Method and apparatus for multi-dimensional shape representation via shock flows
First Claim
1. A method for representing a multidimensional shape, comprising the steps of:
- receiving as input a plurality of points in space;
forming a plurality of shocks based on said plurality of points by initiating a plurality of wavefronts at selected points of said plurality where shocks are formed at collisions of said plurality of wavefronts, said plurality of shocks holding topology information about the multidimensional shape, said topology information including flow speed and accelerations and direction from boundaries of said multidimensional shape; and
generating a shock scaffold from said plurality of shocks, said shock scaffold representing the multidimensional shape where the multidimensional shape is capable of being reconstructed from said shock scaffold.
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Abstract
A method and apparatus for representing a multi-dimensional shape includes deriving a shock scaffold from an unorganized point cloud. The shock scaffold is derived by shocks recovered from collisions of logical wavefronts. The logical wavefronts are initialized from selected points in the unorganized point cloud. Shocks hold topology information including speed accelerations and direction from boundaries of the multi-dimensional shape. The shocks recovered from wavefront collisions define shock sheets of the multi-dimensional shape. Representative shock points of the shock sheets are paired to find shock curve representatives as another set of special shock points. The latter are also paired to find shock vertices and the remaining nodes and links defining the full shock scaffold representation of the multi-dimensional shape.
19 Citations
23 Claims
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1. A method for representing a multidimensional shape, comprising the steps of:
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receiving as input a plurality of points in space;
forming a plurality of shocks based on said plurality of points by initiating a plurality of wavefronts at selected points of said plurality where shocks are formed at collisions of said plurality of wavefronts, said plurality of shocks holding topology information about the multidimensional shape, said topology information including flow speed and accelerations and direction from boundaries of said multidimensional shape; and
generating a shock scaffold from said plurality of shocks, said shock scaffold representing the multidimensional shape where the multidimensional shape is capable of being reconstructed from said shock scaffold. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14)
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15. A method for representing a multidimensional shape, comprising the steps of:
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receiving as input a plurality of polygons in space;
determining pairs of generator polygons based on visibility constraints between polygons in said plurality;
generating a first plurality of wavefronts from a first generator polygon in each pair;
generating a second plurality of wavefronts from a second generator polygon in each pair, where said pluralities of wavefronts include planar wavefronts from planes of said first and said second generator polygons, spherical wavefronts from said vertices of said first and said second generator polygons, and cylindrical wavefronts from edges of said first and said second generator polygons;
determining shocks from collisions of said first plurality of wavefronts and said second plurality of wavefronts; and
generating a shock scaffold representing said multidimensional shape from said plurality of shocks where the multidimensional shape can be reconstructed from the shock scaffold.
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16. A shock scaffold for representing a multidimensional shape, comprising:
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a plurality of shocks, each shock holding topology information about the multidimensional shape by storing position information from a plurality of generator points related to the surface of the multidimensional shape and flow direction of the surface of the multidimensional shape;
a plurality of implicit curve segments connecting said plurality of shocks; and
a plurality of implicit shock sheets described by said plurality of implicit curve segments, wherein said plurality of shocks, said plurality of implicit curve segments, and said implicit shock sheets form a directed graph that is a representation of the multidimensional shape where the multidimensional shape can be reconstructed from the information contained in the shock scaffold. - View Dependent Claims (17, 18, 19)
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20. A system for representing a multidimensional shape, comprising:
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a memory;
an interface which is configured to receive a plurality of sample points corresponding to the multidimensional shape; and
a controller coupled to said memory and said interface, said controller being configured to (i) generate a shock scaffold to represent the multidimensional shape based on said plurality of sample points, and (ii) store said shock scaffold in said memory, wherein said shock scaffold includes nodes defined as critical points of flow speed and direction of surface boundaries of said multidimensional shape. - View Dependent Claims (21, 22, 23)
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Specification