Mesh simplification and construction of progressive meshes
First Claim
1. In a computer, a method of simplifying an arbitrary initial mesh having a plurality of vertices and a connectivity of the vertices defining edges between connected pairs of the vertices and faces defined by plural connected edges for representing multi-dimensional objects with computer graphics, comprising:
- (a) choosing an edge of the mesh;
(b) performing an edge collapse transformation on the edge to produce a simpler mesh wherein the pair of vertices connected by the edge is replaced by the edge collapse transformation with a single vertex; and
(c) performing a plurality of iterations of the steps (a) and (b) to produce a base mesh having a desired level of detail.
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Accused Products
Abstract
An efficient, lossless, continuous-resolution representation (the "PM representation") of highly detailed geometric models for computer graphics specifies a succession of progressively more detailed polygonal meshes (i.e., "progressive meshes") as a base polygonal mesh and a sequence of complete mesh refinement transformations (e.g., the vertex split transformation) that approximate the model at progressively finer levels of detail. Procedures for storing and transmitting geometric models using the PM representation address several practical problems in computer graphics: smooth geomorphing of level-of-detail approximations, progressive transmission, mesh compression, and selective refinement. An optimized mesh simplification procedure constructs the PM representation of a model from an arbitrary polygonal mesh, while preserving the geometry of the original mesh as well as its overall appearance as defined by its discrete and scalar appearance attributes such as material identifiers, color values, normals, and texture coordinates. In particular, the PM representation and these procedures preserve discontinuity curves such as creases and material boundaries of the geometric model.
177 Citations
21 Claims
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1. In a computer, a method of simplifying an arbitrary initial mesh having a plurality of vertices and a connectivity of the vertices defining edges between connected pairs of the vertices and faces defined by plural connected edges for representing multi-dimensional objects with computer graphics, comprising:
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(a) choosing an edge of the mesh; (b) performing an edge collapse transformation on the edge to produce a simpler mesh wherein the pair of vertices connected by the edge is replaced by the edge collapse transformation with a single vertex; and (c) performing a plurality of iterations of the steps (a) and (b) to produce a base mesh having a desired level of detail. - View Dependent Claims (2, 3, 4)
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5. In a computer, a method of constructing a variable resolution representation of a multi-dimensional object from an arbitrary initial mesh representation of the object for displaying computer graphics views of the objects the arbitrary initial mesh having a plurality of vertices and a connectivity of the vertices defining a plurality of edges between connected pairs of the vertices, the method comprising:
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choosing a succession of mesh simplifying transformations that, when applied successively beginning with the arbitrary initial mesh, yield a succession of progressively simpler meshes, and a last in the succession of mesh simplifying transformations yielding a base mesh; and recording the base mesh and a succession of mesh refining transformations which are an inverse of the mesh simplifying transformations and in a reverse order of the succession of mesh simplifying transformations, the mesh refining transformations exactly reproducing the arbitrary initial mesh when applied successively beginning with the base mesh. - View Dependent Claims (6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19)
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20. A computer based system for constructing a variable resolution representation of a multi-dimensional object from an arbitrary initial mesh representation of the object for displaying computer graphics views of the object, the arbitrary initial mesh having a plurality of vertices and a connectivity of the vertices defining a plurality of edges between connected pairs of the vertices, the system comprising:
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a mesh transformation processor for iteratively choosing a mesh simplifying transformation, and applying the chosen mesh simplifying transformation to a current mesh in a succession of progressively simpler meshes beginning with the initial arbitrary mesh to yield a next mesh in the succession, a last in the succession of mesh simplifying transformations yielding a base mesh; and an encoder for recording the base mesh and a succession of mesh refining transformations which are an inverse of the mesh simplifying transformations and in a reverse order of the succession of mesh simplifying transformations;
the mesh refining transformations exactly reproducing the arbitrary initial mesh when applied successively beginning with the base mesh. - View Dependent Claims (21)
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Specification