JP2005208867A - Three-dimensional computer graphics modeling system - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an easier three-dimensional computer graphics modeling system easy to grasp three-dimensional shape as compared to a conventional three-dimensional figure modeling system. <P>SOLUTION: In this system, (1) the front face of a polyhedron object is determined, (2) all vertexes and sides when viewing the polyhedron object from the front face are drawn on a drawing screen of a display, two-dimensional shape of the front face of the polyhedron object is determined, (3) depth direction information about all the vertexes when viewing it from the front face is determined, (4) the sides connecting the respective vertexes of the front face and the respective vertexes of the backside are edited, (5) and three-dimensional polyhedron figure image data are converted into two-dimensional screen coordinate system data to display a three-dimensional figure on the computer display. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

  The present invention relates to a three-dimensional computer graphics modeling system that inputs and generates a three-dimensional model from a two-dimensional figure shape.

  In recent years, a method has been proposed in which a three-dimensional model of a product is virtually created 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 frame model is most frequently used. In general, a wire screen model as shown in FIG. 1 is represented by information on each surface of the object.

  According to the conventional modeling method, the wireframe model first defines all vertices (x, y, z), all sides, and surface lists on each surface as shown in FIG. 2 by a three-dimensional world coordinate system. These data are incorporated into a drawing program or a data file, and then data in the three-dimensional world coordinate system is converted into data in the two-dimensional screen coordinate system to represent the object three-dimensionally on the computer display.

  However, in such a method, as the shape of the object to be expressed becomes complicated, it becomes very difficult to input the definition and data of each vertex of the object by the 3D world coordinate system. It's difficult for people with no knowledge of graphics.

Several proposals have been made for a simplified method of the three-dimensional drawing method using the wire frame model. For example, Patent Document 1 displays a conceptual diagram or drawing on a screen, defines a cross-sectional shape by tracing them, defines dimension values, constraint conditions, and depth, and defines a three-dimensional shape based on these definitions. A method of generating is proposed. Although this method is simple, since it is necessary to obtain the value of each element, it is not easy to collect the data.
JP 7-78271 A JP 2001-6004 A

  Patent Document 2 is a system related to a method of generating a two-dimensional image data from a plurality of mutually different coordinate planes, specifically, a three-dimensional screen using a front view and a side view. It is hard to say that the system is large and inexpensive.

  An object of the present invention is to provide a three-dimensional computer graphics modeling system that is easier and easier to grasp a three-dimensional shape than a conventional three-dimensional graphic modeling system.

That is, the present invention
(1) Determine the front of the polyhedral object,
(2) Draw all the vertices and sides when the polyhedral object is viewed from the front on the drawing screen of the display, determine the two-dimensional shape of the front of the polyhedral object,
(3) Determine the depth direction information of all vertices when viewed from the front,
(4) Edit the edges connecting the front vertices and the back vertices as necessary,
(5) Next, the three-dimensional computer graphics modeling of the polyhedron figure comprising converting the three-dimensional polyhedron figure image data into two-dimensional screen coordinate system data and displaying a three-dimensional figure on a computer display.・ It is a system.

The present invention also provides
(1) Determine the front and back of the cylinder or cone object,
(2) On the input screen, determine the radius (lateral radius) in the x-axis direction and the radius (vertical radius) in the y-axis direction when the object is viewed from the front,
(3) The x-axis direction radius (lateral radius) and the y-axis direction radius (longitudinal radius) on the back surface are determined by questions.
(4) Determine the length of the cylinder and the inner diameter of the cylinder,
(5) Determine the relative positional relationship between the front surface and the back surface,
(6) The obtained three-dimensional cylinder or cone graphic image data is converted into two-dimensional screen coordinate system data to display a three-dimensional graphic on a computer display. Modeling system.

The present invention also provides
(1) Determine the number of cuts of the spherical object (2) Radius with respect to the x-axis,
(3) radius with respect to the y-axis,
(4) Determine the radius with respect to the z-axis,
(5) The obtained three-dimensional spherical figure image data is converted into two-dimensional screen coordinate system data, and a three-dimensional computer graphics of spherical figure consisting of displaying a three-dimensional figure on a computer display Modeling system.

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

  It is preferable that the three-dimensional figure displayed by the perspective method can be rotated.

It is preferable that the three-dimensional figure displayed by the perspective method can be scale-deformed.

  According to the three-dimensional computer graphics modeling system of the present invention, in the conventional three-dimensional animation method, it is necessary to calculate the coordinates of each vertex every time a solid is changed, which requires much labor. Compared to the above, a three-dimensional object can be obtained by a simple method. In addition, by using the perspective method, a three-dimensional model can be easily obtained, and the computational effort in animation is simply changed by changing ρ, φ, θ of the matrix V and the distance variable d between the viewpoint E and the screen. Is shortened. Moreover, animation can be smoothly displayed on the display screen.

An embodiment of the present invention will be described in detail. As hardware for implementing 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 graphic object is formed by inputting using a mouse of a personal computer. In the 3D computer graphics modeling system of the present invention, the screen on the display includes a front 2D shape drawing screen, a system control screen linked to the drawing screen, a depth data input screen, a front side editing screen, A plurality of screens such as a back side edit screen, a perspective three-dimensional object representation and rotation screen, a cylinder and sphere data input screen, and a data display screen are prepared. These screens may be switched one by one or may be displayed as a number of frames on one screen.

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

  In the three-dimensional computer graphics modeling system of the present invention, the front and back shapes of an object are defined by drawing all vertices and sides when viewed from the front directly on the drawing input screen of the system. By defining the depth direction information of all front vertices on the depth data input screen of the system, the side between the front and back sides, that is, the shape of the object in the depth direction is defined, and the front side list and back side By editing the edge list on the edge editing screen of the system, a plurality of edges and vertices having the same position on the front surface and different positions in the depth direction can be expressed, thereby forming a three-dimensional object.

  In the system of the present invention, first, attention is paid to the front surface of the object, and the positions of all vertices and sides of the object viewed from the front surface are defined by drawing. The surface to be selected as the front surface of the object is not particularly limited, but preferably, the surface of the present invention can be obtained by selecting a surface that is easy to draw and has many overlapping vertices on the back surface when viewed from the front surface. It is preferable because it is easy. In the case of an object in which a circle is a part of the constituent surface, such as a cylinder or a cone, it is preferable to use the circle as the front surface or back surface because it is easy to draw.

  FIG. 3 is a drawing screen on the display for drawing the two-dimensional shape of the front surface of the object in the system of the present invention. Preferably, a grid is also displayed on the screen to facilitate the definition of the cross-sectional shape. As a guideline for the drawing screen size, the center is (0,0), the x axis is (-10,10), and the y axis is (-10,10). In conjunction with this screen, system control functions such as data reset, data storage / display, proceed to the next, and system termination may be provided.

  In order to obtain a three-dimensional wire model by the three-dimensional computer graphics modeling system of the present invention, an operator first draws the front surface of an object to be created on the screen using a mouse.

  In a preferred embodiment of the present invention, the operator drags from any point on the screen with a left click when drawing a straight line. When the mouse button is released when the target point is reached, a straight line is drawn between the two points. At the same time, the numbers of the start and end vertices of this line are displayed. By repeating such an operation, a front two-dimensional shape model can be created.

  As an example, the object of FIG. 1 is represented. An embodiment of the front vertex input screen in the present invention is shown in FIG. In FIG. 4, the top left vertex of the two-dimensional drawing screen as viewed from the front is started with the number 0, and for example, the vertex numbers whose numerical values are sequentially increased in the clockwise direction are displayed.

  In the above input operation, it is preferable that the vertex numbers are automatically assigned. Further, the drawing positions and drawing order of vertices and straight lines are arbitrary.

Consider the case where there are multiple vertices at the same position on the front. When there are two vertices, it is preferable that vertices other than the front face are automatically displayed as vertices on the back face. If there are three or more vertices, click the mouse for the number of vertices. Vertex numbers are displayed in a line according to the number of clicks. Next, it is preferable that the positions in the depth direction of these vertices are determined separately using a depth data input screen.

On the other hand, if there are multiple sides that overlap the front side, draw only one side, draw an appropriate vertex on this side by clicking the mouse, and then edit the front edge (side) Alternatively, it is preferable that the plurality of sides are distinguished and drawn using the back edge editing screen.

  Once the shape of the two-dimensional figure on the front surface is determined, information on the depth direction of each vertex on the front surface is input next. FIG. 5 is a screen for determining the data in the depth direction of the vertex. A vertex is one vertex when viewed from the front, but in reality this vertex may be two points or one side instead of one point when viewed in the depth direction. For convenience of description and input, the coordinate value in the depth direction of each vertex on the front is called DF. The coordinate value in the depth direction of the vertex on the back surface is called DB. The fact that this vertex has two different depth positions on the front and back surfaces is said to be mapped to the back surface. In the embodiment of FIG. 5, all the front vertices are mapped. For one vertex number, the left numerical value is the DF value of that vertex, and the right numerical value is the DB value corresponding to that vertex. is there. In addition, the initial value of the DF and DB values at each vertex is (10, -10), and can be changed by selection from the respective choice menu.

In the depth data input screen shown in FIG. 5, if the DF and DB values of a vertex do not match, the vertex actually has the same two-dimensional position on the two-dimensional screens on the front and back sides. This means that there are two vertices and there is an edge between the front and back that connects the two vertices. However, it is possible to select whether to draw an edge connecting the front surface and the back surface of the vertex depending on the situation. If the selection is omitted, this edge is automatically drawn. On the other hand, in the depth data input screen shown in FIG. 5, if DF is equal to DB for a certain vertex, it means that there is no edge connecting the vertex between the front surface and the back surface. In this case, it is not necessary to input the drawing check box.

In the system according to the embodiment of the present invention, when the definition by drawing the two-dimensional shape of the front surface is completed, the side of the back surface is automatically defined as the same projection surface as the front surface exists on the back surface. In depth information, the front vertex is automatically entered as 10 and the back vertex is entered as -10 in advance. It is automatically defined. Therefore, since the data input of the 3D object can be completed simply by completing the definition by drawing the 2D shape on the front surface, the OK button on the drawing screen of the 2D shape can be directly pressed to display the 3D object by perspective. This object can be represented and rotated by switching to the representation and rotation screen. If the depth information needs to be corrected, press the EDIT button on the 2D shape drawing screen to switch to the depth information input screen shown in FIG. 5. After changing the front vertex DF or DB value, click the drawing button shown in FIG. Press to switch to a perspective 3D object representation / rotation screen.

In the system of the present invention, side editing is performed next. Even if only one side can be seen at the same position on the front side, if there are actually multiple sides at different positions in the depth direction, or if you want to change the side defined by drawing the front two-dimensional shape, Work with the screen as the editing screen. The screen may be switched to the front edge editing screen by pressing an edit button on the screen of FIG.

On the front edge editing screen, the side defined by the drawing of the front two-dimensional shape is automatically presented. The editing of the front edge is performed, for example, on the front edge editing screen shown in FIG. In the screen of FIG. 6, it is selected and specified whether or not there is an edge connecting from the start point on the left side to a plurality of end points displayed on the right-side choice menus, or a new uninput side is input. The numbers in FIG. 6 indicate that the top row is drawn from vertex 0 to vertex 1 and vertex 5, and the second row shows that the edge is drawn from vertex 1 to vertex 2. . Such side creation is preferably performed while confirming with reference to FIGS. White space indicates no edge. When the front edge editing is completed, press the OK button to switch to the back edge editing screen.

As with the front surface, the edge between the vertices on the back surface is determined by selecting and inputting a numerical value from the choice menu on the screen shown in FIG. When the back edge editing is completed, the screen can be switched to the 3D object representation / rotation screen with the OK button.

  As described above, in the embodiment of the present invention, there are preferably five or more data input screens (frames) for creating a three-dimensional model. After the front two-dimensional shape input by the drawing of FIG. 3 is completed or the input of the depth data of FIG. 5 is completed, the screen may be immediately switched to the three-dimensional object representation / rotation screen of FIG. Further, after completion of the above input, after the front edge editing and the back edge editing performed for editing the vertex and the side superimposed on the same position on the front surface, the screen can be switched to the three-dimensional object representation / rotation screen of FIG. It may be. FIG. 8 shows how the input object of FIG. 1 is expressed and rotated.

In order to check whether or not the input data matches the figure to be drawn, it is preferable to be able to switch to the three-dimensional object representation / rotation screen at any stage of data input. Further, as shown in FIG. 9, it is preferable that the input data is displayed in a frame so that each data can be confirmed in a list. It is preferable to save and redraw figures using these data saving and reading.

  In the above embodiment, the cross-sectional definition position is the two surfaces of the front surface and the back surface of the object. However, in the object, when there are many irregularities between the front surface and the back surface, it is not limited to two surfaces. Using the cross-section definition position as the cross-section definition position where the element between the front and back surfaces changes, the two-dimensional shape and depth information input method is used to define the coordinates of each vertex or side on that surface. May be.

  The procedure for creating the three-dimensional object will be described with reference to another embodiment. The three-dimensional object to be drawn is a rectangular parallelepiped with a triangular missing part in the upper right part shown in FIG. In order to obtain this object, first, on the drawing screen of FIG. 11, a rectangle is drawn by dragging the cursor in the order of 0 → 1 → 2 → 3 → 0 and clicking repeatedly. Next, the side between the vertex 4 and the vertex 5 is drawn by clicking and dragging with the mouse. This completes the definition of the secondary shape in front of the object.

  Next, data in the depth direction is determined on the depth direction determination screen. In the depth direction determination screen, as shown in FIG. 12, in the initial direction screen, all DFs are defined 10 and DB is −10 for vertices 0 to 5 in advance. Therefore, the DF and DB of the vertex whose initial value is different from the target screen are corrected. In the figure of FIG. 10, as shown in FIG. 13, it is not necessary to correct the vertices 1 to 3. Since the vertex 0 is located at a position deeper than the surface formed by the vertices 1, 2, 3, 4, and 5 in the depth direction, the DF of the vertex 0 is corrected to 0. The DB value -10 at the vertex 0 is left as it is. Moreover, since vertices 4 and 5 are the vertices on the front surface, both DF and DB are changed to 10.

  Next, the edge relation is corrected on the front edge relation determination screen. In accordance with the input two-dimensional shape data, the sides on the front side determination screen are automatically displayed in advance as shown in FIG. That is, in the initial state, there are edges between vertex 0 to vertex 1 and vertex 3, between vertex 1 and vertex 2, between vertex 2 and vertex 3, and between vertex 4 and vertex 5. Is assumed to exist. Next, as shown in FIG. 15, the sides on the front face are edited so as to have the side relation of the graphic shown in FIG. That is, of these, the side relation different from the entity is corrected. The sides of the vertices 1, 2 and 3 and the sides of the vertices 4 and 5 do not need to be corrected according to the pre-input data. On the other hand, since there is an edge between vertex 0 to vertex 4 and vertex 5, a new edge having a start point of 0 and an end point of 4 and 5 is inserted. Also, since there are no edges between vertex 0 and vertex 1 and between vertex 0 and vertex 3, 1 and 3 are deleted. Also, a side having a start point of 1, an end point of 5, and a side having a start point of 3 and an end point of 4 are newly added.

  Next, the rear side is corrected in the same manner on the rear side (edge) editing screen. In the graphic shown in FIG. 10, the edge relation does not need to be corrected according to the pre-input data. Finally, when the screen is switched to the three-dimensional object drawing screen, the object shown in FIG. 10 is obtained.

If the object is a cylinder, cone, sphere, or ellipsoid, there are no vertices. In such a case, a figure is created by inputting figure data using a circle or an ellipse using the constraint condition mode.

In the present invention, the constraint condition refers to a condition in a figure constrained by a circle, such as a specific shape and a radius, and a three-dimensional figure composed of a circle can be drawn only by these constraint conditions. Especially when the object is a cylinder, cone, sphere, etc. Data such as the horizontal radius and vertical radius of the circle on the front and back of the cylinder or cone, data such as the radius on the x-axis, the radius on the y-axis, the radius on the z-axis That is, the shape of the figure can be determined by defining constraint conditions.

When creating a cylindrical wire frame model, in the screen of FIG. 16, in the first row of the data input pocket, the circle data on the front surface, from the left, the vertical and horizontal radii of the front circle, and on the second row, the circle on the back surface. Enter the data, vertical radius and horizontal radius of the back circle from the left. Enter the length of the cylinder to the left of the third row. These data define an initial value of 10 in advance, and even if the length input is omitted, the cylinder screen shown in FIG. 17 can be drawn immediately by pressing the cylinder OK button. If the horizontal radius is different from the vertical radius, an ellipse is drawn, and if the length is set to 0, a circle is drawn instead of a cylinder. Further, if one of the front surface, the back surface, and the two circular surfaces is designated as 0, a cone as shown in FIG. 18 is drawn. In the middle of the third stage, there is a choice menu for entering the inner diameter of the cylinder. When the inner diameter is designated, a donut-shaped cylinder as shown in FIG. 19 is drawn.

When creating a three-dimensional model of a cylinder, it is preferable that various figures can be drawn by selecting the number in the cylinder type selection menu and specifying the positional relationship between the front surface and the back surface. For example, 1 indicates a positional relationship in which the front surface and the back surface are connected in parallel with each other as shown in FIG. Reference numeral 2 denotes a positional relationship in which the front surface and the back surface are parallel and connected by an envelope made of a concave curve. 3 indicates a positional relationship in which the front surface and the back surface are parallel and are connected by an envelope made of a convex curve. 4 indicates that the front surface of the ellipse and the back surface of the ellipse are in a positional relationship having an angle of 45 ° as shown in FIG.

  On the other hand, when creating a spherical wire frame model, at the bottom of the input screen in FIG. 16, the constraint conditions such as the number of cuts of the sphere, the radius of the X axis, the radius of the Y axis, the radius of the Z axis are displayed in the choice menu. specify. Data regarding these radii is defined in advance as an initial value of 10. When the sphere (spherical) OK button is pressed with no input, a sphere as shown in FIG. 22 is drawn. If different values are input for the x-axis radius and the y-axis radius, an elliptical sphere as shown in FIG. 23 is drawn.

Similarly, in the case of a free curve, an arc, and a free curved surface, it is preferable that a program for drawing an arc is defined by defining the start point and end of the arc, the radius, and the like. In addition, it is preferable that a defined figure is drawn on the screen when a system control screen object is clicked for squares, rectangles, trapezoids, and other star shapes.

  It is preferable that various data input in the above manner can be corrected. Moreover, it is preferable that the side can be deleted or added by a correction operation. Specifically, it is preferable that the data can be converted or canceled by replacing or deleting the numerical values on the input screens of FIGS. 4 to 7 and pressing the “OK” button.

In the three-dimensional computer graphics modeling system of the present invention, a plurality of differently input figures are simultaneously displayed on a plurality of three-dimensional object drawing screens in parallel, and a plurality of figures using the data of each figure are used. It is preferable that a more complicated new figure is assembled as required by the figure.

  Next, in the three-dimensional computer graphics modeling system of the present invention, the three-dimensional model obtained by the above system is preferably expressed on a display as a two-dimensional image using a perspective method.

  A method for expressing the three-dimensional model obtained by the above method as a two-dimensional image using a perspective method on a display will be described. As a premise, the three-dimensional coordinates are (x, y, z), and the two-dimensional coordinates are (X, Y). The coordinates in the three-dimensional model are called world coordinates. In order to represent the three-dimensional model in two dimensions on the display, each vertex of the world coordinates P (x, y, z) is mapped by the procedure shown in FIG. 'Mapping work to (X, Y).

In the computer graphics modeling system of the present invention, in order to convert the world coordinate system to the screen coordinate, the world coordinate system is once converted to the eye coordinate system, and then the eye coordinate system is converted to the screen coordinate system. Take the technique. To convert the world coordinate system to the eye coordinate system, a viewing transformation is performed. In this viewing transformation, first, by moving the origin O of the world coordinate system where the object is located to the viewpoint E, the object is simultaneously moved so that the midpoint of the object becomes the origin E of the eye coordinate system. .

In order to convert the viewpoint, not only the object but also the viewpoint (viewpoint) E is required. Then place the origin O at the center of the object and look at the object from E to O. In the world coordinate system, given polar coordinates (ρ: distance between object and eye, ψ: value for vertical rotation, θ: value for horizontal rotation), the world coordinates of _E (x _E, y _{E ,} z _E ) can be expressed by the following equation (1), and is graphed as shown in FIG.

  The vector EO (-EO) direction is called viewing direction. The eye coordinate system whose origin is E is as shown in FIG.

By the way, in order to convert the world coordinate system (x _w , y _w, z _w ) into the eye coordinate system (x _e , y _e , z _e ), a viewing matrix V is necessary, and the following equation (2) is established. .

Therefore, if the world coordinates (x _w , y _w, z _w ) are given and the matrix V is obtained, the eye coordinates (x _e , y _e , z _e ) can be obtained. By the way, when the origin is moved from O to E, the matrix T is expressed by the following equation (3). The coordinate system at that time is as shown in FIG.

  Here, a coordinate processing method when rotating the figure will be described. First, consider a case where the image rotates about the Z axis, that is, the image rotates horizontally.

When the coordinate system is rotated by θ around the z-axis, the matrix R _z resulting from this rotation is expressed by the following equation (4). The coordinate system is as shown in FIG. In FIG. 28, the coordinate system is rotated about the z-axis by θ + 90 ° after the origin is moved.

Next, consider the case where the object rotates around the x axis, that is, the object rotates vertically. When the coordinate system is rotated by φ around the x-axis, the matrix R _x resulting from this rotation is expressed by the following equation (5). The coordinate system is as shown in FIG. In FIG. 29, the coordinate system is rotated about the x axis by φ after moving the origin.

When the object is subjected to z-axis and x-axis rotation, that is, combined front-rear and left-right rotation, the object is rotated about the x-axis after the z-axis rotation. As a result, an eye coordinate system having x _e , y _e , and z _e as shown in FIG. 26 is completed. By the multiplication of the above matrices T, R _z , R _x , a viewing matrix V as shown in the following equation (6) is obtained. By substituting this matrix V into equation (2), the eye coordinates (x _e , y _e , z _e ) can be obtained from the world coordinates (x _w , y _w, z _w ).

  Next, a method of incorporating a perspective method into a two-dimensional display in the three-dimensional computer graphic modeling method of the present invention will be described. After converting to the eye coordinate system, perspective transformation (conversion based on perspective) is performed.

  The effect of perspective is inversely proportional to the distance between the object and the eye. If the eyes and the object are close, the perspective effect becomes stronger and the object looks larger. If the object is far away, it will appear small.

  The principle of obtaining the screen coordinates by the perspective method will be described with reference to FIG. In FIG. 30, a point Q whose eye coordinates are (0,0, -d) is first selected. However, d is positive.

  From the viewpoint, the screen in the eye coordinate system is in the z = -d plane. That is, the plane passes through Q and is perpendicular to the z-axis. At that time, the origin of the screen coordinate system is Q, and the X and Y axes of the screen coordinate system are parallel to the x and y axes of the eye coordinate system. In order to obtain x in FIG. 30, a point P having a y value of 0 is newly placed.

  In FIG. 30, the following formulas (7) and (8) are obtained by utilizing the fact that the triangles EPR and EP′Q are similar.

  Similarly, the following equation (9) is obtained.

  If the origin Q of the screen coordinate system (X, Y) is placed at the center of the screen, equations (8) and (9) are used. FIG. 31 shows the relationship between the viewpoint E, the screen, and the object projected on the screen.

The following formula (10) is obtained from the distance d between the viewpoint E and the screen and the similarity between the triangles EP ′ ₁ P ′ ₂ and EP ₁ P ₂ .

  In the above equation, since the distance ρ between the viewpoint and the screen is known and the size and depth of the object are already obtained from the three-dimensional model, these values are substituted into equation (10), The coordinates of the image on the screen can be obtained.

Specifically, the following procedure is used.
(1) Number each vertex P on the front of the solid and specify the coordinates (DF, DB, Tx, Ty) of each vertex.
(2) If DF and DB have the same value, conversion is performed only once (DF, Tx, Ty) or (DB, Tx, Ty).
(3) When DF and DB are different, (DF, Tx, Ty) and (DB, Tx, Ty) are converted.
(4) Finally, in accordance with the front edge list and the back edge list, an object is drawn by connecting vertices that specify the start point number and end point number of each edge (side) with a line.
(5) In the case of a circle, cylinder, or cone, the position coordinates of the circle and the coordinates (FD, Tx, Ty) obtained by dividing the circumference are converted and drawn by the above procedure. In the case of a sphere, three coordinate values (x, y, z) in the spherical coordinate system are calculated according to the number of cuts of the sphere and the three axis radii, and conversion and line drawing are performed according to the above procedure.

  With the above conversion, the three-dimensional eye coordinates are converted into the two-dimensional screen coordinates, and the conversion by the perspective method is completed. Also, the three-dimensional world coordinates are converted into two-dimensional screen coordinates, and a three-dimensional object can be expressed in two dimensions.

  In the system of the present invention, the figure can preferably be rotated. As shown in FIG. 8, buttons for performing horizontal rotation, vertical rotation, horizontal and vertical simultaneous rotation, arbitrary axis rotation that rotates around a specified arbitrary linear axis, rotation pause, etc. are provided. It may be. Specifically, when φ increases, it rotates upward, and when it decreases, it rotates downward. Further, when θ is increased, it rotates to the left, and when it decreases, it rotates to the right. A rotation speed variable button may be provided so that the rotation speed can be adjusted.

  In the system of the present invention, it is preferable that the scale of the figure can be enlarged or reduced. A scale button and a scale adjustment screen may be provided on the three-dimensional figure rotation screen. It is preferable that the three-dimensional figure obtained according to the figure scale adjustment is enlarged or reduced while rotating to further enhance the perspective effect. By changing the distance variable d between the viewpoint E and the screen, the scale deformation of the figure, that is, the enlargement and reduction of the figure can be executed together with the rotation. If the adjustment value is small, d increases and the figure is enlarged. Conversely, if the adjustment value is large, d decreases and the figure is reduced.

  Since the system of the present invention can be used for 3D computer graphics education, the figure screen of the obtained 3D model can be enlarged to the full screen of the display or reduced to a quarter of the display. A button may be provided.

In addition, a color adjustment button that can freely set colors such as the whole object, surface, line color, and background color of the obtained three-dimensional model screen may be provided. For example, three scroll bars can be provided to adjust the degree of red, green, and blue. Furthermore, by providing a brightness button, the entire screen, background, or object brightness or darkness can be changed.

The picture data created by the above method can be saved. As is well known, storage can be performed by hardware such as a ROM, CD-ROM, MO, flexible disk, flash memory, and server of a personal computer.
You can also open a saved graphic file and display the graphic again.

  The system of the present invention is provided with functions such as system start, data reset, and system end as in other general systems.

Next, three-dimensional figures obtained using the three-dimensional computer graphics modeling system of the present invention will be exemplified, but the present invention is not limited to these examples. These are all three-dimensional figures drawn and drawn using this system.

(Example 1 / cuboid)
A rectangular shape is drawn using the input screen of FIG. 3 described above, and the wireframe model expressed using the initial values on the depth data input screen of FIG. 5 as they are is shown in FIG.

(Example 2 / Cube with a part missing)
Using the input screen of FIG. 3, a rectangle and a triangle were drawn, and the values on the depth data input screen, front edge and back edge determination screen were corrected. The obtained wire frame model is shown in FIG.

(Example 3 / triangular pyramid)
The two-dimensional front shape of FIG. 34 was drawn, and depth data was designated as shown in FIG. The obtained triangular pyramid wire frame model is shown in FIG.

(Example 4 / Square pyramid)
The two-dimensional front shape of FIG. 37 was drawn, and depth data was designated as shown in FIG. FIG. 39 shows the obtained wire frame model of a quadrangular pyramid.

(Example 5/8 cube in which a part of the ridges is missing)
The front two-dimensional shape was drawn, the depth data was input, the front edge was edited, and the back edge was edited in the same procedure as in FIGS. FIG. 40 shows a cubic wire frame model in which some of the obtained eight edges are missing.

(Example 6 / polyhedron)
This example is an example of a polyhedron having a plurality of vertices at the same position on the front surface. First, one square was drawn on the drawing input screen of the front two-dimensional shape. Next, each vertex of the square is clicked once to generate three vertices at the same position when viewed from the front. Further, the depth data of each vertex was input in the same manner as in the above example, and the front edge and the back edge were edited. The obtained polyhedron wire frame model having a plurality of sides and faces in the depth direction is shown in FIG.

(Example 7 / star prism)
A star shape was drawn using the input screen of FIG. The initial values on the depth data input screen in FIG. 5 were used as they were. FIG. 42 shows the obtained wire frame model of a star prism.

(Example 8 / Oval cylinder)
On the circle input screen of FIG. 16, the horizontal radius of the front circle is set to 10, the vertical radius is set to 5, the horizontal radius of the back circle is set to 5, and the vertical radius is set to 10 in the choice menu. The obtained elliptical cylindrical wire frame model is shown in FIG.

(Example 9 / doughnut-shaped cylinder)
On the circle input screen in FIG. 16, the horizontal radius and vertical radius of the front circle and the horizontal radius and vertical radius of the back circle are the choices except that the length of the cylinder is changed to 5 and the inner diameter is specified as 5. The initial value on the menu was used as it was. The obtained donut-shaped cylindrical wire frame model is shown in FIG.

(Example 10 / sphere with 12 cuts)
On the circle input screen of FIG. 16, the initial value on the choice menu is used as it is for the x-axis radius, y-axis radius, and z-axis radius of the sphere, and the number of cuts of the sphere is specified as 12. FIG. 45 shows a sphere wire frame model in which the obtained number of cuts is 12.

Example 11 Synthesis of Cube and Square Pyramid
Draw squares and triangles using the input screen shown in Fig. 3. On the depth data input screen shown in Fig. 5, modify both the DF and DB values of the vertices above the triangle to 0, and the initial values of DF and DB at the other vertices. The value was left as it was. FIG. 46 shows a wire frame model of a composite of the obtained cube and square pyramid.

(Example 12 / house type)
The house-type front surface was drawn using the input screen of FIG. 3, and the initial values on the depth data input screen of FIG. 5 were used as they were. The house type wire frame model obtained is shown in FIG.

(Example 13 / Composition of a plurality of square pyramids)
In the same procedure as described above, a rectangle was drawn and input, and the sides were further edited to create a plurality of quadrangular pyramids. The obtained wire frame model is shown in FIG.

(Example 14 / Composition of a plurality of rectangular parallelepipeds)
In the same procedure as described above, drawing of a plurality of squares was input, and the sides were further edited. FIG. 49 shows the obtained wire frame model.

(Example 15 / Composition of a plurality of rectangular parallelepipeds)
In the same procedure as described above, a trapezoidal quadrangle and a rectangle were drawn and input, and depth information was input and sides were edited. The obtained wire frame model is shown in FIG.

  The 3D computer graphics modeling system of the present invention has a simple configuration, can be manufactured at low cost, and its operation is simple and easy to understand. It is useful for computer graphics enthusiasts, or as a 3D computer graphics education software by drawing 3D figures easily, especially as a drawing software for elementary, junior high and high school students. It is.

FIG. 1 is an example of a polyhedral wire frame model. FIG. 2 is an example of a data list used in the conventional modeling system for the polyhedron of FIG. FIG. 3 is an example of a screen for drawing and inputting the two-dimensional shape of the front surface. FIG. 4 is a drawing input screen of the front two-dimensional shape of the object shown in FIG. FIG. 5 is an example of a depth determination direction data determination screen. FIG. 6 is an example of the front edge editing screen. FIG. 7 is an example of the back edge editing screen. FIG. 8 is an example of the polyhedral three-dimensional object representation / rotation screen of FIG. FIG. 9 is an example of the polyhedron input data list display screen shown in FIG. FIG. 10 shows an example of a polyhedral three-dimensional object. FIG. 11 is a two-dimensional drawing screen for obtaining the three-dimensional object of FIG. FIG. 12 is an initial screen of the depth direction determination screen for obtaining the three-dimensional object of FIG. FIG. 13 is a modification screen of the depth direction determination screen for obtaining the three-dimensional object of FIG. FIG. 14 is an initial screen of the front side edit screen for obtaining the three-dimensional object of FIG. FIG. 15 is a correction screen of the front side editing screen for obtaining the three-dimensional object of FIG. FIG. 16 is an example of a circle and cylinder constraint condition input screen. FIG. 17 is a cylindrical three-dimensional object created by the system of the present invention. FIG. 18 is a conical three-dimensional object created by the system of the present invention. FIG. 19 is a three-dimensional object of a donut-shaped cylinder created by the system of the present invention. FIG. 20 is an example of a deformed cylindrical three-dimensional model. FIG. 21 is an example of a deformed cylindrical three-dimensional model. FIG. 22 shows an example of a three-dimensional sphere object created by the system of the present invention. FIG. 23 is an example of an elliptic sphere three-dimensional object created by the system of the present invention. FIG. 24 is a process chart showing a procedure for mapping world coordinates to screen coordinates. FIG. 25 is a graph showing the viewpoint in world coordinates. FIG. 26 is a graph showing eye coordinates whose origin is E. FIG. 27 is a graph showing eye coordinates. FIG. 28 is a graph showing a coordinate system when rotated by θ + 90 ° around the z-axis. FIG. 29 is a graph showing a coordinate system when rotated by ψ + 90 ° about the x-axis. FIG. 30 is an explanatory diagram for explaining the principle of obtaining screen coordinates by perspective. FIG. 31 is a diagram showing the relationship between the viewpoint, the object projected on the screen, and the screen. FIG. 32 is an example of a three-dimensional wire frame model created by the system of the present invention. FIG. 33 is an example of a three-dimensional wire frame model created by the system of the present invention. FIG. 34 is a front drawing screen for obtaining the three-dimensional wire frame model of FIG. FIG. 35 is a depth direction determination screen for obtaining the three-dimensional wire frame model of FIG. FIG. 36 is an example of a three-dimensional wire frame model created by the system of the present invention. FIG. 37 is a front drawing screen for obtaining the three-dimensional wire frame model of FIG. FIG. 38 is a depth direction determination screen for obtaining the three-dimensional wire frame model of FIG. FIG. 39 is an example of a three-dimensional wire frame model created by the system of the present invention. FIG. 40 is an example of a three-dimensional wire frame model created by the system of the present invention. FIG. 41 is an example of a three-dimensional wire frame model created by the system of the present invention. FIG. 42 is an example of a three-dimensional wire frame model created by the system of the present invention. FIG. 43 is an example of a three-dimensional wire frame model created by the system of the present invention. FIG. 44 shows an example of a three-dimensional wire frame model created by the system of the present invention. FIG. 45 is an example of a three-dimensional wire frame model created by the system of the present invention. FIG. 46 shows an example of a three-dimensional wire frame model created by the system of the present invention. FIG. 47 is an example of a three-dimensional wire frame model created by the system of the present invention. FIG. 48 is an example of a three-dimensional wire frame model created by the system of the present invention. FIG. 49 shows an example of a three-dimensional wire frame model created by the system of the present invention. FIG. 50 is an example of a three-dimensional wire frame model created by the system of the present invention.

Claims (6)

(1) Determine the front of the polyhedral object,
(2) Draw all the vertices and sides when the polyhedral object is viewed from the front on the drawing screen of the display, determine the two-dimensional shape of the front of the polyhedral object,
(3) Determine the depth direction information of all vertices when viewed from the front,
(4) Edit the edges connecting the front vertices and the back vertices as necessary,
(5) Next, the three-dimensional computer graphics modeling of the polyhedron figure comprising converting the three-dimensional polyhedron figure image data into two-dimensional screen coordinate system data and displaying a three-dimensional figure on a computer display. ·system. (1) Determine the front and back of the cylinder or cone object,
(2) On the input screen, determine the radius (lateral radius) in the x-axis direction and the radius (vertical radius) in the y-axis direction when the object is viewed from the front,
(3) Next, determine the radius in the x-axis direction (lateral radius) and the radius in the y-axis direction (longitudinal radius) on the back surface,
(4) Determine the length of the cylinder and the inner diameter of the cylinder,
(5) Determine the relative positional relationship between the front surface and the back surface,
(6) The obtained three-dimensional cylinder or cone graphic image data is converted into two-dimensional screen coordinate system data to display a three-dimensional graphic on a computer display. Modeling system. (1) Determine the number of cuts of the spherical object (2) Radius with respect to the x-axis,
(3) radius with respect to the y-axis,
(4) Determine the radius with respect to the z-axis,
(5) The obtained three-dimensional spherical figure image data is converted into two-dimensional screen coordinate system data, and a three-dimensional computer graphics of spherical figure consisting of displaying a three-dimensional figure on a computer display Modeling system.   The three-dimensional computer graphics modeling system according to claim 1, wherein the two-dimensional screen coordinate system data is two-dimensional screen coordinate system data displayed by perspective.   The three-dimensional computer graphics modeling system according to claim 4, wherein the three-dimensional figure displayed by perspective is rotatable.   6. The three-dimensional computer graphics modeling system according to claim 4, wherein the three-dimensional figure displayed by perspective is deformable in scale.