Representation of Objects in Virtual Reality Environment using B-Spline Blending Matrices

H. Pungotra, G.K. Knopf, and R. Canas (Canada)


B-spline surface, blending matrices, collision detection, deformable objects, virtual reality, and physics-based modeling.


B-spline representation is one of the main methods for free-form surface modeling and has become the standard for CAD systems. However, the high computational cost of continuously computing the blending functions for merging, collision detection and physics-based deformation system, while the model is deforming, restricts the use of B-spline representation in a Virtual Reality (VR) environment. This paper presents an alternative method to represent B-spline surface patches for an interactive VR environment. A uniformly discretized B-spline surface patch can be represented by a set of control points and two pre-calculated B-spline blending matrices. The proposed technique exploits the fact that these B-spline blending matrices are independent of the position of control points and therefore can be pre calculated. The blending matrices enable the algorithm to merge B-spline surface patches, accurately check the collision, and generate nodes for the mass spring system to determine deformation using the physics-based model. This technique does away with the need to calculate computationally intensive blending functions for the B spline surfaces, and inverse of large matrices during the run-time. The computational efficiency achieved by using blending matrices helps, in a virtual reality environment, to achieve real time interactions between the virtual model and the tool, represented as B-spline surfaces.

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