Computer graphics processing and selective visual display system – Computer graphics processing – Shape generating
Reexamination Certificate
1997-04-30
2001-07-31
Zimmerman, Mark (Department: 2671)
Computer graphics processing and selective visual display system
Computer graphics processing
Shape generating
Reexamination Certificate
active
06268871
ABSTRACT:
This application includes a section of a user manual for Alias Auto Studio™ Version 8.0 entitled “Introduction to Blend Curves” (pages 45 to 72). 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 generation for computer graphics.
Many computer applications generate or model curves. Computer aided design (CAD) systems, computer animation tools, and computer graphics applications all attempt to replicate smoothly curved real-world objects, or to generate new curved objects designed and developed with these tools. 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 edges and surfaces. Since computers have finite storage and processing capacity, an object cannot be modeled with an infinite number of coordinate points. Instead, object surfaces are approximated by segments such as curves, lines, planes, and other object “primitives” that are easier to describe mathematically.
Certain modeling methods use parametric polynomial curves to build up a model of an object. Typically, polynomial curve methods employ parametric equations based on cubic polynomial equations of a parameter (for a line segment, one parameter is used, e.g., “s”; for a surface, two parameters are used, e.g., “u” and “v”). A number of different polynomial forms for lines and surfaces have been developed, including Hermite, Bézier, and B-spline. Whatever parameter form is chosen, one or more curved lines or surfaces can be generated based upon a compact set of control points (or vertices) that unambiguously define the shape of those curves or surfaces. Parametric curves can be “re-parameterized” by a substitution of one ordered set of parameters for another in a one-for-one transformation, without changing the curve's appearance.
Often, a computer model of an object will require that several separately created curves match at their boundaries to create one seamless integrated object.
SUMMARY
In general, in one aspect, the invention features a method of computer generation of a curve through points including accepting positions of the points, accepting a geometric continuity condition for at least one of the points, constructing the curve through the points, the curve obeying the geometric continuity condition, and storing constructed curve in a memory.
Embodiments of the invention may include the following the features. The geometric continuity conditions may be at least G
0
, G
1
, or at least G
2
. At least one of the points may be on a constraint curve, or on a constraint surface. The curve may be constructed using a least squares approximation. The least squares approximation may use control vertices of the constructed curve as variables. The least squares approximation may be an iterative series of least squares approximations, and each iterative least squares approximation may calculate a successively higher geometric continuity order for each of the points that requires the successively higher geometric continuity order. The method may include displaying the constructed curve.
In general, in another aspect, the invention features a method of computer generation of a curve through points including accepting positions of the points, accepting a geometric continuity condition for at least one of the points, constructing the curve through the points using a least squares approximation, wherein the least squares approximation uses control vertices of the constructed curve as variables, the curve obeying the geometric continuity condition, storing the constructed curve in a memory, and displaying the constructed curve.
In general, in another aspect, the invention features a computer program, residing on a computer-readable medium, comprising instructions for generating a curve through points by causing a computer to accept positions of the points, accept a geometric continuity condition for at least one of the points, construct the curve through the points, the curve obeying all accepted geometric continuity conditions, and store the constructed curve in a memory.
In general, in another aspect, the invention features a computer system for generating a curve through points including a central processing unit, a user input device for accepting positions of the points, and for accepting a geometric continuity condition for at least one of the points, a memory, a curve generation program stored in the memory, the curve generation program, when loaded and operated by the central processing unit, adapted to construct the curve through the points, the curve obeying the geometric continuity condition.
The advantages of the invention may include one or more of the following. A blended curve can be constructed that intersects constraint curves, surfaces, and clouds of points, and matches, to a defined order of geometric continuity, their curvature at the intersections. Such blended curves can exhibit a curve history, meaning that the blended curves remain attached to their constraint curves and surfaces even as those curves and surfaces are moved. Blended curves can be created and edited without placing control vertices: constraint points are simply placed anywhere the blended curve should pass through. An arbitrary number of constraint points can be selected, and each of these points can prescribe an arbitrary order of geometric continuity at that point. Very smooth blended curves can be constructed, which have desirable aesthetic properties, particularly by setting higher orders of geometric continuity where one curve must join another curve or surface.
Other features and advantages of the invention will become apparent from the following description and from the claims.
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Parametric Technology Corp., Pro/Designer User's Guide, http://www.me.fau.edu/computer/prohelp/proids/model: “About This Guide” at page /about.htm#1002253 and “Overview” at page /oview.htm#1005723; also “Customer Support” at http://www.ios.chalmers.se/data/da...ualer/proe/support/cs/designer.htm; all copyrighted in 1997.
Adobe Systems Inc., Adobe Illustrator 8.0 product information, at http://www.adobe.com/proindex/illustrator/main.html, copyright 1999.
James D. Foley et al., Computer Graphics Principles and Practice, Second Edition in C, Addison-Wesley Publishing Co., Reading, MA, 1997, Chapter 8, “Input Devices, Interaction Techniques and Interaction Tasks, ” pp. 347-389.
James D. Foley et al., Computer Graphics Principles and Practice, Second Edition in C, Addison-Wesley Publishing Co., Reading, MA, 1997, Chapter 9, “Dialog Design, ” pp. 391-433.
James D. Foley et al., Computer Graphics Principles and Practice, Second Edition in C, Addison-Wesley Publishing Co., Reading, MA, 1997, Chapter 11, “Representing Curves and Surfaces, ” pp. 471-531.
John A. Gregory, “Geometric Continuity, ” Mathematical Methods in Computer Aided Geometric Design, Academic Press, Boston, 1989, pp. 353-356 and 367-371.
McPheeters Craig W.
Rice Richard E.
Padmanabhan Mano
Silicon Graphics Inc.
Staas & Halsey , LLP
Zimmerman Mark
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