Geometric design of motions constrained by a contacting surface pair
Computer Aided Geometric Design
Geometry and Convergence Analysis of Algorithms for Registration of 3D Shapes
International Journal of Computer Vision
Partial and approximate symmetry detection for 3D geometry
ACM SIGGRAPH 2006 Papers
Reassembling fractured objects by geometric matching
ACM SIGGRAPH 2006 Papers
ACM SIGGRAPH 2007 papers
Subdivision schemes for the fair discretization of the spherical motion group
Journal of Computational and Applied Mathematics
Generalized penetration depth computation based on kinematical geometry
Computer Aided Geometric Design
Meshless modeling of deformable shapes and their motion
Proceedings of the 2008 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Constructing 3D motions from curvature and torsion profiles
Computer-Aided Design
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We discuss the following problem, which arises in computer animation and robot motion planning: given are N positions or keyframes Σ(ti) of a moving body Σ⊂ℝ3 at time instances ti. Compute a smooth rigid body motion Σ(t) that interpolates or approximates the given positions Σ(ti) such that chosen feature points of the moving system run on smooth paths. We present an algorithm that can be considered as a transfer principle from curve design algorithms to motion design. The algorithm relies on known curve design algorithms and on registration techniques from computer vision. We prove that the motion generated in this way is of the same smoothness as the curve design algorithm employed.