Apparatus and method for geometric morphing
First Claim
1. A method of geometric morphing between a first object having a first shape and a second object having a second shape comprising the steps in combination:
- generating a first Delaunay complex corresponding to said first shape and a second Delaunay complex corresponding to said second shape;
generating a plurality of intermediary Delaunay complexes defined by a continuous family of mixed shapes corresponding to a mixing of said first shape and said second shape;
extracting a plurality of alpha complexes corresponding to said plurality of intermediary Delaunay complexes;
generating a first alpha complex corresponding to said first shape and a second alpha complex corresponding to said second shape;
constructing a first skin corresponding to said first alpha complex and a second skin corresponding to said second alpha complex;
constructing a plurality of intermediary skins corresponding to said plurality of alpha complexes; and
visually displaying said first skin, said second skin and one or more of said plurality of intermediary skins on an output device.
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Abstract
A method of geometric morphing between a first object having a first shape and a second object having a second shape. The method includes the steps of generating a first Delaunay complex corresponding to the first shape and a second Delaunay complex corresponding to the second shape and generating a plurality of intermediary Delaunay complexes defined by a continuous family of mixed shapes corresponding to a mixing of the first shape and the second shape. The method further includes the steps of constructing a first skin corresponding to the first Delaunay complex and a second skin corresponding to the second Delaunay complex and constructing a plurality of intermediary skins corresponding to the plurality of intermediary Delaunay complexes. The first skin, second skin and plurality of intermediary skins may be visually displayed on an output device.
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Citations
23 Claims
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1. A method of geometric morphing between a first object having a first shape and a second object having a second shape comprising the steps in combination:
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generating a first Delaunay complex corresponding to said first shape and a second Delaunay complex corresponding to said second shape; generating a plurality of intermediary Delaunay complexes defined by a continuous family of mixed shapes corresponding to a mixing of said first shape and said second shape; extracting a plurality of alpha complexes corresponding to said plurality of intermediary Delaunay complexes; generating a first alpha complex corresponding to said first shape and a second alpha complex corresponding to said second shape; constructing a first skin corresponding to said first alpha complex and a second skin corresponding to said second alpha complex; constructing a plurality of intermediary skins corresponding to said plurality of alpha complexes; and visually displaying said first skin, said second skin and one or more of said plurality of intermediary skins on an output device. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10)
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11. A method of transforming a source shape corresponding to a source object to a target shape corresponding to a target object comprising the steps in combination:
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storing in a memory a first set of data points corresponding to said source shape and a second set of data points corresponding to said target shape; generating a four dimensional simplical complex corresponding to said source shape and said target shape; and extracting one or more mixed shapes from one or more cross-sections of said four dimensional simplical complex, each of said mixed shapes depending on said source shape and said target shape; constructing one or more skins, each of said skins corresponding to one or more of said mixed shapes; and displaying one or more of said skins on an output device. - View Dependent Claims (12, 13, 14, 15, 16, 17)
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18. Apparatus for graphically transforming a source shape to a target shape comprising, in combination:
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a storage device for storing a first data point set corresponding to said source shape and a second data point set corresponding to said target shape; a memory for storing a series of computer instructions and data structures; a microprocessor for executing said series of computer instructions, said microprocessor generating a first Delaunay complex and a first skin corresponding to said first data point set, said microprocessor generating a second Delaunay complex and a second skin corresponding to said second data point set, said microprocessor generating a plurality of alpha complexes corresponding to the transformation of said source shape to said target shape, and said microprocessor generating a plurality of skins corresponding to said plurality of alpha complexes; an output device for graphically depicting said first skin, said second skin, and one or more of said plurality of skins. - View Dependent Claims (19, 20, 21)
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22. Apparatus for graphically transforming a first geometric object to a second geometric object comprising, in combination:
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measuring means for generating a first point set corresponding to said first object and generating a second point set corresponding to said second object; storage means for storing said first data point set and said second data point set; generating means for; (a) generating a first combinatorial representation of said first data point set; (b) generating a second combinatorial representation of said second data point set; (c) defining a motion between said first point set and said second point set and between said first combinatorial representation and said second combinatorial representation; and transforming said first combinatorial representation into said second combinatorial representation in response to said motion. - View Dependent Claims (23)
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Specification