1. Field of the Invention
The present invention relates to a three-dimensional graphic displaying system equipped with a capability for allowing a change of a viewpoint from which a user sees a graphic, when a displayed graphic is rotated or moved, and more particularly into a three-dimensional graphic displaying system for allowing positions of scale marks on a coordinate axis to be identified at any time, even if such a viewpoint change is made.
2. Description of the Related Art
With a conventional three-dimensional graphic displaying system, scale marks are normally displayed in one direction, for example, when three-directional axes and scale marks are displayed in a three-axial graph. FIG. 1 exemplifies a method for displaying three-dimensional axes and scale marks. In this figure, the scale marks on the x, y, and z axes are respectively displayed only on an x-y plane, y-z plane, and an x-z plane.
Such a displaying method works properly for a three-dimensional graphic displaying system which uses a fixed viewpoint. However, it prevents the position of scale marks from being identified in a displaying system which enables a viewpoint of a displayed graphic to change, after a user operation such as a rotation operation, move operation, etc. This is because the scale marks are seen as mere dots and an axis is drawn over the dots, when a viewpoint comes to an extended portion of the scale marks;.
FIG. 2 is a schematic diagram illustrating such a problem. This figure illustrates the coordinate axes seen from a direction perpendicular to the y-z plane, that is, the axes and scale marks seen from the x-axis. Since the scale marks of the z axis overlap the z axis, the positions of the scale marks cannot be identified. Similarly, if the coordinate axes shown in FIG. 1 are seen from a direction perpendicular to the z-x plane or a direction perpendicular to the x-y plane, the scale marks of the x axis or the y axis respectively overlap the x axis or the y axis. As a result, the position of the scale marks cannot be identified.
When other axes become invisible from the display area due to a viewpoint move or expansion in the region of a particular mark, on the condition that the axes and scales are displayed as shown in FIG. 1, the direction from which the user sees the displayed portion, cannot be recognized. This is because the other axes serving as direction indicators are not displayed. FIG. 3 exemplifies such a case. It shows a display state of the y axis when the other two axes except for the y axis, that is, the x and z axes are outside the display area. In this display state, the direction from which the user sees the portion of the y axis appearing in the displayed area, cannot be recognized. That is, scale marks themselves on an axis do not possess the capability for indicating a viewpoint direction, according to the conventional scale displaying method.
Provided next is the explanation about a method for displaying a vector for use in the conventional three-dimensional graphic displaying system. FIG. 4 is a schematic diagram for explaining an example of a conventional vector display. In this figure, the vector is one-dimensionally displayed using both a line linking its start and end points (hereinafter referred to as the trunk of the vector), and two short lines attached to the end point (hereinafter referred to as branches) in order to form an arrow as the whole, or displayed using a two-dimensional graphic such as a triangle.
With such a vector displaying method for use in a three-dimensional graphic displaying system which uses a fixed viewpoint, a distinction between start and end points of a vector can normally and constantly be made, and a suitable display can be made. However, if such a method is used in a displaying system which allows a viewpoint to change, the trunk and branches of the vector overlap on the condition that the vector is located on the plane identical to the direction of the viewpoint. Therefore, the distinction between the start and end points cannot be made.
FIGS. 5A to 5C are schematic diagrams for explaining such a problem. As shown in FIG. 5A, if a viewpoint exists in the direction perpendicular to the x-y plane, the distinction between the start and end points of a vector can be made. However, if the viewpoint exists in the direction perpendicular to the y-z plane as shown in FIG. 5B, or in the direction perpendicular to the z-x plane as shown in FIG. 5C, the trunk and branches of the vector overlap. Therefore, the distinction between the start and end points of the vector cannot be made.
Furthermore, if a coordinate axis is outside a display area due to the expansion of a region of a particular mark when a vector is displayed with the conventional displaying method, the direction indicator disappears. As a result, the direction from which the vector is seen, cannot be identified.
FIG. 6 is a schematic diagram explaining such a problem. This figure shows a display state of a vector when the three axes are outside the display area. Since the three axes disappear from the display area in this figure, the direction from which the vector is seen cannot be identified.
Provided last is the explanation about a method of displaying an inside of a solid body.
FIG. 7 exemplifies a conventional method for displaying an inside of a solid body. This figure shows one cube included in the rectangular solid body. In this figure, the graphic display is made by removing the front, upper, and right surfaces of the solid body in order to exhibit the existence of the included cube.
As described above, the method for displaying an internal state of a solid body by removing a portion of the solid body, works properly in a three-dimensional graphic displaying system which uses a fixed viewpoint. However, if this method is used in a displaying system which allows a viewpoint to change, the inside of the solid body cannot be displayed when an unremoved side exists, for example, between the cube to be identified and the viewpoint. As a result, the included cube cannot be identified.
FIG. 8 is a schematic diagram explaining such a problem. This figure shows the state in which a solid body in the form of FIG. 7 is seen obliquely from the left front. Since surfaces to be removed are determined in a conventional displaying system, a portion of the included cube is hidden by the left side surface, as shown in FIG. 8. Accordingly, the included object cannot be completely identified.
If the conventional method for displaying scale marks on an axis is used in a three-dimensional graphic displaying system which allows a viewpoint of a displayed graphic to change, by a user operation such as a rotation operation and a move operation for the displayed graphic, the scale marks are merely seen as dots when the viewpoint exists in an extended portion of the scale marks on the axis. Since the axis is drawn over the dots, a first problem that the positions of the scale marks cannot be identified, arises.
Additionally, a second problem exists, in that the direction from which the display area is seen cannot be recognized when the other axes become invisible in the display area, according to the conventional method for displaying coordinate axes and scales when used in such a three-dimensional graphic displaying system.
Additionally, if the conventional method for displaying a vector is used in such a system for displaying a three-dimensional graphic, which allows a viewpoint to change, the trunk and branches of the vector overlap when the vector display graphic is drawn on a plane whose direction is identical to that of a sightline. As a result, a third problem that the distinction between the start and end points cannot be made, arises.
Furthermore, if a coordinate axis disappears from a display area due to an enlargement of the region of a graphic for which a vector is displayed, in such a displaying system, a fourth problem that a direction from which the vector is seen cannot be recognized, arises.
Still further, when an attempt is made to identify an object included in a solid body in such a three-dimensional graphic displaying system which allows a viewpoint to change, a fifth problem arises in that an object included in a solid body cannot be identified when an unremoved surface of the solid body exists between the included object to be displayed and the viewpoint.