MODELING

Award Information
Agency: National Science Foundation
Branch: N/A
Contract: N/A
Agency Tracking Number: 2713
Amount: $40,000.00
Phase: Phase I
Program: SBIR
Awards Year: 1985
Solicitation Year: N/A
Solicitation Topic Code: N/A
Solicitation Number: N/A
Small Business Information
8386 Pleasantview Dr, Minneapolis, MN, 55432
DUNS: N/A
HUBZone Owned: N
Woman Owned: N
Socially and Economically Disadvantaged: N
Principal Investigator
 PRADEEP SINHA
 RESEARCH SCIENTIST
 (607) 257-7901
Business Contact
Phone: () -
Research Institution
N/A
Abstract
THE GROWING NEED FOR GEOMETRIC MODELING INFIELDS RANGING FROM CAD/CAM TO MATHEMATICAL MODELING HAS NESSECITATED RELIABLE INTERSECTIONS OF NOT ONLY SURFACES IN 3-SPACE BUT, MORE GENERALLY, ARBITRARY SUBMANIFOLDS OF EUCLIDEAN SPACES OF HIGHER DIMENSIONALITY. PURELY ALGORITHMIC METHODS BASED ON DISCRETIZATION OF THE INTERSECTING SHAPES OR THE IMBEDDING SPACE TEND TO BE UNRELIABLE. ON THE OTHER HAND, PURELY MATHEMATICAL APPROACHES BASED ON THE GEOMETRY OF THE INTERSECTING SHAPES ARE FAR TOO RESTRICTED IN THEIR DOMAIN OF APPLICATION BECAUSE OF THEIR SHAPE-SPECIFIC FORMULATION. THIS PROPOSAL ADDRESSES THE NEED TO COMBINE THE TWO APPROACHES INTO A SINGLE METHODOLOGY FOR INTERSECTION OF ARBITRARY SHAPES IN FINITE DIMENSIONAL SPACES. THE APPROACH TAKEN MAKES USE OF RESULTS RELATING TO THE TOPOLOGY AND GEOMETRY OF THE INTERSECTION OF TWO SUBMANIFOLDS THAT MEET CERTAIN REPRESENTATIONAL REQUIREMENTS. IT IS SHOWN THAT THE SHAPES COMMONLY USED CANBE SUBDIVIDED UNTIL THEY MEET THE PRESCRIBED REQUIREMENTS. THIS RESULTS IN RELIABLE ALGORITHMS THAT ARE ALSO GENERAL IN DOMAIN OF APPLICATION. SUCH RESULTS RELATING TO INTERSECTIONS OF SURFACES IN 3-SPACE HAVE ALREADY BEEN ESTABLISHED AND AN ALGORITHM INCORPORATING THEM HAS BEEN IMPLEMENTED SUCCESSFULLY; THE WORK PROPOSED HERE IS INVESTIGATION OF THE MATHEMATICAL BASIS TO EXTEND IT TO COMPUTE INTERSECTION OF GENERAL SHAPES IN HIGHER DIMENSIONS.

* Information listed above is at the time of submission. *

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