System, method, and computer program product for radial functions and distributions of three dimensional object models
View Patent ↗A system, method, and computer program product for determining a radial function and distribution of a three-dimensional object model. One method includes retrieving a three-dimensional object model in a CAD system and sampling random points on the surface of the object model. The method also includes determining a normal vector corresponding to each of the random points and determining a radial function corresponding to each normal vector and respective random point. The method also includes determining, by the CAD system, a radial distribution corresponding to at least two of the radial functions and storing the radial distribution and average values of the radial functions in the CAD system.
1. A method for determining a radial function and distribution of a three-dimensional object model, comprising:
retrieving a three-dimensional object model in a CAD system;
sampling, by the CAD system, random points on the surface of the object model;
determining, by the CAD system, a normal vector corresponding to each of the random points;
determining, by the CAD system, a radial function corresponding to each normal vector and respective random point;
determining, by the CAD system, a radial distribution corresponding to at least two of the radial functions; and
storing the radial distribution and average values of the radial functions in the CAD system.
2. The method of claim 1 , further comprising associating the radial distribution with the object model as a CAD object descriptor.
3. The method of claim 1 , wherein the random points are sampled using a uniform distribution.
4. The method of claim 1 , wherein the radial function is determined according to a projection of the random point on a sphere.
5. The method of claim 1 , wherein determining the radial function includes using a correcting term to adjust for non-uniform distribution of the sampled points as projected on a sphere.
6. The method of claim 1 , wherein the radial function is associated with a function on three-dimensional space and the three-dimensional object model.
7. The method of claim 1 , wherein sample points within a preselected normal distance from the origin are ignored.
8. The method of claim 1 , wherein the radial distribution is associated with a function on three-dimensional space and the three-dimensional object model as the quotient of a first radial function and a second radial function, wherein the second radial function is associated with a function on three-dimensional space that is constant and equal to 1.
9. The method of claim 1 , wherein the radial functions and the radial distribution corresponding to the object model are stored in the CAD system as average values on elements of a partition of a sphere.
10. A data processing system comprising a processor and accessible memory, the data processing system implementing a CAD system and configured to perform the steps of:
retrieving a three-dimensional object model;
sampling random points on the surface of the object model;
determining a normal vector corresponding to each of the random points;
determining a radial function corresponding to each normal vector and respective random point;
determining a radial distribution corresponding to at least two of the radial functions; and storing the radial distribution and average values of the radial functions.
11. The data processing system of claim 10 , further configured to perform the step of associating the radial distribution with the object model as a CAD object descriptor.
12. The data processing system of claim 10 , wherein the random points are sampled using a uniform distribution.
13. The data processing system of claim 10 , wherein the radial function is determined according to a projection of the random point on a sphere.
14. The data processing system of claim 10 , wherein determining the radial function includes using a correcting term to adjust for non-uniform distribution of the sampled points as projected on a sphere.
15. The data processing system of claim 10 , wherein the radial function is associated with a function on three-dimensional space and the three-dimensional object model.
16. The method of claim 10 , wherein sample points within a preselected normal distance from the origin are ignored.
17. The data processing system of claim 10 , wherein the radial distribution is associated with a function on three-dimensional space and the three-dimensional object model as the quotient of a first radial function and a second radial function, wherein the second radial function is associated with a function on three-dimensional space that is constant and equal to 1.
18. The data processing system of claim 10 , wherein the radial functions and the radial distribution corresponding to the object model are stored in the CAD system as average values on elements of a partition of a sphere.
19. A non-transitory computer-readable medium encoded with computer-executable instructions that, when executed, cause a data processing system to perform the steps of:
retrieving a three-dimensional object model;
sampling random points on the surface of the object model;
determining a normal vector corresponding to each of the random points;
determining a radial function corresponding to each normal vector and respective random point;
determining a radial distribution corresponding to at least two of the radial functions; and
storing the radial distribution and average values of the radial functions.
20. The computer-readable medium of claim 19 , further encoded with computer-executable instructions that, when executed, cause the data processing system to perform the step of associating the radial distribution with the object model as a CAD object descriptor.