JPH0766309B2 - How to display points on a three-dimensional figure - Google Patents

Description

The present invention relates to a method of displaying three-dimensional coordinate points suitable for operating a three-dimensional curved surface defined in a computer.

In an interactive graphic processing system, an operator displays a graphic defined in a computer on a screen of a graphic display, and while watching it, operates a defined graphic or defines a new graphic. In that case, coordinate input becomes indispensable.

The coordinate input method includes a method of directly inputting coordinate values by a keyboard or the like, and a method of using a graphic display and a coordinate input device (tablet, dial, etc.) included in the graphic processing system.

The method of directly inputting the numerical value is effective when the numerical value is known in advance, but it is necessary to check the points on the curve or curved surface generated in the computer or the points that are not displayed in the design drawing input to the computer. Although it takes a lot of desk calculation to input, there are cases where it is impossible as described later.

In interactive graphic processing, how to use a coordinate input method using a graphic display and a coordinate input device is very important. The two conventional methods will be described below.

The first conventional method is shown in FIGS. 1 and 2. FIG. 1 shows a method for designating points on a plane in a two-dimensional space, and FIG. 2 shows a method for designating points on a plane in a three-dimensional space. First, the planes (4 and 5) in the coordinate space in the computer are associated with the display screen 1, and the input area 2 of the coordinate input device is associated with the display screen 1. The operator moves the cursor or pen (or dial) of the coordinate input device to display the local echo 7 of the pointing point 6 on the screen 1, moves the pen to a desired position while watching it, and then depresses the pen. By doing so, the coordinates are input to the computer. The input point is the point 8 corresponding to the local echo 7 on the display surface 1.

In these methods, since the input method is essentially two-dimensional, there is a drawback that it is impossible to specify a curve that does not lie on a plane or a point on a curved surface.

An object of the present invention is to provide a display method capable of inputting a desired point on a three-dimensional curved curved surface defined in a computer in an interactive graphic processing system configured by using a two-dimensional graphic display. Especially.

In the present invention, it is utilized that the curved surface defined inside the computer is obtained by mapping the virtual two-dimensional square area (hereinafter referred to as UV area) with a predetermined relationship. That is, the three-dimensional curved surface stored in the computer is projected on a certain projection plane, and the graphic in the projection plane is displayed on the display screen. When designating a point on this three-dimensional curved surface, the designated point coordinates on the coordinate input device (or its fixed area) are converted into coordinates within the UV area.

Further, the U and V coordinates are converted into points on the three-dimensional curved surface by using the above-mentioned mapping relation. Further, the changed point is projected on the above-mentioned projection plane, and a predetermined fixed pattern such as + shown in FIGS. 1 and 2 is displayed at the display position corresponding to the projected point position. Or a pattern as shown in FIGS. 5 and 6 described later is generated, and this is displayed as a local echo.

An embodiment of the present invention will be described below with reference to FIGS. 3 and 4.

FIG. 3 shows a configuration example of the present invention. In this figure,
A computer (hereinafter referred to as CPU) 12 inputs and controls data from an input device such as a keyboard (not shown) and a coordinate input device 2 (hereinafter referred to as a tablet), and also forms a curve or curved surface according to an operator command. Along with the creation and storage, the output of those figures is displayed on the display screen 100, and 13 is a timer, which gives the CPU 12 an input cycle from a device such as the coordinate input device 2 which needs to periodically input data. . The coordinate input device 2 transfers the position coordinates of the cursor (or pen) at that time to the CPU 12 via the signal line 14 in response to an input request from the CPU 12. These position coordinates are two-dimensional data unique to the tablet, and here (X,
It is written as Y). The converter 15, which is the core of the present invention, is preprogrammed to convert the two-dimensional data (U, V) given from the CPU 12 via the signal line 19 into three-dimensional coordinates (x, y, z). It consists of a microcomputer.
The conversion condition data is given from the CPU 12 via the signal line 16. The converter 17 projectively converts the three-dimensional coordinate point data (x, y, z) given from the CPU 12 into coordinates (x ₁ , y ₁ ) on the designated projective plane, and further the display device 1
Is converted into display coordinates (x ₂ , y ₂ ) unique to the display 1 and output to the display 1 via the signal line 40. Here, the data designating the projection plane is given from the CPU 12 via the signal line 18. In addition, the converter 17 uses the coordinates (x, y,
For z), a plurality of coordinate points (x ₂ , y ₂ ) for displaying a local echo mark centered at a point on the display screen 100 of FIG. 4 corresponding to this point are generated.
The converter 17 comprises a microcomputer preprogrammed to perform such an operation.

Next, the operation will be described.

In the interactive graphic processing system, as shown in FIG. 4, the data of each point of the curved surface graphic (hereinafter referred to as curved surface) 21 is represented by the coordinates (x, y, z) of the virtual three-dimensional coordinate system 3. However, the graphic display 1 is prepared for the display (peep window), and a portion with the curved surface 21 is cut out on the display screen 100, and the design work is successively carried out while watching it. In the case of a three-dimensional figure, since the display screen 100 is essentially two-dimensional, the projection plane 41 is determined and the image 50 projected on the projection plane 41 is determined.
Alternatively, a part of it is displayed as a graphic 42 on the screen.

The curved surface 21, whether it is a parallel moving surface, a rotating surface or a free curved surface, is represented by a conversion formula from the virtual square area 23 to the curved surface 21. This area 23 is represented by coordinates (U, V). The conversion formula is the formula C ₁ (U), C ₂ (V), C ₃ of the peripheral curve of the curved surface.
(U), C ₄ (V) and the function F. That is,
The relationship between the position vector γ of the point (x, y, z) on the curved surface and the arbitrary point (u, v) on the UV region 23 is expressed by the following equation.

γ = F (C ₁ (U), C ₂ (V), C ₃ (U), C ₄ (V), U, V) where C _{1 to} C ₂ are vector representations of the surrounding curve and the function F is a vector expression of a conversion formula. Therefore, in reality, the coordinates (x, y, z) of each point on the curved surface 21 are obtained by the following equation.

x = F _X (C _1X (U), C _2X (V), C _3X (U), C _4X (V), U,
V) y = F _Y (C _1Y (U), C _2Y (V), C _3Y (U), C _4Y (V), U,
V) z = F _Z (C _1Z (U), C ₂₂ (V), C _3Z (U), C _4Z (V), U,
V) The u and v coordinate values in the U and V areas 23 may be arbitrary, but for the sake of simplicity, 0 ≦ U ≦ 1 and 0 ≦ V ≦ 1 are set. The characteristic of this conversion formula is that the surrounding curves C ₁ -C ₂ are one function of U or V, and the four surrounding straight lines of the UV region 24, namely (i) V = 0,0 ≦ V ≦ 1, ( ii) U = 1,0 ≦ V ≦
1, (iii) V = 1,0 ≦ U ≦ 1, (iv) U = 0,0 ≦ V ≦ 1 points are mapped to points on the _four peripheral curves C _{1 to} C _{4 of} the curved surface 21, respectively. And the points in the area 24 are mapped to the points inside the graphic 21.

That is, in vector display, C ₁ (U) = F (C ₁ (U), C ₂ (O), C ₃ (U), C ₄ (O),
U, O) C ₂ (V) = F (C ₁ (1), C ₂ (V), C ₃ (1), C ₄ (V),
1, V) C ₃ (U) = F (C ₁ (U), C ₂ (1), C ₃ (U), C ₄ (1),
U, 1) C ₄ (V) = F (C ₁ (O), C ₂ (V), C ₃ (O), C ₄ (V),
The relationship of O, 1) is established. On the contrary, C ₁ (U) to C ₄ (V), F are determined so that these relationships are satisfied. The curved surface 21
A method of obtaining such C ₁ (U) to C ₄ (V), F given the shape of the above and the coordinate range in the U, V region 24 is known.
For example, when the curved surface 21 is a parallel moving surface, a rotating surface, etc., this F is expressed by the curve and the movement amount from which it is moved. It is expressed by the conversion formula for.

Since the coordinate data of the arbitrary curved surface 21 is generated by the above conversion principle, the CPU 12 does not store the coordinate data of each curved surface, the curved surface name for each of the plurality of curved surfaces, and the above-mentioned curve formulas C ₁ and C. _A pair of ₂ , C ₃ , C ₄ and the conversion formula F is stored in advance. Then, when it becomes necessary to display one curved surface, various points (U, V) on the four surrounding straight lines in the UV region 23 are calculated based on the periodic curve formulas C _{1 to} C ₄ and the conversion formula F for the curved surface.
Is programmed to generate coordinate data (x, y, z) on the _four surrounding curves C ₁ -C _{4 of} the curved surface 21 corresponding to

Now, the input flow of points on the curved surface 21 defined in the computer 12 will be described. The operator first selects the curved surface for which point input is desired.
Report to CPU12. As a method, for example, a predefined curved surface may be named, and the name may be designated by a keyboard (not shown) or the like.

The CPU 12 sets the peripheral curve formulas C ₁ (U), C ₂ (V), C ₃ (U), C ₄ (U) and the conversion formula F indicated by the converter 15 via the signal line 16. . Next, the CPU 12 generates two-dimensional coordinates (x ₂ , y ₂ ) on the display screen 1 from the coordinate point (x, y, z) in the three-dimensional space in the converter 17 via the signal line 18. Set the pre-stored data required for. This data includes a point P on the projection plane 41 for defining the projection plane 41, a normal vector U of the projection plane, and a point (x, y, z) on the projection plane 41 based on these information ( x ₁ , y ₁ ) conversion formula G ₁ (that is, G ₁ (X, Y, Z, P, U) gives x ₁ , y ₁ ) and a point on the projection plane 41 ( A conversion formula G ₂ (that is, G ₂ (x ₁ , y ₁ ) gives x ₂ , y ₂ by converting x ₁ , y ₁ ) to point coordinates (x ₂ , y ₂ ) on the display screen ) And. The conversion formula G ₂ is used for enlarging a part of the image 23 on the projection plane 41 or reducing the whole image and displaying it on the display screen 1.

After that, the CPU 12 uses the peripheral curve equations C _{1 to} C ₄ corresponding to the specified curved surface and the function F to determine the four perimeters C ₁ of the curved surface 21 corresponding to various points on the four perimeters of the UV region 23. Generate the coordinates (x, y, z) of the point on ~ C ₄ and send it to the transducer 17 via line 30.

The converter 17 uses the data P, U, G previously input via the line 18.
Based on the above, the coordinates (x, y, z) of various input points are converted into the coordinates (x ₁ , y ₁ ) on the corresponding projection plane 41, and this is further converted using the data G ₂ for the corresponding display. The coordinates (x ₂ , y ₂ ) of a point on the screen 100 are generated and sent to the graphic display 1. The graphic display 1 displays each point in response to each of the input various coordinate points (x ₂ , y ₂ ). In this way, the graphic 42 consisting of four surrounding curves is displayed on the screen 100.

CPU12 is a pre-defined area 2 on the tablet 12
The coordinate values (X, Y) with respect to the inside of 6 are the coordinates (U,
V) is programmed to convert. Therefore, for example, when a cursor (not shown) is present at the point 6 in this area 26, the (X, Y) of the point 6 taken into the CPU 12 by the signal line 14 is the coordinates (U, V) of the point 24. ) Is converted to. Then, this coordinate (U, V) is converted by the signal line 19 into the converter 1
It is given to 5 and converted into three-dimensional coordinates (x, y, z) on the curved surface. For example, point 24 in FIG. 4 is converted to point 25. For this purpose, the converter 15 has a pre-entered curve C ₁ ~
It is pre-programmed to convert coordinates (U, V) to coordinates (U, V) into coordinates (x, y, z) using the above-described relational expression represented by C ₄ and function F. Next, the three-dimensional coordinates (x, y, z) are given to the converter 17 by the signal line 20, and in the converter 17, the data P, U, G ₁ and G ₂ previously inputted are inputted from the line 30. Coordinate data (x ₂ , y ₂ ) on the display 1 in the same way as for the generated data (x, y, z)
Is converted to. Transducer 17 also uses this coordinate (x ₂ , y ₂ )
Generate the coordinates (x ₂ , y ₂ ) of multiple points needed to display a local echo mark centered at. The coordinates (x ₂ , y ₂ ) of these multiple points pass through the signal line 40, and the display 1
Is output to. For example, the point 25 in FIG. 4 is displayed at the point 43 and further as the local echo shown at the point 7.

As described above, in FIG. 4, if the operator moves the cursor within the area 26, the local echo mark 7 of the cursor pointing point 6 moves all over the designated curved surface 42 and moves the cursor to an arbitrary point on the curved surface 42. It is possible to move. Therefore, if the operator moves the cursor to a desired position on the curved surface 42 while watching the local echo 7 on both sides of the display 100, and then presses a button (or pen) (not shown) attached to the cursor, the CPU 12 The (U, V) coordinate with respect to the cursor position is stored as the input coordinate, or the coordinate (x, y, z) obtained by converting this coordinate (U, V) based on the conversion formula F is stored as the input coordinate. In this way, three-dimensional points can be input.

According to the present embodiment, as described above, by having the input means on the defined arbitrary curved surface, the defined data that is indispensable in the interactive graphic processing, especially on the curved surface which has been impossible in the past, can be obtained. It is possible to input points directly to.

Next, an example of a method for avoiding overlapping on the screen when displaying using the two-dimensional display 1 will be described. By the above method, it is possible to move the cursor on the curved surface. In the above method, the two points on the curve 21 that overlap on the projective surface 41 have their local echoes at the corresponding two curl positions. It is displayed in exactly the same position and cannot be identified. In this embodiment, a preset value as shown in FIG. 5 (this is stored in advance in the CPU 12 or the operator specifies the value), for example, 0.01
Only the U or V coordinates are deviated from the input point 29, surrounding points 30,31,3
CPU2 generates 2,33. CPU is 29,30,31,32,33 U, V
The coordinates are given to the converter 15 in FIG. Transducer 15 uses the coordinates (x, y, z) for these points as described above.
(This is all on the specified curved surface 21) and sends it to the converter 17 in the order of coordinates for the points 29-33.
The converter 17 converts the input coordinate data into the coordinates (x ₂ , y ₂ ) of the points 29 'to 33' on the display, respectively, and also connects the points 29 'to the surrounding points 30' to 33 '. The data for the display of points on the minute is output so that each of these lines is displayed in a different display state.

For example, if the display 1 is a color type, the coordinates on the line segment connecting the input point 29 'to the surrounding points 31' to 33 'and the respective data are provided for each line segment and in the order of the points 30' to 333 '. Color data for displaying in a predetermined color is output in association with the coordinate points on each line segment. When the display 1 is a black and white type, this is realized by a line type or the like. That is, the coordinates (x ₂ , y ₂ ) of a plurality of points are output so that the line segment connecting the point 29 ′ and the surrounding points 31 ′ to 33 ′ has a predetermined line type (solid line, broken line, etc.).

According to this method, as shown in FIG.
Even when the points A and B correspond to the same point on the display 100, the directions of the line segments forming the cursor echo marks 40 and 41 with respect to the points A and B are different, and the line segments are displayed in different color arrangements. Therefore, the operator can determine which of the overlapping points A and B is displayed by the color arrangement. According to the local echo display of the cursor, the unevenness on the curved surface is expressed by the deformation and discoloration of the local echo cursor, and the overlapping of the curved surface and the unevenness, which cannot be expressed by the two-dimensional display, can be identified by the operator.

Further, in the above-described present embodiment, both UV given from the coordinate input device are variable, but if either U or V is fixed (this is after conversion to the (X, Y) coordinates input from the tablet 2). Program the CPU 12 to replace one of the U and V coordinates with a previously specified value, or use an input device such as a dial for individually inputting U and V as the coordinate input device instead of the tablet 2 It can be easily realized by changing only the other while it is fixed), the cursor can move on a U-fixed or V-fixed curve on the curved surface, and in particular, it can also move on the peripheral curve of the curved surface. In FIG. 7, 27 and 28 show the loci of the local echo of the cursor when U or V is fixed.

Further, although the present embodiment has been described with respect to a curved surface as an input method of points on the curved surface, it is a virtual line segment (hereinafter referred to as U) and a curved line from there on a three-dimensional curve. Paying attention to the fact that it is expressed by the conversion formula to, the input is exactly the same as the above method, that is, (X,
By converting one of the Y) coordinates to the U coordinate, the cursor can be moved on the curve, and a desired point can be input on the curve. FIG. 8 shows the movement of the local echo of the cursor at that time.

The method described in the present embodiment is simple and can be realized with a small amount of hardware, and in that case, there is an advantage that the load on the CPU is not different from the conventional one. In addition, the converter 18 can be used in combination with normal figure output, which has the effect of reducing the load on the CPU 12 and displaying a three-dimensional figure at high speed. However, it is also possible to have the CPU 12 carry out all the processing of the converters 15 and 17.

As described above, according to the present invention, the cursor on the coordinate input device is constrained on the designated three-dimensional curve or curved surface, and the dynamic local echo of the cursor is displayed, which is conventionally impossible. There is an effect that it becomes possible to input an accurate straight line point on a curve or curved surface.

In addition, it is possible to input a point on the desired figure / curved surface side even for figures / curved surfaces that are displayed overlapping on a two-dimensional display, enabling three-dimensional input using only a two-dimensional input / output device. Has the effect of

Further, according to the present invention, it is sufficient to input the two-parameter UV in comparison with the conventional case where the three parameters of XYZ have to be designated in order to input the desired three-dimensional coordinates. If you use
Less than 2/3. If this is realized by an interactive device, the number of commands will be halved.

[Brief description of drawings]

FIG. 1 is a two-dimensional relationship diagram showing the conventional concept of correspondence between a coordinate input device, a display and a coordinate system, and FIG. 2 is a three-dimensional relationship diagram thereof. FIG. 3 is a block diagram of an embodiment of the present invention, and FIG. 4 is a correspondence diagram of the coordinate input device, the display and the coordinate system at that time. FIG. 5 is an explanatory diagram of a method for displaying a local echo of a cursor used in the present invention. FIG. 6 is a diagram showing a display example of the local echo of the present invention. FIG. 7 is a display diagram of an application example of the present invention to a three-dimensional curved surface, and FIG. 8 is a display diagram of an application example to a curved line. 1 …… Graphic display 2 …… Tablet 12 …… Computer 15 …… Converter from UV coordinates to (x, y, z) coordinates on a three-dimensional curved surface 17 …… Projection from (x, y, z) coordinates Surface (x ₁ , y ₁ ) and display both sides (x ₂ , y ₂ ) converter 100 …… Display screen of graphic display 1

Claims (8)

[Claims] 1. First graphic data representing a three-dimensional curved surface located in a predetermined three-dimensional space, wherein the coordinates of a point on the three-dimensional curved surface are either within a predetermined two-dimensional reference area. A two-dimensional projective figure obtained by transforming what is represented by the function of the coordinates of the corresponding points of 1 using the first transformation formula and projecting the 3D curved surface onto a plane located in the 3D space. For generating the second graphic data representing the above, converting the generated second graphic data by the second conversion equation, and displaying the two-dimensional projected graphic on the two-dimensional display screen on the display device. Third graphic data representing a two-dimensional display graphic is generated, the two-dimensional display graphic is displayed on the display screen based on the third graphic data, and any one of the points in the reference area is displayed. Enter the coordinates between the coordinates of the point in the reference area and the coordinates of the corresponding point on the curved surface. The coordinates of the point on the three-dimensional curved surface corresponding to the input point are determined based on a predetermined relational expression and the coordinates of the input point, and the coordinates of the point on the three-dimensional curved surface are determined. And the point on the three-dimensional curved surface should be displayed based on
A display device in the three-dimensional display screen is determined, the displayed two-dimensional display figure is superimposed, a pattern for indicating an input position is generated at the determined display position, and the pattern is displayed at the display position. How to display points on a three-dimensional figure to be displayed. 2. The method for displaying dots on a three-dimensional figure according to claim 1, wherein the pattern is a fixed pattern that is determined in advance. 3. The process of generating the pattern includes a process of determining coordinates of a plurality of neighboring points having a predetermined positional relationship with respect to an input point in the reference area, and the input point. On the three-dimensional curved surface corresponding to the plurality of neighboring points on the basis of the relational expression between the coordinates of and the coordinates of the corresponding points on the three-dimensional curved surface and the coordinates of the plurality of neighboring points. A process of determining the coordinates of a plurality of points and a plurality of display positions in the two-dimensional display screen based on the coordinates of the plurality of points on the three-dimensional curved surface and the first and second conversion equations. 2. The method for displaying a point on a three-dimensional figure according to claim 1, further comprising: a process of performing a pattern for connecting the plurality of display positions and the display position determined with respect to the input point. . 4. A three-dimensional graphic according to claim 3, wherein the display of the portion connecting the input display positions of the points and the display positions of the plurality of neighboring points is changed for each of the plurality of neighboring points. How to display dots. 5. The three-dimensional graphic according to claim 4, wherein the color of a portion connecting the display position of the input point and the display positions of the plurality of neighboring points is changed for each of the plurality of neighboring points. How to display dots. 6. The three-dimensional graphic according to claim 4, wherein the line type of a portion connecting the display position of the input point and the display positions of the plurality of neighboring points is changed for each of the plurality of neighboring points. How to display points. 7. The point on the three-dimensional figure according to claim 3, wherein the plurality of neighboring points are points located at ends of a cross having the input point as a center. Display method. 8. The process of inputting the coordinates of any point in the reference region includes the process of inputting the coordinates of any point in a predetermined two-dimensional input region on the coordinate input device, and the inputting process. The method for displaying a point on a three-dimensional figure according to claim 1, further comprising: determining from the coordinates of the point in the area, a corresponding point in the reference area corresponding to the input as an input point.