ACS Algorithms for Complex Shapes with Certified Numerics and Topology Minimizing the symmetric difference distance in conic spline approximation

Algorithms for Complex Shapes with Certified Numerics and Topology Complexity of Approximation by Conic Splines

We show that the complexity of a parabolic or conic spline approximating a sufficiently smooth curve with non-vanishing curvature to within Hausdorff distance ε is c1ε − 1 4 + O(1), if the spline consists of parabolic arcs, and c2ε − 1 5 + O(1), if it is composed of general conic arcs of varying type. The constants c1 and c2 are expressed in the Euclidean and affine curvature of the curve. We a...

ACS Algorithms for Complex Shapes with Certified Numerics and Topology Application of algebraic tools to CSG operations on curves and surfaces

Minimizing the symmetric difference distance in conic spline approximation

We show that the complexity (the number of elements) of an optimal parabolic or conic spline approximating a smooth curve with nonvanishing curvature to within symmetric difference distance ε is c1 ε −1/4 + O(1), if the spline consists of parabolic arcs and c2 ε −1/5 +O(1), if it is composed of general conic arcs of varying type. The constants c1 and c2 are expressed in the affine curvature of ...

ACS Algorithms for Complex Shapes with Certified Numerics and Topology Computation of the medial axis of smooth curves with topological guarantees

Project co-funded by the European Commission within FP6 (2002–2006) under contract nr. IST-006413

ACS Algorithms for Complex Shapes with Certified Numerics and Topology Anisotropic mesh generation

Project co-funded by the European Commission within FP6 (2002–2006) under contract nr. IST-006413