Method and apparatus for displaying altitude of form characteristics generated from a geometric model in a computer using a graph

Claims

What is claimed is:

1. A method of expressing a geometric form characteristic in a computer, said method comprising the steps of:

inputting geometric data of a geometric model;

displaying said geometric model on a display screen;

indicating of said displayed form by using a pointing device;

converting coordinates indicated on said display screen into coordinates of a point on said geometric model;

calculating geometric analysis data of said arbitrarily indicated point using said converted coordinates, said geometric analysis data including altitude, normal and curvature of said arbitrarily indicated point on said geometric model;

converting the calculated geometric analysis data into data for display as graph; and

displaying said calculated altitude of form characteristic on said display screen as a graph expressing quantities.

2. A method of expressing an altitude of form characteristic according to claim 1, wherein said graph includes any one of a bar graph for showing one-dimensional data, a circle graph for showing cyclic one-dimensional data, a three-dimensional arrow graph for showing a direction in three or lower dimensional space, a two-dimensional graph having two axes which respectively are the maximum value and the minimum value of the principal curvature of a curved surface at said instructed point, a graph showing a two-dimensional region having two axes which respectively are the maximum value and the minimum value of the principal curvature of said curved surface at an instructed point, as a background thereof sectioned in accordance with the form characteristic such as the concave, convex and plane portions, and a graph showing a two-dimensional region having two axes which respectively are the maximum value and the minimum value of the principal curvature of said curved surface at said instructed point, as a background thereof sectioned in accordance with the form characteristic such as the concave, convex and plane portions and as well as showing characterstat information indicating said form characteristic at said instructed point.

3. A method of expressing an altitude of form characteristic according to claim 1, wherein said graph is formed by synthesizing at least one of a bar graph, a circle graph and a three-dimensional arrow graph, and a graph showing a two-dimensional region having two axes which respectively are the maximum value and the minimum value of the principal curvature of said curved surface at an instructed point, as a background thereof sectioned in accordance with the form characteristic such as the concave, convex and plane portions, or a graph showing a two-dimensional region having two axes which respectively are the maximum value and the minimum value of the principal curvature of said curved surface at said instructed point, as a background thereof sectioned in accordance with the form characteristic such as the concave, convex and plane portions and as well as showing character information indicating said form characteristic at said instructed point.

4. A method of expressing a geometric form characteristic in a computer, said method comprising the steps of:

inputting geometric data of a geometric model;

displaying said geometric model on a display screen;

indicating an arbitrary point of said displayed form;

converting coordinates indicated on said display screen into coordinates of a point on said geometric model;

calculating geometric analysis data of said arbitrarily indicated point using said converted coordinates, said geometric analysis data including altitude, normal and curvature of said arbitrarily indicated point on said geometric model;

converting the calculated geometric analysis data into data for display as a graph;

processing said converted geometric analysis data for display as a graph on said display screen at a high rate of speed; and

changing plotting positions on said graph corresponding to movement of said pointing device on said display screen.

5. A method of expressing an altitude of form characteristic according to claim 4, wherein said graph is any one of bar graph for showing one-dimensional data, a circle graph for showing a cyclic one-dimensional data, a three-dimensional arrow graph for showing a direction in three or lower dimensional space, a two-dimensional graph having an ordinate axis and an abscissa axis which respectively are either of the maximum value and the minimum value of the principal curvature of a curved surface at said indicated point, a graph showing a two-dimensional region having two axes which respectively are the maximum value and the minimum value of the principal curvature of said curved surface at an indicated point, as a background thereof sectioned in accordance with the form characteristic such as the concave, convex and plane portions, and a graph showing a two-dimensional region having two axes which respectively are the maximum value and the minimum value of the principal curvature of said curved surface at said indicated point, as a background thereof sectioned in accordance with the form characteristic such as the concave, convex and plane portions and as well as showing characteristic information indicating said form characteristic at said indicated point.

6. A method of expressing an altitude of form characteristic according to claim 4, wherein said graph is formed by synthesizing at least any one of a bar graph, a circle graph and a three-dimensional arrow graph, and a graph showing a two-dimensional region having two axes which respectively are the maximum value and the minimum value of the principal curvature of said curved surface at an instructed point, as a background thereof sectioned in accordance with the form characteristic such as the concave, convex and plane portions, or a graph showing a two-dimensional region having two axes of which respectively are the maximum value and the minimum value of the principal curvature of said curved surface at said indicated point, as a background thereof sectioned in accordance with the form characteristic such as the concave, convex and plane portions and as well as showing characteristic information indicating said form characteristic at said instructed point.

7. A method of expressing a geometric form characteristic in a computer, said method comprising the steps of:

inputting geometric data of a geometric model;

displaying said geometric model on a display screen;

generating nodes on a surface of said geometric model to store said nodes as node data;

previously calculating a geometric form characteristic at each of said nodes in accordance with said geometric data to store said geometric form characteristic as data of said geometric form characteristic;

indicating an arbitrary point of said displayed form;

calculating a distance from each node to a point that can be obtained by converting coordinates of said indicated point into coordinates in a display space to obtain a node nearest said indicated point;

reading the geometric form characteristic corresponding to said obtained node from said data of said geometric form characteristic which has been previously stored; and

displaying said read geometric form characteristic on said display screen as a graph.

8. A method of expressing a geometric form characteristic according to claim 7, wherein said graph is any one of a bar graph for showing one-dimensional data, a circle graph for showing cyclic one-dimensional data, a three-dimensional arrow graph for showing a direction in three or lower dimensional space, a two-dimensional graph having an ordinate axis and an abscissa axis which respectively are either of the maximum value and the minimum value of the principal curvature of a curved surface at said indicated point, a graph showing a two-dimensional region having two axes which respectively are the maximum value and the minimum value of the principal curvature of said curved surface at an indicated point, as a background thereof sectioned in accordance with the form characteristic such as the concave, convex and plane portions, and a graph showing a two-dimensional region having two axes which respectively are the maximum value and the minimum value of the principal curvature of said curved surface at said indicated point, as a background thereof sectioned in accordance with the form characteristic such as the concave, convex and plane portions and as well as showing characteristic information indicating said form characteristic at said indicated point.

9. A method of expressing an altitude of form characteristic according to claim 7, wherein said graph is formed by synthesizing at least any one of a bar graph, a circle graph and a three-dimensional arrow graph, and a graph showing a two-dimensional region having two axes which respectively are the maximum value and the minimum value of the principal curvature of said curved surface at an indicated point, as a background thereof sectioned in accordance with the form characteristic such as the concave, convex and plane portions, or a graph showing a two-dimensional region having two axes which respectively are the maximum value and the minimum value of the principal curvature of said curved surface at said instructed point, as a background thereof sectioned in accordance with the form characteristic such as the concave, convex and plane portions and as well as showing characteristic information indicating said form characteristic at said indicated point.

10. A method of expressing a geometric form characteristic in a computer, said method comprising the steps of:

inputting geometric data of a geometric model;

displaying said geometric model on a display screen;

generating nodes on a surface of said geometric model to store said nodes as node data;

previously calculating a geometric form characteristic at each of said nodes in accordance with said geometric data to store said geometric form characteristic as data of said geometric form characteristic;

indicating an arbitrary point of said displayed form;

calculating the distance from each node to a point that can be obtained by converting coordinates of said indicated point into coordinates in a display space to obtain a node nearest said indicated point;

reading the geometric form characteristic corresponding to said obtained node from said data of said geometric form characteristic which has been previously stored; and

sequentially plotting and displaying in a timesequential manner a plurality of said read geometric form characteristics on a graph on said display screen.

11. A method of expressing a geometric form characteristic according to claim 4, wherein said graph is any one of a bar graph for showing one-dimensional data, a circle graph for showing cyclic one-dimensional data, a three-dimensional arrow graph for showing a direction in three or lower dimensional space, a two-dimensional graph having an ordinate axis and an abscissa axis which respectively are either of the maximum value and the minimum value of the principal curvature of a curved surface at said indicated point, a graph showing a two-dimensional region having two axes of which respectively are the maximum value and the minimum value of the principal curvature of said curved surface at an indicated point, as a background thereof sectioned in accordance with the form characteristic such as the concave, convex and plane portions, and a graph showing a two-dimensional region having two axes which respectively are the maximum value and the minimum value of the principal curvature of said curved surface at said indicated point, as a background thereof sectioned in accordance with the form characteristic such as the concave, convex and plane portions and as well as showing characteristic information indicating said form characteristic at said indicated point.

12. A method of expressing a geometric form characteristic according to claim 4, wherein said graph is formed by synthesizing at least any one of a bar graph, a circle graph and a three-dimensional arrow graph, and a graph showing a two-dimensional region having two axes which respectively are the maximum value and the minimum value of the principal curvature of said curved surface at an indicated point, as a background thereof sectioned in accordance with the form characteristic such as the concave, convex and plane portions, or a graph showing a two-dimensional region having two axes which respectively are the maximum value and the minimum value of the principal curvature of said curved surface at an indicated point, as a background thereof sectioned in accordance with the form characteristic such as the concave, convex and plane portions and as well as showing characteristic information indicating said form characteristic at said indicated point.

13. A method of expressing a geometric form characteristic in a computer, said method comprising the steps of:

inputting geometric data of a geometric model;

generating nodes on a surface of said geometric model to store said nodes as node data;

previously calculating the maximum value and the minimum value of the principal curvature of a curved surface at each of said nodes for storing as data of the geometric form characteristic;

displaying said geometric model on a display screen;

displaying, in a portion of said display screen, a principal curvature graph showing a two-dimensional region having two axes which respectively are the maximum value and the minimum value of the principal curvature of said curved surface at an indicated point, as a background thereof sectioned in accordance with the form characteristic such as the concave, convex and plane portions;

indicating an arbitrary point of said displayed form;

calculating a distance from a point obtained by converting coordinates of said indicated point into coordinates in a display space to each of said nodes to obtain a node nearest said indicated point;

reading the maximum value and the minimum value of the principal curvature of a curved surface corresponding to said obtained node from said data of said geometric form characteristic which has been previously stored; and

sequentially plotting and displaying in a timesequential manner said read data on said principal curvature graph on said display screen.

14. A method of expressing a geometric form characteristic according to claim 13, wherein said calculated maximum value k.sub.max and minimum value k.sub.min of said principal curvature of said curved surface at each node are used to calculate D=.sqroot.{(k.sub.max).sup.2 +(k.sub.min).sup.2 } as degree of deformation of an indicated point of said form from the plane, said degree of deformation D is stored together with the maximum value k.sub.max and the minimum value k.sub.min of said principal curvature of said curved surface at each node, the maximum value and the minimum value of the principal curvature of a curved surface corresponding to said obtained node and stored previously are read from said data of said geometric form characteristic, said degree of deformation D is, as characteristic data, displayed on said principal curvature graph when plotting said read data on said principal curvature graph on said display screen, and a concave, convex, saddle portion or plane to which the form of said indicated point belongs is, as said characteristic data, displayed on said principal curvature graph.

15. An apparatus for displaying an altitude of form characteristic in a computer comprising:

means for storing geometric data of an input geometric model;

form display means for displaying said geometric model on a display screen;

a pointing device for indicating an arbitrary point of said displayed form;

position instruction means for converting coordinates indicated on said display screen into coordinates of said point on said input geometric model;

geometric form characteristic calculating means for calculating the geometric form characteristic at said indicated point on said geometric model; and

altitude of form characteristic display means for displaying said calculated altitude of form characteristic on said display screen as a graph.

16. An apparatus for displaying an altitude of form characteristic in a computer comprising:

means for storing geometric data of an input geometric model;

form display means for displaying said geometric model on a display screen;

a pointing device for indicating an arbitrary point of said displayed form;

position indicating means for converting coordinates indicated on said display screen into coordinates of said point on said input geometric model;

geometric form characteristic calculating means for calculating the geometric form characteristic at said indicated point on said geometric model; and

geometric form characteristic display means for sequentially plotting and displaying in a time-sequential manner a plurality of said calculated geometric form characteristics on a graph on said display screen.

17. An apparatus for displaying an altitude of form characteristic in a computer comprising:

means for storing geometric data of an input geometric model;

form display means for displaying said geometric model on a display screen;

node calculating means for generating nodes on a surface of said geometric model to store said nodes as node data;

geometric form characteristic calculating means for previously calculating a geometric form characteristic at each of said nodes in accordance with said geometric data to store said geometric form characteristic;

a pointing device for indicating an arbitrary point of said displayed form;

position indicating means for calculating a distance from each node to a point that can be obtained by converting coordinates of said indicated point into coordinates in a display space to obtain a node nearest said indicated point;

geometric form characteristic reading means for reading the geometric form characteristic corresponding to said obtained node from said data of geometric form characteristic which has been previously stored; and

geometric form characteristic display means for display said read geometric form characteristic on a display screen as a graph.

18. An apparatus for displaying an altitude of form characteristic in a computer, comprising:

means for storing geometric data of an input geometric model;

form display means for displaying said geometric model on a display screen;

node calculating means for generating nodes on a surface of said geometric model to store said nodes as node data;

geometric form characteristic calculating means for previously calculating a geometric form characteristic at each of said nodes in accordance with said geometric data to store said geometric form characteristic as data of said geometric form characteristic;

a pointing device for indicating an arbitrary point of said displayed form;

position indicating means for calculating a distance from each node to a point that can be obtained by converting coordinates of said indicated point into coordinates in a display space to obtain a node nearest said indicated point;

geometric form characteristic reading means for reading the geometric form characteristic corresponding to said obtained node from said data of geometric form characteristic which has been previously stored; and

geometric form characteristic display means for sequentially plotting and displaying in a time-sequential manner a plurality of said read geometric form characteristic on a graph on said display screen.

19. An apparatus for displaying an altitude of form characteristic in a computer comprising:

a display device having a display screen for displaying a form characteristic;

a geometric data file for storing geometric data of an input geometric model;

form display means for reading said geometric data to display said geometric model on said display screen of said display device;

geometric form characteristic display region processing means for displaying a principal curvature graph showing a two-dimensional region having two axes which respectively are the maximum value and the minimum value of the principal curvature of said curved surface, as background thereof sectioned in accordance with the form characteristic such as the concave, convex and plane portions;

node calculating means for generating a plurality of nodes, as node data on a surface of said geometric model to calculate the correspondence between the positions of said nodes on said geometric model and the coordinates on said display screen;

node data file for storing said calculated node data;

geometric form characteristic calculating means for calculating, as geometric form characteristic, maximum value k.sub.max, minimum value k.sub.min and degree of deformation D=.sqroot.{(k.sub.max) .sup.2 +(k.sub.min)} of the principal curvature at each of said nodes in accordance with said geometric data and said node data;

geometric form characteristic data file for storing said calculated geometric form characteristic together with said node;

a pointing device for instructing, on said screen, an arbitrary point of said form displayed on said screen;

a screen coordinate calculating portion for calculating the coordinates of said point on said screen instructed by said pointing device;

a space coordinate calculating portion for converting said calculated coordinates on said screen into the coordinates in a display space;

a node candidate searching portion for calculating the distance from each of said nodes to a point indicated with said coordinates in said display space obtained by said conversion to obtain a node nearest said indicated point;

geometric form characteristic reading means for reading the geometric form characteristic corresponding to the obtained nearest node from said geometric form characteristic data file to output said geometric form characteristic;

geometric form characteristic display means for plotting maximum value k.sub.max and minimum value k.sub.min of the principal curvature among said geometric form characteristic output from said geometric form characteristic reading means on a principal curvature graph on said display screen to display said degree of deformation D as character data in said principal curvature graph; and

a keyboard for inputting control signals to said form display means and said geometric form characteristic display region processing means.

BACKGROUND OF THE INVENTION

The present invention relates to a method and an apparatus for displaying a geometric form characteristic, and more particularly to a method of displaying a form for use in a form designing/machining analyzing/visualizing system incorporating a computer, for example, mechanical CAD (Computer Aided Design)/CAM (Computer Aided Manufacturing)/CAE (Computer Aided Engineering), and CG (Computer Graphics).

When the form of an industrial product or the like is designed by using a form design aiding system such as a mechanical CAD, the form is usually expressed by using a geometric model in the computer. However, the geometric model designed in the computer does not necessarily meet the form imagined by the user. The reasons for this are that the form expressing method in the computer is based on the geometric model and, accordingly, the form expressing command function of the computer is unsatisfactory to express the form imagined by the user, and in particular, to express a free form surface as a geometric model and that performance is insufficient to display the three-dimensional geometric model constituted in the computer on a display device such as a CRT (Cathode Ray Tube).

As a means for overcoming the foregoing problems, it might be considered feasible to employ a method for actually making a model by a model making machine adapted to NC (Numerical Control) cutting work or a method for making a resin model by a perspective resin model making system which uses photosetting resin. In any case, a machining operation must be performed and the model cannot be made in real time. Therefore, the form cannot be modified while establishing a dialogue with the computer.

Another method can be employed capable of displaying a geometric model, designed in a computer, on a display device such as a CRT in a short time, while eliminating the necessity of machining the geometric model. A major portion of the foregoing methods is arranged to perform an optical simulation by using a computer to simulate how a three-dimensional form may appear under a certain light source.

Since the internal portion of a free form surface is expressed by a functional equation, a method may be employed in which a problem of a geometric model designed in a computer is found out by adding a geometric form characteristic, such as the distribution of a normal vector, a curvature vector, a Gaussian curvature, and the mean curvature to the form, followed by displaying them. For example, Japanese Patent Laid-Open No. 62-271067 titled "FREE FORM SURFACE EXPRESSING METHOD" discloses a method of displaying a normal vector at a boundary line between patches to check smoothness connected between a plurality of patches that constitute the free form surface. However, any of the foregoing method simply confirms whether or not the geometric form characteristics are distributed continuously, resulting in a form considerably different from that imagined by a user. Therefore, it is difficult to quickly modify the form by making use of the result of the display.

In Japanese Patent Laid-Open No. 3-278182 titled "METHOD AND APPARATUS FOR SENSITIVELY NOTIFYING FORM", the foregoing problem experienced with a geometric form characteristic expressed by three-dimensional vector such as a normal vector or a curvature vector has been partially overcome in terms of the machine interface by instructing a point on the form displayed on the screen by using a pointing device such as a mouse. However, the geometric form characteristic has not been displayed with which the user is able to easily understand the form.

SUMMARY OF THE INVENTION

An object of the present invention to easily compare the geometric form characteristic of a free form surface input in a computer and an image of a form input by a user to reduce the work required to complete modification of the form by means of a dialogue with the computer. The geometric form characteristic to be dealt with in the present invention includes multi-dimensional tensor quantities such as scalar quantities as well as three-dimensional vectors.

In order to achieve the foregoing object, according to the present invention, there is provided a method of expressing a geometric form characteristic comprising the steps of: inputting geometric data of a geometric model; displaying the geometric model on a display screen; indicating an arbitrary point of the displayed form; converting coordinates indicated on the display screen into coordinates of a point on the designed geometric model; calculating the geometric form characteristic at the indicated point on the geometric model; and displaying the calculated geometric form characteristic on the display screen as a graph expressing quantities.

In order to achieve the foregoing object, according to the present invention, there is provided a method of expressing a geometric form characteristic comprising the steps of: inputting geometric data of a geometric model; displaying the geometric model on a display screen; indicating an arbitrary point of the displayed form; converting coordinates indicated on the display screen into coordinates of a point on the designed geometric model; calculating the geometric form characteristic at the indicated point on the geometric model; and sequentially plotting and displaying in a time-sequential manner a plurality of the calculated geometric form characteristic on a graph on the display screen.

In any case, a plurality of geometric form characteristics are sequentially plotted on the graph on the display screen to be time-sequentially displayed.

Specifically, the graph may be any one of a bar graph for showing a one-dimensional data, a circle graph for showing cyclic one-dimensional data, a three-dimensional arrow graph for showing a direction in a three or lower dimensional space, a two-dimensional graph, the axis of ordinate and the axis of abscissa which respectively are the maximum value and the minimum value of the principal curvature of a curved surface at the indicated point. In this case, it is preferable that the two-dimensional graph is a graph showing a two-dimensional region, the axis of ordinate and the axis of abscissa of which, or the axis of abscissa and the axis of ordinate of which respectively are the maximum value and the minimum value of the principal curvature of a curved surface at the indicated point, which is sectioned in accordance with the form characteristics such as a concave, convex and a plane portion as a background thereof. It is also preferable that the foregoing graph is a graph showing a two-dimensional region, the axis of ordinate and the axis of abscissa of which, or the axis of abscissa and the axis of ordinate of which respectively are the maximum value and the minimum value of the principal curvature of a curved surface at the indicated point, which is sectioned in accordance with the form characteristics such as a concave, convex and a plane portion as a background thereof, the graph also displaying character information expressing the form characteristic at the indicated point.

The graph may be formed by synthesizing at least any one of a bar graph, a circle graph and a three-dimensional arrow graph, and a graph showing a two-dimensional region, the axis of ordinate and the axis of abscissa of which, or the axis of abscissa and the axis of ordinate of which respectively are the maximum value and the minimum value of the principal curvature of a curved surface at the indicated point, or a graph showing a two-dimensional region, the axis of ordinate and the axis of abscissa of which, or the axis of abscissa and the axis of ordinate of which respectively are the maximum value and the minimum value of the principal curvature of a curved surface at the indicated point, which is sectioned in accordance with the form characteristics such as a concave, convex and a plane portion as a background thereof and as well as showing characteristic information indicating the form characteristic at the indicated point.

In order to achieve the foregoing object, according to the present invention, there is provided an apparatus for displaying a geometric form characteristic comprising: means for storing geometric data of an input geometric model; form display means for displaying the geometric model on a display screen; a pointing device for indicating an arbitrary point of the displayed form; position instruction means for converting coordinates instructed on the display screen into the coordinates of the point on the input geometric model; geometric form characteristic calculating means for calculating the geometric form characteristic at the indicated point on the geometric model; and geometric form characteristic display means for displaying the calculated geometric form characteristic on the display screen as a graph.

In order to achieve the foregoing object, according to the present invention, there is provided an apparatus for displaying a geometric form characteristic comprising: means for storing geometric data of an input geometric model; form display means for displaying the geometric model on a display screen; node calculating means for generating nodes on the surface of the geometric model to store the nodes as node data; geometric form characteristic calculating means for previously calculating a geometric form characteristic at each of the nodes in accordance with the geometric data to store the geometric form characteristic as data of the geometric form characteristic; a pointing device for indicating an arbitrary point of the displayed form; position instruction means for calculating the distance from each node to a point that can be obtained by converting the coordinates of the indicated point into the coordinates in a display space to obtain a node nearest the instructed point; geometric form characteristic reading means for reading the geometric form characteristic corresponding to the obtained node from the data of the geometric form characteristic which has been previously stored; and geometric form characteristic display means for displaying the read altitude of form characteristic on a display screen as a graph.

Any apparatus for displaying the geometric form characteristics may include a geometric form characteristic display means for sequentially plotting a plurality of geometric form characteristics on a graph on the display screen to time-sequentially display them.

According to the present invention, the form display means shading-displays the geometric model input in the computer on a display device such as a CRT. The user uses a pointing device such as a mouse to indicate an arbitrary point of the display form with a mouse cursor. The position of the mouse cursor is input into the computer as the coordinates on the display screen. The position instruction means converts the coordinates of the mouse cursor on the display screen into the coordinates of the point on the geometric model designed in the computer. The geometric form characteristic calculating means calculates the geometric form characteristic at the indicated point on the geometric model. The geometric form characteristic display means displays the calculated altitude of the form characteristic on the display screen.

When the geometric form characteristic is displayed, a one-dimensional graph such as a bar graph is used if the geometric form characteristic is a one-dimensional quantity. If it is a two-dimensional quantity, a two-dimensional graph such as an x-y graph is used. More specifically, maximum value k.sub.max and minimum value k.sub.min (principal curvature) at an arbitrarily indicated point on a curved surface are used as the geometric form characteristic, followed by plotting the geometric form characteristic on a graph, in which the foregoing two parameters are made to be the axis of ordinates and the axis of abscissa, that is, on a principal curvature graph.

The geometric form characteristic to be dealt with in the present invention may include multi-dimensional tensor quantities such as scalar quantities as well as three dimensional vectors.

If the time taken from a moment the user instructs an arbitrary point on the displayed form with the mouse cursor to a moment, at which the display of the geometric form characteristics at the indicated point is performed, is sufficiently short, the user is able to recognize the form designed in the computer as if the user touches the form by using the mouse.

The geometric form characteristic display means is arranged in such a manner that, for example, the background color of the principal curvature graph is changed and the area is divided in accordance with the form characteristics such as the concave, the convex and the plane portion classified in accordance with the numeral or the size of k.sub.max and k.sub.min of the principal curvature. Therefore, the form characteristic to which the plotted point belongs, that is, the form characteristic of the portion indicated with the mouse cursor can instantaneously be conformed.

The geometric form characteristic display means thus constituted enables the user to easily produce an image having the form characteristic such as the concave, the convex and the plane from the geometric form characteristic such as the principal curvature of a free form surface constituted in the computer. Therefore, the user is able to easily, quickly and accurately recognize or modify the form by utilizing the displayed result.

BRIEF DESCRIPTION OF THE DRAWINGS

Preferred embodiments of the present invention will be described more in detail with reference to the following drawings.

FIG. 1 illustrates an example of the structure of an apparatus and an example of a display on a screen according to an embodiment of the present invention;

FIG. 2 is a block diagram which illustrates the apparatus shown in FIG. 1 in detail;

FIG. 3 is a block diagram which illustrates another example of the apparatus shown in FIG. 2;

FIG. 4 illustrates an example of a display screen where a geometric form characteristic is displayed in the form of a bar graph;

FIG. 5 illustrates an example of a display screen where the geometric form characteristic is displayed in the form of a circle graph;

FIG. 6 illustrates an example of a display screen where the geometric form characteristic is displayed in the form of a perspective arrow;

FIG. 7 illustrates an example of a display screen where the geometric form characteristic is displayed in the form of a principal curvature graph;

FIG. 8 illustrates another example of a display screen where the geometric form characteristic is displayed in the form of a principal curvature graph;

FIGS. 9A to 9B are flow charts of a process when the display on the screen shown in FIG. 8 is performed.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1 illustrates the structure of a system according to an embodiment of the present invention and an example of a displayed image. FIG. 2 is a block diagram which illustrates the structure of a computer employed in the embodiment shown in FIG. 1. The embodiment shown in FIG. 1 includes a computer 18, a display device 10, such as a CRT, connected to the computer 18, a keyboard 19 similarly connected to the computer 18, and a mouse 17 belonging to the keyboard 19 and serving as a pointing device. The computer 18 is, as shown in FIG. 2, includes a position indicating means 22 to be connected to the pointing device 17, a geometric form characteristic calculating means 23 connected to the position instruction means 22, a geometric form characteristic display means 24 connected to the geometric of form characteristic calculating means 23, a geometric data file 20 connected to the position indicating means 22 to store data of the form, and a shape display means 21 connected to the geometric data file 20. The position indicating means 22 includes a drawing coordinate calculating portion connected to the pointing device, and a space-coordinate calculating portion connected to both the drawing-coordinate calculating portion and the foregoing geometric data file 20. The geometric form characteristic calculating means 23 and the form display means 21 are connected to the foregoing display device 10.

The screen of the display device 10 displays a form display region 11 and a geometric form characteristic display region 14 which is the characteristic of the present invention. In the form display region 11, a displayed form 12 and a mouse cursor 13 for indicating an arbitrary point of the form 12 to correspond to the movement of the mouse 17 are displayed in such a manner that they are superimposed. In the geometric form characteristic display region 14, a graph 15 of a two-dimensional quantity is displayed in this case. In the graph 15, a point 16 is plotted at a parameter position indicating the characteristic of the position of the displayed form 12, the position being instructed by the mouse cursor 13.

The flow of the process to be performed according to this embodiment is as follows: (1) The form display means 21 generates display data for performing shading-display from the form data stored in the geometric data file 20 to be displayed on the display device 10, such as a CRT. The display screen of the display device 10 shown in FIG. 1 shows an example of a displayed image. As another effective example, a form display method based on a stereoscope vision may be employed. (2) A user uses the mouse 17 to move the mouse cursor 13 on the displayed form 12 via the position indicating means 22 so as to indicate a portion on the displayed form 12 that is required. The screen coordinate calculating portion of the position indicating means 22 calculates coordinates A (x,y) on the screen plane of the display device 10 in response to an input signal supplied through the mouse cursor 13. The space coordinate calculating portion calculates coordinates B of the mouse cursor 13 on a three-dimensional geometric model input in the computer from the coordinates A (x,y ) on the screen plane of the display device 10. If the three-dimensional geometric model is a free form surface expressed by parameter (u,v) for example, the coordinates are converted from a space (x,y) to a space (u,v). As the conversion met