Abstract: Computer systems may be used to generate and display objects represented by triangles defined by coordinates of vertices. The present invention generates coordinates of a simplified vertex based upon coordinates of vertices adjacent to a first vertex and to a second vertex that define an edge of the triangles. First, a set of triangles that are adjacent to the edge is identified, Second, a first volume associated with the set of triangles is calculated. Finally, the coordinates of the simplified vertex are calculated such that a second volume associated with the simplified vertex corresponds to the first volume. In addition, a technique is presented that generates a second object which is a simplified representation of a first object. The technique begins by identifying first and second vertices that define an edge. The coordinates of a simplified vertex that corresponds to first and second vertices of the edge is determined. Error values and tolerance values are assigned to vertices.

Abstract: Computer systems may be used to generate and display objects represented by triangles defined by coordinates of vertices. The present invention generates coordinates of a simplified vertex based upon coordinates of vertices adjacent to a first vertex and to a second vertex that define an edge of the triangles. First, a set of triangles that are adjacent to the edge is identified, Second, a first volume associated with the set of triangles is calculated. Finally, the coordinates of the simplified vertex are calculated such that a second volume associated with the simplified vertex corresponds to the first volume.

Abstract: Computer systems generate and display objects represented by triangles defined by coordinates of vertices. The present invention generates potential coordinates of a simplified vertex based upon coordinates of a first vertex and a second vertex that define an edge of the triangles. A first set of triangles that are adjacent to the edge are identified, and a first set of error values corresponding to the vertices of the first set of triangles are derived. A second set of triangles tat share the simplified vertex are identified, and a second set of error values corresponding to the vertices of the second set of triangles are derived. The coordinates of the simplified vertex are stored in memory for reuse based upon a predetermined criterion involving the second error values and, preferably, one or more tolerance values. The second error values are derived from error values of a plurality of planar polygons corresponding to the first set of triangles.

Abstract: Disclosed is a representation and file format for a multi-level progressive transmission or display of a triangular mesh, referred to as a Progressive Multi-Level Representation (PMR). Methods are disclosed for generating the PMR, for progressively building a triangular mesh from a PMR representation, and for extracting a particular level of detail of a triangular mesh from the PMR representation.

Abstract: A is a computer implemented method for converting a non-manifold surface to a manifold surface. The method includes the steps of (a) providing data in a memory of a computer for representing a non-manifold polyhedral surface comprised of a plurality of triangles each bounded by edges and having vertices; (b) analyzing the data to determine and record singular edges and singular vertices; and (c) cutting through the singular edges and singular vertices, and optionally other edges and vertices, to provide a plurality of connected polygonal surfaces that are free of singularities. The step of analyzing may include the initial steps of analyzing the data to remove isolated vertices and repeated triangles. The step of cutting operates in accordance with one of a local cutting method or a global cutting method, and may further include a step of stitching the cut surface along boundary edges.

Abstract: A method and system for obtaining and processing acquired images of an object to extract a small scale geometry (a bump map) of the object that is independent of object curvature.

Abstract: A method and system is disclosed for registering two dimensional fluoroscopic images with a three dimensional model of a surgical tissue of interest.