 Electronic device and lead frame used thereon |
| An object of the invention is to provide an electronic device and a lead frame thereof which are ... |
|
| Automatic generation of a set of contiguous surface patches on a computer modeled solid |
| I claim: 1. A method of operating a computer for generating a plurality of machine tool paths for ... |
|
| Rendering polygons |
| The invention provides a method and an apparatus for scanning a polygon that selects scan ... |
|
| Data decompression system and method |
| The present invention is an improvement in data decompression for images, using relatively simple ... |
|
| Method of measuring three dimensional shape |
| Accordingly, the object of the present invention is to provide a method of measuring a three-... |
|
| Method of and system for encoding digital images |
| Accordingly, an objective of the present invention is to efficiently store edge information which ... |
|
| Surface covering tiles |
| Having thus set forth the nature of the invention what is claimed is: 1. A plurality of identically ... |
|
|
Creating and modifying parameterizations of surfaces
| Details |
Inventors: Krishnamurthy, Venkat;
Assignee: Paraform, Inc. (Santa Clara, CA); The Board of Trustees of the Leland Stanford Junior University (Palo Alto, CA)
Primary Examiner: Cuchlinski, Jr.; William A.
Assistant Examiner: Nguyen; Thu
Attorney, Agent or Firm: Lumen Intellectual Property Services, Inc.
A method for creating a parameterization of an input surface in a 3-D computer graphics system comprises specifying a plurality of boundary curves on the surface that define a patch of the surface. The boundary curves are typically specified using a user-interactive curve editing procedure, but may also be specified automatically. Similarly, a feature curve is specified on the surface. The method then automatically generates a parameterization of the patch such that a discretized higher order energy functional defined on the surface is minimized subject to the constraint that iso-curves of the parameterization are attracted to follow the feature curve. The method is useful for converting dense irregular polygon meshes into surface models suitable for interactive modification and animation. |
|
DETAILED DESCRIPTION In the following description we explain the details of a parameterization algorithm according to the present invention within the context of the specific application of surface fitting to scanned 3-dimensional data.
The same parameterization technique, however, can be used within the context of a number of other applications, some of which have been detailed above.
DEFINITIONS Throughout this document, we define a surface to be a 2-dimensional manifold and an unparameterized surface to be a 2-dimensional manifold without any smooth global parameterization.
A polygon mesh is an example of an unparameterized surface because no single differentiable formula can be used to define it globally.
We define a polygon mesh or polygon surface to be a 2-dimensional manifold represented as a union of polygons.
Typically, the polygons and the polygon surface are represented as 2-manifolds embedded in 3-D Euclidean space.
For example, a polygon mesh may be represented as a set of points (called vertices) in 3-D Euclidean space, together with a set of faces (groups of 3 or more vertices that share a common face), a set of edges (groups of 2 vertices that share an edge), and an adjacency structure that can be used to easily determine which vertices, edges, and faces are adjacent to any given vertex, edge, or face.
A surface curve on a surface is defined to be a 1-dimensional manifold embedded in a 2-D manifold (the surface).
A face-point curve is a surface curve defined by a sequence of connected face points, where a face point is simply a point on some face of a polygonal surface.
A face-point curve may be represented, for example, by a sequence of points embedded in 3-D Euclidean space, where each point is contained in a face of the polygon mesh.
A feature curve is a surface curve that rigidly or loosely guides a parameterization.
A feature curve that loosely guides the parameterization are refereed to as a flow curve to distinguish it from a feature curve that rigidly guides the parameterization
|
|
Graphic Cards 
