surfaces using three-dimensional computer graphics that makes it easy to draw any three-dimensional configuration consisting of simpler and smooth curves passing through designated points, and a system therefor. <P>SOLUTION: The apparatus for creating models of curves or curved surfaces using three-dimensional computer graphics comprises: (1) a means for inputting a plurality of designated points on a drawing screen; (2) a means for linking the inputted designated points together using a spline curve to create a free curve; (3) a means for determining an axis of rotation, an angle of rotation, and the range of display angles on an input screen associated with the drawing screen, and rotating the curve to form a free-form surface; (4) and a means for converting three-dimensional curved surface image data into two-dimensional screen coordinate system data by use of rules of perspective and displaying a figure on a computer display. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a three-dimensional computer graphics curve / curved surface model generation apparatus and a curve / curved surface modeling system for inputting / generating a three-dimensional curve model from a two-dimensional shape.

  In recent years, a method has been proposed in which a three-dimensional model of a product is virtually generated on a computer and the product model is imaged or prototyped based on the three-dimensional model.

  For such a three-dimensional model, a wire screen model is most often used. The present inventor has filed an application and a system for generating a three-dimensional model of a straight line, a cylindrical object, and a spherical object as Japanese Patent Application No. 2004-013767. In the present invention, the above-mentioned idea is applied to a curve.

  In a curve model, it is important what kind of curve is drawn by connecting a plurality of designated points. As a conventional curve forming method, for example, Patent Document 1 proposes a method of maximizing the curvature of a curve in the vicinity of a designated point. In this method, a method of drawing a curve having a maximum value at each point has been proposed. However, with this method, the smoothness of the curve connecting the points cannot be said to be sufficient.

JP-A-9-138855

  Further, as a method of displaying a curve connecting fixed points, a Bezier curve that is composed of n + 1 control point sequences and is defined by a Bernstein polynomial is known. However, this method has a problem that the drawn curve does not pass over a specified point. In any case, these proposals have not been proposed for three-dimensional modeling.

  An object of the present invention is to provide a three-dimensional computer graphic model device that is simpler and more easily drawn than a conventional three-dimensional modeling system and that can easily draw a three-dimensional shape consisting of a smooth curve passing through a specified point, and a system therefor There is to do.

That is, the present invention
(1) means for inputting a plurality of designated points on the drawing screen;
(2) means for connecting the input designated points sequentially with a spline curve to form a free curve;
(3) Next, a means for determining a rotation axis, a rotation angle, and a width of the display angle on the input screen linked with the drawing screen, and rotating the curve to form a free-form surface;
(4) Next, means for converting the 3D curved surface image data into 2D screen coordinate system data using a perspective method and displaying a figure on a computer display,
Is a three-dimensional computer graphics curve / curved surface model generation device.

  The two-dimensional screen coordinate system data is preferably two-dimensional screen coordinate system data displayed by perspective.

  It is preferable that the apparatus further includes means capable of seeding.

  The two-dimensional figure displayed by the perspective method is preferably rotatable.

The present invention also provides
(1) Enter multiple specified points on the drawing screen.
(2) Connect the designated points that you entered sequentially with a spline curve to form a free curve,
(3) Next, on the input screen linked with the drawing screen, the rotation axis, the rotation angle, the width of the display angle are determined, the curve is rotated, and a free-form surface is formed.
(4) Next, three-dimensional computer graphics curve / curved surface modeling comprising converting the above three-dimensional image data into two-dimensional screen coordinate system data using a perspective method and displaying a figure on a computer display. system.

  The two-dimensional screen coordinate system data is preferably two-dimensional screen coordinate system data expressed in perspective.

  It is preferable that the system further includes means capable of seeding.

  It is preferable that the obtained two-dimensional figure can be rotated.

The three-dimensional computer graphic model apparatus of the present invention and the system therefor have an effect that it is easier to draw a three-dimensional shape composed of smooth curves passing through a designated point, as compared with a conventional three-dimensional modeling system. .

  The apparatus and system of the present invention can draw a three-dimensional model of a three-dimensional curved body. In the present invention, several devices and systems are provided to draw these various three-dimensional models.

(apparatus)
Embodiments of the apparatus and system of the present invention will be described in detail. As a device for carrying out the system of the present invention, a personal computer (personal computer) is preferably used. The personal computer has a display for displaying data and diagrams, a keyboard and mouse for inputting data, a main body for calculating, outputting and storing the data entered by launching the stored program, and necessary. In accordance with the above, it is composed of an additional storage device such as a computer disk or a server for storing programs and data.

  In the present invention, a three-dimensional object is formed by inputting on a drawing screen or an input screen using a mouse of a personal computer. In the model generation apparatus or modeling system of the present invention, a plurality of screens such as a drawing screen, a perspective three-dimensional object representation and rotation screen, and a data display screen are prepared as screens on the display. These screens may be switched one by one or may be displayed as a number of frames on one screen.

(object)
In this specification, the object includes both an object to be three-dimensionalized and a three-dimensional object on the screen in which the object is drawn by the method of the present invention.

Next, an apparatus and a generation system for a curved body three-dimensional computer model will be described. To generate a curved body 3D computer model,
(1) means for inputting a plurality of designated points on the drawing screen;
(2) means for connecting the input designated points sequentially with a spline curve to form a free curve;
(3) Next, a means for determining a rotation axis, a rotation angle, and a width of the display angle on the input screen linked with the drawing screen, and rotating the curve to form a free-form surface;
(4) Next, means for converting the 3D curved surface image data into 2D screen coordinate system data using a perspective method and displaying a figure on a computer display,
Is used.

  In the system of the present invention, in order to obtain a curved body three-dimensional computer graphic model, first, three or more points are drawn by clicking the mouse on the two-dimensional input screen.

  The input designated points are automatically connected sequentially in a curve to form a free curve. As a curve at this time, a cubic spline curve is used in the present invention.

Therefore

Substituting equation (3) into equation (6) yields equation (7).

(Boundary condition for cubic spline interpolation function)
Since the above equation (8) has n unknowns, two conditional equations are insufficient to solve the above simultaneous equations. This deficiency can be solved by additionally specifying boundary conditions at the start and end points of the curve. There are the following four kinds of boundary conditions, and the user can select and use one of them according to the purpose.

(Natural condition: When the second derivative at the end point is 0)
The natural condition is equivalent to setting the curvature at the end point to 0, and corresponds to a natural state where bending is not applied to the end point when the curve is considered as a beam. In this case, since the following equation (9) holds, an n-ary simultaneous equation obtained by adding equation (10) to equation (8) is solved.

(Fixed condition: When specifying the first derivative at the end point)

(Periodic condition: When the values of the first and second derivatives at both end points are equal)
The ambient condition is effective when generating a sine curve or a closed curve. In the case of the periodic condition, since Equation (12) is established, an n-1 element simultaneous equation obtained by adding Equation (13) to Equation (8) is solved.

(Anti-periodic condition: Periodic condition that inverts the positive and negative of the first and second derivatives at both ends)
In the case of an anti-periodic condition, an n-1 element simultaneous equation obtained by adding equation (14) to equation (9) is solved.

(Solution of cubic spline interpolation function)
When the boundary conditions are a natural condition and a fixed condition, an n-ary ternary equation such as Expression (15) is obtained by adding Expressions (10) and (11) to Expression (8). The diagonal term is dominant and a unique solution is required.

An efficient LU decomposition method can be used for solving the equation (13).

The periodic condition and the anti-periodic condition can be solved by a more general LU decomposition method or Gaussian elimination method.

(Curve modeling algorithm)
The curve modeling algorithm of the present invention will be described with reference to the flow sheet of FIG. The curve modeling according to the present invention is created, for example, by the following procedure.

Step 1 Draw a two-dimensional curve.
A point is drawn on a two-dimensional drawing screen, and a curve is drawn with a cubic spline interpolation function.
Step 2 Adjust the curve.
Adjust the shape of the curve in the interface.
Step 3 The curved surface is rotated to form a curved surface.
The curve is expressed in three dimensions, the rotation axis, the rotation angle, and the width of the display angle are determined, and the curved surface is constructed by adding rotation.
Step 4 Express a free-form surface.
Display the curved surface on the 2D screen using perspective. Rotate animation.

A procedure for creating a three-dimensional curve model in the system of the present invention will be described in detail step by step according to one embodiment. In the present invention, first, in step 1, a two-dimensional curve is drawn. Specifically, first, the mouse is left-clicked at an arbitrary position on the two-dimensional drawing screen, and three or more points are designated as shown in FIG. After specifying the points, click the curve drawing button.

In the system of the present invention, the system calculates a cubic spline interpolation function, and a curve passing through a specified point is drawn on the first frame as shown in FIG.

If you want to change the curve, click the point move button in step 2 and drag the mouse point to the drawn point to move the point to an arbitrary position as shown in Fig. 5. Is drawn. (Refer to FIG. 5) It is also possible to delete an existing point and add a new point for correction.

(Setting of angle and axis)
In the system of the present invention, in step 3, a curve is expressed in a three-dimensional relative coordinate space, as shown in FIG. For easier confirmation, the curve drawing body can be rotated around the axis as shown in FIG. The data required for rotation is the rotation angle (from 0 to 360 degrees), the width of the angle, and the reference axis (x axis, y axis, z axis, arbitrary axis) for rotation. One.

An initial value is given in advance for easy use. In addition, an interface that can set these data and is easy to visually determine is prepared. That is, the start point coordinate and the end point coordinate of each of the x axis, the y axis, and the z axis are provided, and it is possible to rotate around any axis. Click the angle button to rotate, you can change the angle. When data that rotates around an arbitrary axis is set, a simple demo can be displayed as shown in FIG. 8 to confirm whether the rotation surface is satisfactory.

  In the system of the present invention, in step 4, a free-rotation curved surface is expressed as shown in FIG. That is, a rotating curved surface is created based on the set data and the coordinates of the curve. At this time, a rotating curved surface defined in three dimensions using a perspective method is expressed on a two-dimensional screen screen so that the rotating curved surface created using animation can be easily grasped visually.

A step of creating a three-dimensional curve model is shown in the first embodiment. 11, 12, and 13 show the rotation curved surfaces drawn by rotating the spline curve arbitrarily drawn in FIG. 10 around the x, y, and z axes in the first embodiment. First, the user designates a plurality of points by sequentially clicking on the drawing screen shown in FIG. A spline curve that passes through these points is automatically drawn.

  The rotation curved surface drawn by rotating the spline curve of FIG. 10 around the x axis is shown in FIG. 11, the rotation curved surface drawn by rotating around the y axis is rotated around the z axis in FIG. The drawn curved surfaces are shown in FIG.

(Example 2)
The procedure for generating a partially rotated curved surface in the curved line model of the present invention will be shown by another embodiment. First, the user designates five points on the drawing screen shown in FIG. A spline curve that passes through these points is automatically drawn.

  Next, a curved surface generated by partially rotating the spline curve of FIG. 14 around the y axis is shown on the left in FIG. 15, and a curved surface obtained by partially rotating around the z axis is shown on the right of FIG.

(Hidden line processing)
The three-dimensional curve / curved surface model obtained by the apparatus and system of the present invention is further three-dimensionally expressed by hidden line erasure that erases invisible lines hidden by the surface in front when viewed from the viewpoint. can do. As a specific processing process of hidden line removal, first, each line segment is tested with respect to all surfaces to see whether a part or all of them are hidden by the surface from the viewpoint. If there is an invisible part, extract only the visible part. A boundary point between the visible part and the invisible part is obtained from the line segment and the surface. If the line is not hidden on any surface, draw this line. When a face is obstructed by other faces when viewed from the viewpoint, the invisible part is erased. For this hidden surface removal, a Z sort method (painter algorithm, depth sort method, paint overlay method), a Z buffer method (depth buffer method, depth buffer method) or the like can be used.

(shading)
Next, in order to display an object in a more three-dimensional manner, input the object shape specification, object color specification, light source color, position, etc. The shading that fills with can be performed.

The three-dimensional computer graphics curve / curved surface model generation apparatus and system thereof according to the present invention can be widely used for applications such as computer graphics education for elementary and junior high school students, or animation creation in television advertisements and the like.

FIG. 1 is an explanatory diagram of a spline curve. FIG. 2 is a diagram showing an example of a flow sheet of the system of the present invention. FIG. 3 is a diagram showing a state in which a point is designated in the first frame. FIG. 4 is a diagram illustrating a state in which a spline curve is drawn in the first frame. FIG. 5 is a diagram showing a state in which the spline curve drawn in FIG. 3 is corrected in the first frame. FIG. 6 is a diagram showing three-dimensional modeling formed by rotating a spline curve. FIG. 7 is a diagram illustrating a situation where the three-dimensional model is rotated. FIG. 8 is a screen for confirming the drawn three-dimensional curve model. FIG. 9 is a screen representing a free-form surface in the second embodiment. FIG. 10 is an image depicting a spline curve in the second embodiment. FIG. 11 is a diagram showing a three-dimensional frame model formed by rotating the spline curve of FIG. 10 around the x axis. FIG. 12 is a diagram showing a three-dimensional frame model formed by rotating the spline curve of FIG. 10 around the y axis. FIG. 13 is a view showing a three-dimensional frame model formed by rotating the spline curve of FIG. 10 around the z-axis. FIG. 14 is an image depicting a spline curve in the third embodiment. FIG. 15 is a diagram showing a three-dimensional frame model formed by rotating the spline curve of FIG. 14 around the y-axis. FIG. 16 is a diagram showing a three-dimensional frame model formed by rotating the spline curve of FIG. 14 around the z axis.

Claims (8)

(1) means for inputting a plurality of designated points on the drawing screen;
(2) means for connecting the input designated points sequentially with a spline curve to form a free curve;
(3) Next, a means for determining a rotation axis, a rotation angle, and a width of the display angle on the input screen linked with the drawing screen, and rotating the curve to form a free-form surface;
(4) Next, means for converting the 3D curved surface image data into 2D screen coordinate system data using a perspective method and displaying a figure on a computer display,
A three-dimensional computer graphics curve / curved surface model generation device.   2. The three-dimensional computer graphics curve / curved surface model generating apparatus according to claim 1, wherein the two-dimensional screen coordinate system data is two-dimensional screen coordinate system data displayed by perspective.   3. The three-dimensional computer graphics curve / curved surface model generating apparatus according to claim 1, further comprising means capable of shading.   4. The three-dimensional computer graphics curve / curved surface model generating apparatus according to claim 1, wherein a two-dimensional figure displayed by a perspective method is arbitrarily rotatable. (1) Enter multiple specified points on the drawing screen.
(2) Connect the designated points that you entered sequentially with a spline curve to form a free curve,
(3) Next, on the input screen linked with the drawing screen, the rotation axis, the rotation angle, the width of the display angle are determined, the curve is rotated, and a free-form surface is formed.
(4) Next, three-dimensional computer graphics curve / curved surface modeling comprising converting the above-mentioned three-dimensional image data into two-dimensional screen coordinate system data using a perspective method and displaying a figure on a computer display. system.   6. The three-dimensional computer graphics curve / curved surface modeling system according to claim 5, wherein the two-dimensional screen coordinate system data is two-dimensional screen coordinate system data displayed by perspective.   The three-dimensional computer graphics curve / curved surface modeling system according to claim 5, further comprising means capable of seeding. The three-dimensional computer graphics curve / curved surface modeling system according to claim 5, wherein a two-dimensional figure displayed by perspective is rotatable.

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