Method for global blending of computer modeled solid objects using a convolution integral
First Claim
1. A method for generating a set of blended surfaces for a computer representation of a solid model having a set of curvilinear surfaces, comprising the steps of:
- offsetting the curved surfaces of the solid model;
generating an octree representation of the solid model;
generating a complementary octree representation of the volume outside the solid model;
assigning blend radius values to each individual cell of the octree;
defining a plurality of rays substantially normal to and intersecting the solid model surface;
repetitively solving a convolution integral in an iterative manner at a plurality of locations along each ray, wherein the convolution integral includes a gaussian sphere blending factor with a size responsive to the blend radius assigned to the octree cell;
storing the location on each ray at which the solution of the convolution integral is equal to a preselected value, said stored locations defining the set of blended surfaces of the solid model.
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Abstract
A method for generating a plurality of points that lie on the surface of a blended solid model. These points are obtained from the unblended solid model by a numerical solution to a convolution integral, wherein the convolution integral includes a spherically symmetric blending function with a size responsive to the blend radius desired for each of one or more regions on the solid model. For example, the spherical blending function may possess a constant value everywhere inside a sphere of radius R, and a value of zero outside (here called a "hard sphere"), or it may be represented by other functions of the radial direction, more specifically, the gaussian bell curve, in which case it will be called a "gaussian sphere". The numerical solution to the convolution integral is performed iteratively by placing the blending sphere at a plurality of locations along each of a set of rays that are defined substantially normal to and intersecting the solid model surface. The location on each ray at which the convolution integral is equal to a preselected value is stored. These stored locations may be used directly, or they may be used to define a set of surfaces that interpolate the blended solid model.
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Citations
19 Claims
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1. A method for generating a set of blended surfaces for a computer representation of a solid model having a set of curvilinear surfaces, comprising the steps of:
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offsetting the curved surfaces of the solid model; generating an octree representation of the solid model; generating a complementary octree representation of the volume outside the solid model; assigning blend radius values to each individual cell of the octree; defining a plurality of rays substantially normal to and intersecting the solid model surface; repetitively solving a convolution integral in an iterative manner at a plurality of locations along each ray, wherein the convolution integral includes a gaussian sphere blending factor with a size responsive to the blend radius assigned to the octree cell; storing the location on each ray at which the solution of the convolution integral is equal to a preselected value, said stored locations defining the set of blended surfaces of the solid model. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 11)
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10. A method for generating a set of blended surfaces for a computer representation of a solid model having a set of curvilinear surfaces, comprising the steps of:
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assigning a blend radius to the solid model; offsetting the curved surfaces of the solid model; defining a plurality of rays substantially normal to and intersecting the solid model surface; repetitively solving a convolution integral in an iterative manner at a plurality of locations along each ray, wherein the convolution integral includes a hard sphere blending factor with a radius equal to the blend radius assigned to the solid model; and storing the location on each ray at which the convolution integral is equal to a preselected value, said stored locations defining the set of blended surfaces of the solid model.
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12. a method for generating a set of blended surfaces for a computer representation of a solid model comprising the steps of:
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representing the solid model as a set of geometric cells; defining a plurality of rays substantially normal to and intersecting the solid model surface; assigning blend radius values to cells which a ray intersects; repetitively solving a convolution integral in an iterative manner at a plurality of locations along each ray, wherein the convolution integral includes a blending factor with a size responsive to the blend radius assigned to the cell intersecting the ray; and storing the location on each ray at which the convolution integral is equal to a preselected value, said stored locations defining the set of blended surfaces of the solid model. - View Dependent Claims (13, 14, 15, 16, 17, 18, 19)
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Specification