Computer graphics processing and selective visual display system – Computer graphics processing – Three-dimension
Reexamination Certificate
1996-08-02
2003-10-28
Jankus, Almis R. (Department: 2671)
Computer graphics processing and selective visual display system
Computer graphics processing
Three-dimension
C345S423000, C345S606000
Reexamination Certificate
active
06639592
ABSTRACT:
REFERENCE TO APPENDIX
This application includes a section of a user manual for PowerAnimator™ Version 7.5 entitled “Introduction to Curve Networks” (pages 363 to 399). The copyright owner has no objection to paper reproduction of the appendix as it appears in this patent document, or in the official files of the U.S. Patent & Trademark Office, but grants no other license and reserves all other rights whatsoever. The entire appendix is hereby incorporated by reference as if fully set forth herein.
BACKGROUND
This invention relates to curve networks for computer modeling.
Many computer applications generate or model smooth curved surfaces. Computer aided design (CAD) systems, computer animation tools, and computer graphics applications are often used to replicate inherently smooth real-world objects, or to generate novel objects. Many objects are not susceptible to exact mathematical description, and are often modeled interactively by a user employing artistic instead of scientific criteria. Computer systems require satisfactory methods of representing these objects and their surfaces. Since computers have finite storage and processing capacity, an object cannot be modeled with an infinite number of coordinate points. Instead, various methods approximate object surfaces with segments such as planes, lines, and other object “primitives” that are easier to describe mathematically.
One modeling method uses a polygon mesh, a set of connected polygonally bounded planar surfaces. Rectilinear objects, such as boxes or buildings, can be easily modeled with polygon meshes. Representing objects with curved surfaces using a polygon mesh requires approximating a curved surface by a number of smaller planar segments. Error between the approximated representation and the real object can be made arbitrarily small by using more polygons. Using larger numbers of segments requires greater computer memory storage and computation capacity.
Another modeling method uses sets of parametric bivariate (two-variable) polynomial surface patches to represent a curved object. By using inherently curved surface segments, this method enables a computer modeler to represent arbitrary curved surfaces very accurately. Typically, an object is broken down into a set of connected surface area faces, each face is modeled with a parametric polynomial surface, and the surfaces are connected together to yield the final object representation. The algorithms for employing bivariate polynomial surfaces are more complex than those for polygons, but fewer polynomial surface patches are required to approximate a curved surface to a given accuracy than with polygon meshes.
Typically, polynomial surface methods employ parametric equations based on cubic polynomial equations of a parameter (for a curve segment, one parameter is used, e.g., “t”; for a surface, two parameters are used, e.g., “u” and “v”). A number of different polynomial forms for curves and surfaces have been developed, including Hermite, Bezier, and B-spline. Whatever parameter form is chosen, one or more surfaces can be generated based upon a compact set of control points (or vertices) that unambiguously define the shape of a given curve or surface. The boundaries or edges between two polynomial surfaces can be continuous in position, tangent and curvature (0th, 1st, and 2nd derivatives). As a modeler builds up an object representation, each surface can be attached to the next, and continuity constraints across the boundary can be set to yield transitions having an arbitrary sharpness or smoothness, as desired.
SUMMARY
In general, in a first aspect, the invention features a method of computer surface modeling including the steps of storing in a computer memory a curve network of intersecting curves, and automatically determining faces from the curve network.
Implementations of the invention may include the following features. The intersections of the curves may be automatically determined, the intersections forming vertices. Curve segments between intersections of the curves may be automatically determined, the curve segments forming edges. The faces may be closed regions formed by curve segments of the intersecting curves. An interpolated curved surface for a corresponding one of the faces may be automatically calculated and stored in the computer memory. The faces may be automatically determined by a topology estimation routine. The topology estimation routine may search coupled curve segments lying between intersections of the-curves. The intersecting curves may include b-spline, non-uniform rational b-spline, or non-uniform non-rational b-spline parameterized curves. The interpolated surface may include a b-spline parameterized surface. The face may be formed from any number of coupled curve segments, or may be only three-sided or four-sided, or only four-sided. The interpolated surface may be four-sided, or the interpolated surface may be generated as four-sided and then clipped if the corresponding face is not four-sided. The curve network may be interactively generated by a user of the computer surface modeling method. Forming the curve network may include calculating and recording each intersection between all intersecting pairs of the plurality of intersecting curves as vertices, and calculating and recording each curve segment along each of the plurality of curves between successive vertices as edges.
In general, in another aspect, the invention features a method of computer surface modeling including the steps of storing in a computer memory a curve network of intersecting curves, and an interpolated surface for a face of the curve network, and modifying the interpolated surface in response to manipulation of a control curve.
Implementations of the invention may include the following features. Modifying the interpolated surface may include sampling the control curve at a sampling point, coupling the sampling point to a projection point on the interpolated surface, and controlling the shape of the interpolated surface at the projection point based upon the coupled sampling point. Controlling the shape of the interpolated surface may include performing a constrained least squares minimization calculation in which the coupled projection point is a constraint, and a control vertex of the interpolated surface is a free variable.
In general, in another aspect, the invention features, a method of computer surface modeling including the steps of storing in a computer memory a curve network of intersecting curves defining faces and edges, setting a continuity constraint at an edge of a first one of the faces, and automatically generating and storing in the computer memory an interpolated curved surface for the first face based on the set continuity constraint.
Implementations of the invention may include the following features. The continuity constraint may include positional continuity, tangential continuity, or curvature continuity. The edge may couple the first face to a second face. An interpolated curved surface for the second subject to the set continuity constraint may be automatically generated and stored in the computer memory.
In general, in another aspect, the invention features an interface method for use with a computer-based surface modeling program including the steps of enabling a user to define interactively curves forming portions of a curve network associated with a surface being modeled, and automatically, in response to the defining of curves by the user, determining faces associated with the curves.
In general, in another aspect, the invention features an interface method for use with a computer-based surface modeling program including the steps of enabling a user to manipulate interactively a curved control element shown on a display, and automatically altering a surface being modeled in response to the user's manipulations of the curved control element.
The advantages of the invention may include one or more of the following. A computer modeler does not have to construct each surface individually, stitching them together into a
Dayanand Sriram
Rice Richard E.
Jankus Almis R.
Silicon Graphics Inc.
Staas & Halsey , LLP
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