California Institute of Technology

Nathan Jacob Litke

Peter Schroeder

Adi Levin

Martin Rumpf

A method, apparatus, and article of manufacture provide the ability to construct an optimal parameterization for a discrete surface patch. A three-dimensional image having a surface is selected. An initial parameterization of the surface onto a two-dimensional plane is constructed. A distortion of the initial parameterization is measured. A length parameter, an area parameter, and an angle parameter are specified. The initial parameterization is then optimized through a discrete deformation of a parameter domain that minimizes the distortion based on the length, area, and angle parameter.

Method for constructing surface parameterizations

A method of subdividing a representation of an object surface comprising a tessellated mesh of polygons is provided. The surface may be bounded by one or more boundary curves. One or more polygons in the mesh may be each subdivided into child polygons, each having one or more vertices. The result is a second mesh representation which may have a finer level of resolution than the original mesh. The locations or parameters of the vertices of the child polygons in the second mesh may be determined using suitable weightings of the locations or parameters of adjacent vertices in the original mesh. The locations of the vertices in the second mesh may be further refined through application of detail vectors. The locations of boundary vertices are always constrained to lie on one of the boundary curves bounding the surface in question. The method may continue iterating until the surface as represented by the subdivided surface representation is fine enough for the intended application.

Object surface representation and related methods and systems

A method of trimming a mesh representation of an object surface comprising a tessellated mesh of polygons. A trim curve is projected onto the mesh representation to determine the trim area. Polygons within or intersecting the trim area are removed, and new polygons are introduced to attach the trimmed mesh to the trim curve projection. Detail data is formed for vertices of polygons near the trim curve, representing information about the object surface not present in the trimmed mesh representation. The detail data is applied to the vertices, thereby refining their locations. Any polygons near the trim curve which are outside a prescribed tolerance of the object surface are subdivided. The steps of forming and applying the detail data followed by the step of subdividing are iteratively performed until the trimmed mesh representation is within a prescribed tolerance of the object surface.

Method of trimming a representation of an object surface comprising a mesh of tessellated polygons and related system

A method of forming detail data corresponding to a vertex of a polygonal mesh representation of an object surface. The mesh representation has a limit surface, and the vertex has a limit point on the limit surface. The detail data for the vertex relates to the shape of the limit surface near the limit point corresponding to the vertex, and may capture detail about the object surface which is not captured by the mesh representation. The method may involve forming difference or detail data for one or more vertices from the group comprising the vertex in question and one or more neighboring vertices, weighting the resulting difference or detail data with prescribed weights, and deriving the detail data for the vertex in question from the weighted difference or detail data. The difference data for a vertex is the difference between the vertex as mapped onto the object surface and the limit point for the vertex on the limit surface.

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Pasadena, CA, United States of America

Nathan Jacob Litke