Clearance Detection for Swept Volumes Using Support Functions
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Solution Overview
Problem
Existing methods for collision detection and clearance computation in computer-based simulations of geometric volumes are inefficient and limited in accuracy, particularly in handling swept-body distance and interference detection, and require explicit calculation of polyhedral approximations, which restricts the types of geometric primitives that can be modeled.
Innovation Solution
The method adapts the Gilbert and Foo algorithm to determine clearance between moving bodies by computing the directionally furthest point on the convex hull of 'virtually swept' volumes without explicitly calculating swept volumes, using bounding volume hierarchies and inverse mappings to efficiently compute distances between convex geometric primitives, allowing for a broader range of geometric primitives including polyhedra, cones, and cylinders.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If explicit polyhedral approximations are used for swept volumes, then collision detection accuracy is improved, but computational complexity and processing time increase significantly
Solution Approach 1:
The patent extracts only the essential geometric information needed for clearance computation by using support functions that directly compute the extremal points of swept volumes without constructing the complete polyhedral approximation. This extraction approach obtains the necessary distance information while avoiding the computational burden of full volume representation.
Solution Approach 2:
Instead of computing the swept volume and then finding its extremal points, the patent inverts the approach by directly computing the support functions that give the extremal points of the swept volume. This inversion eliminates the intermediate step of explicit volume construction, reducing computational complexity while maintaining accuracy.
2Measurement precision
If explicit polyhedral approximations are calculated for swept volumes, then clearance distance information is obtained, but the types of geometric primitives that can be modeled are restricted
Solution Approach 1:
The patent implements a universal support function framework that can handle multiple geometric primitive types (polyhedra, cones, cylinders, and other revolution solids) through a unified mathematical approach. The support function formulation is general enough to accommodate any convex geometry, allowing the same computational method to work across diverse primitive types without requiring explicit polyhedral approximation for each case.
3Reliability
If explicit polyhedral approximations of swept volumes are computed, then interference detection is possible, but real-time computational efficiency is reduced
Solution Approach 1:
The patent performs preliminary computation of support functions and their derivatives before the actual clearance query. By pre-computing the support function representations and storing them in an efficient data structure, the system prepares the geometric information in advance, enabling fast real-time queries without performing heavy computations at query time.
Solution Approach 2:
The patent replaces the mechanical/computational process of explicitly constructing and manipulating polyhedral volume representations with a mathematical field-based approach using support functions. This substitution eliminates the need for discrete geometric construction and manipulation, replacing it with continuous mathematical evaluations that are computationally more efficient and suitable for real-time applications.
Data Source
AI summary
A method for correct and efficient detection of clearances between three-dimensional bodies in computer-based simulations, where one or both of the volumes is subject to translation and/or rotations. The method conservatively determines of the size of such clearances and whether there is a collision between the bodies. Given two bodies, each of which is undergoing separate motions, the method utilizes bounding-volume hierarchy representations for the two bodies and, mappings and inverse mappings for the motions of the two bodies. The method uses the representations, mappings and direction vectors to determine the directionally furthest locations of points on the convex hulls of the volumes virtually swept by the bodies and hence the clearance between the bodies, without having to calculate the convex hulls of the bodies. The method includes clearance detection for bodies comprising convex geometrical primitives and more specific techniques for bodies comprising convex polyhedra.