Computer graphics processing and selective visual display system – Computer graphics processing – Shape generating
Patent
1995-02-07
1997-09-02
Herndon, Heather R.
Computer graphics processing and selective visual display system
Computer graphics processing
Shape generating
G06T 1120
Patent
active
056640854
DESCRIPTION:
BRIEF SUMMARY
TECHNICAL FIELD
The present invention relates to a method of and an apparatus for generating a circle tangential to two figure elements including at least one free curve or ellipse, and more particularly to a method of and an apparatus for stably generating a circle or rounded corner tangential to two figure elements including at least one free curve or ellipse which is generated in an interactive system such as a CAD (computer-aided design) system.
BACKGROUND ART
CAD systems produce drawings such as design drawings on the screen of a graphic display using basic figure elements including straight lines, circles, and arcs, and also free curves such as spline curves. In designing products or decorative patterns, it is commonly practiced to round a corner composed of two figure elements or draw a circle positioned between and tangential to two figure elements, and there is available a function to draw tangential circles or rounded corners with ease.
On a two-dimensional CAD system, a corner of a rectangle can be rounded by executing a command which produces a round having a radius "r" between two figure elements. This is because if the figure to be processed is a rectangle, then the center of curvature of an arc can simply be determined by calculating the length of the radius "r" from the joint between two successive figure elements. In rectangles, therefore, rounded corners or circles tangential to two sides can easily and accurately be calculated geometrically and algebraically.
If at least one of the figure elements is a free curve which is normally called a spline or Bezier curve or an ellipse, then it is not easy to round a corner or generate a tangential circle with respect to those figure elements because the center of a tangential circle cannot be determined geometrically.
FIGS. 1(A) and 1(B) of the accompanying drawings show a tangential circle and a rounded corner, respectively, with .respect to two figure elements at least one of which is a free curve. Specifically, FIG. 1(A) illustrates two figure elements S.sub.1, S.sub.2 which are spline curves and a circle C.sub.1 having a radius "r" which is tangential to these spline curves, and FIG. 1(B) illustrates a rounded corner composed of an arc C.sub.2 having a radius "r" of curvature which is positioned at a point of intersection between a straight line L and a figure element S.sub.3 which is a spline curve. Generally, a convergent calculation method is employed in the generation of such a tangential circle and a rounded corner.
The convergent calculation method is a method of solution that is relied upon when no analytic solution is available. According to the convergent calculation method, a mathematical formula is produced with the condition of being tangential used as an undetermined variable, and the undetermined variable is varied, starting from a suitable initial value, until the formula converges into a final desirable solution. For example, if a figure element is a spline curve which is formed by smoothly joining a plurality of points, then since the spline curve necessarily has a start point and an end point, the start point is used as an initial value, and solutions are successively determined from the initial value. In this manner, the solutions are successively converged, searching for a region where the spline curve and a circle having a radius "r" are tangential to each other. When the region is found, the tangential circle can then be drawn by determining the center of the circle and the point where the circle is tangential to the spline curve. If a rounded corner is to be generated, then since the point of intersection between the spline curve and the tangential circle has been determined, it is similarly possible to generate and display an arc.
However, inasmuch as the undetermined variable is varied, starting from a suitable initial value, until the formula converges into a final desirable solution according to the convergent calculation method, a tangential circle may not necessarily be generated in a position intended by the
REFERENCES:
patent: 4855926 (1989-08-01), Seki et al.
patent: 5345546 (1994-09-01), Harada et al.
patent: 5410489 (1995-04-01), Seki et al.
patent: 5410645 (1995-04-01), Ooka et al.
McCracken, et al "Computing for Engineers and Scientists with Fortran 77", John Wiley & Sons, Inc., 2ed, 1988, pp. 170-235.
DeMaria, Russel, "MGMStation CAD", BYTE Jan. 1988; p. 178; vol. 13, No. 1.
McCarthy, Tim, "Easy arcs", Cadcam, v12, n2, p73(3), Feb., 1993.
Halliday, Caroline, "DesignCAD update has better speed, bigger command set; now competes with fastest low-end CAD packages, but it requires more power, RAM", InfoWorld, v15, n21, p148(3), May 24, 1993.
Choi, B. K., et al, "Constraint-radius Blending in Surface Modeling", Computer Aided Design, vol. 21, No. 4, May 1989, pp. 231-222.
Buchel Rudolph
Fujitsu Limited
Herndon Heather R.
LandOfFree
Method of an apparatus for generating tangential circle does not yet have a rating. At this time, there are no reviews or comments for this patent.
If you have personal experience with Method of an apparatus for generating tangential circle, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Method of an apparatus for generating tangential circle will most certainly appreciate the feedback.
Profile ID: LFUS-PAI-O-314959