Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
A variational approach to subdivision
Computer Aided Geometric Design
Smooth invariant interpolation of rotations
ACM Transactions on Graphics (TOG)
Handbook of discrete and computational geometry
Handbook of discrete and computational geometry
A multiresolution framework for variational subdivision
ACM Transactions on Graphics (TOG)
Animating rotation with quaternion curves
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Robot Motion Planning
Computational Line Geometry
Computing Distances between Surfaces Using Line Geometry
PG '02 Proceedings of the 10th Pacific Conference on Computer Graphics and Applications
Minimizing the Distortion of Affine Spline Motions
PG '01 Proceedings of the 9th Pacific Conference on Computer Graphics and Applications
From curve design algorithms to the design of rigid body motions
The Visual Computer: International Journal of Computer Graphics
Energy-minimizing splines in manifolds
ACM SIGGRAPH 2004 Papers
A variational approach to spline curves on surfaces
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
A variational approach to spline curves on surfaces
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
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We discuss the following problem which arises in robot motion planning, NC machining and computer animation: Given are a fixed surface Φ and N positions Φi of a moving surface Φ such that the Φi are in point contact with Ψ. Compute a smooth and fair Euclidean gliding motion Φ(t) of the surface Φ on the surface Ψ which interpolates (or approximates) the given positions Φi at time instances ti. First we generalize interpolatory variational subdivision algorithms for curves to curves on surfaces. Second we study an unconstraint motion design algorithm which we then extend to the main contribution of this paper, an algorithm for the design of a motion constraint by a contacting surface pair. Both motion design algorithms use a feature point representation of the moving surface, subdivision algorithms for curves, instantaneous kinematics, and ideas from line geometry. Geometric methods are used for the numerical solution of the arising optimization problems.