Updating the inverse of a matrix
SIAM Review
A model for efficient and accurate interaction with elastic objects in haptic virtual environments
Proceedings of the 1st international conference on Computer graphics and interactive techniques in Australasia and South East Asia
Real-Time Elastic Deformations of Soft Tissues for Surgery Simulation
IEEE Transactions on Visualization and Computer Graphics
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We propose a real-time procedure for performing topology modifications on finite element models of objects with linear elastic behaviour. For a 3D tetrahedral model, it requires the inversion of a 6 × 6 matrix and the weighted multiplication of a thin matrix with its transpose. We exemplify with an implementation in our surgical simulator, where we impose the tight computational constraints of haptic feedback. Our experimental results show that we can obtain response times of under one second for objects represented by tetrahedral meshes with more than 2000 nodes.