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US 2018/0293791 A1Published application
Physical object production using a refined model
AssigneeBrigham Young University (BYU)
InventorsThomas W. Sederberg, Xin Li
Life of this patent
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Abstract
Techniques of refining a model of a complex surface can include deriving a set of refinement rules based on eigen polyhedra in a plane. Such rules reduce the refinement of a mesh in the plane to a scale and translation of the eigen polyhedron. Such refinement rules may then be applied to a non-uniform mesh in three-dimensional space having an extraordinary point in place of conventional refinement rules used in Catmull-Clark surfaces or NURBS surfaces. When these refinement rules are applied to a non-uniform mesh having an extraordinary point, the limiting surface is G1 at the extraordinary point, i.e., the tangent surfaces of the limiting mesh are continuous at the extraordinary point.
Claims20
A method, comprising:
- receiving, by processing circuitry configured to generate a surface model representing an object for manufacture, spatial mesh data representing a spatial mesh, the spatial mesh including a vertex of the spatial mesh and a plurality of edges, the vertex being an extraordinary control point of the spatial mesh, each of the plurality of edges being disposed between the vertex and a respective, adjacent control point of the spatial mesh, the vertex having a valence number with respect to the plurality of edges;
- generating, by the processing circuitry, eigen polyhedron data representing a plane mesh including an initial vertex in a plane and a plurality of initial edge points in the plane, the plurality of initial edge points being arranged in the plane with respect to the initial vertex based on the valence number;
- generating, by the processing circuitry, scale data representing a scale factor based on the valence number, the plane mesh being configured to scale in size with respect to the initial vertex in the plane by the scale factor after a plane mesh refinement operation;
- generating, by the processing circuitry, refinement matrix data representing a refinement matrix based on the eigen polyhedron data, the eigen polyhedron data being eigenvectors of the refinement matrix data, the scale factor being an eigenvalue of the refinement matrix corresponding to at least one of the eigenvectors;
- and
- performing, by the processing circuitry, a spatial mesh refinement operation on the spatial mesh data to produce refined mesh data, the spatial mesh refinement operation being based on the refinement matrix data, the refined mesh data representing a refined mesh and providing a surface model that has continuous tangent planes in a neighborhood of a vertex of the refined spatial mesh, thereby providing an accurate surface model of the object for manufacture when the surface model has an extraordinary control point.
3 more elements
A computer program product comprising a nontransitory storage medium, the computer program product including code that, when executed by processing circuitry of a computer configured to generate a surface model representing an object for manufacture, causes the processing circuitry to perform a method, the method comprising:
- receiving spatial mesh data representing a spatial mesh, the spatial mesh including a vertex of the spatial mesh and a plurality of edges, the vertex being an extraordinary control point of the spatial mesh, each of the plurality of edges being disposed between the vertex and a respective, adjacent control point of the spatial mesh, the vertex having a valence number with respect to the plurality of edges;
- generating eigen polyhedron data representing a plane mesh including an initial vertex in a plane and a plurality of initial edge points in the plane, the plurality of initial edge points being arranged in the plane with respect to the initial vertex based on the valence number;
- generating scale data representing a scale factor based on the valence number, the plane mesh being configured to scale in size with respect to the initial vertex in the plane by the scale factor after a plane mesh refinement operation;
- generating refinement matrix data representing a refinement matrix based on the eigen polyhedron data, the eigen polyhedron data being eigenvectors of the refinement matrix data, the scale factor being an eigenvalue of the refinement matrix corresponding to at least one of the eigenvectors;
- and
- performing a spatial mesh refinement operation on the spatial mesh data to produce refined mesh data, the spatial mesh refinement operation being based on the refinement matrix data, the refined mesh data representing a refined mesh and providing a surface model that has continuous tangent planes in a neighborhood of a vertex of the refined spatial mesh, thereby providing an accurate surface model of the object for manufacture when the surface model has an extraordinary control point.
3 more elements
An electronic apparatus configured to generate a surface model representing an object for manufacture, the electronic apparatus comprising:
- a network interface;
- a memory;
- and
- controlling circuitry coupled to the memory, the controlling circuitry being configured to:
- receive spatial mesh data representing a spatial mesh, the spatial mesh including a vertex of the spatial mesh and a plurality of edges, the vertex being an extraordinary control point of the spatial mesh, each of the plurality of edges being disposed between the vertex and a respective, adjacent control point of the spatial mesh, the vertex having a valence number with respect to the plurality of edges;
- generate eigen polyhedron data representing a plane mesh including an initial vertex in a plane and a plurality of initial edge points in the plane, the plurality of initial edge points being arranged in the plane with respect to the initial vertex based on the valence number;
- generate scale data representing a scale factor based on the valence number, the plane mesh being configured to scale in size with respect to the initial vertex in the plane by the scale factor after a plane mesh refinement operation;
- generate refinement matrix data representing a refinement matrix based on the eigen polyhedron data, the eigen polyhedron data being eigenvectors of the refinement matrix data, the scale factor being an eigenvalue of the refinement matrix corresponding to at least one of the eigenvectors;
- and
- perform a spatial mesh refinement operation on the spatial mesh data to produce refined mesh data, the spatial mesh refinement operation being based on the refinement matrix data, the refined mesh data representing a refined mesh and providing a surface model that has continuous tangent planes in a neighborhood of a vertex of the refined spatial mesh, thereby providing an accurate surface model of the object for manufacture when the surface model has an extraordinary control point.
7 more elements
Dependencies are inferred from the claim text.