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

ACS Algorithms for Complex Shapes with Certified Numerics and Topology 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 non-vanishing 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 Prototype implementation of certified approximation of the Medial Axis of smooth curves

In this report we give an algorithm to construct an approximate medial axis of a connected domain without any holes, in 2-D, also known as the simply connected domain. The first part of the report concentrates on the algorithm which gives the approximate medial axis of a domain bounded by simple, closed C curve. In the second part of the report we look at a modified version of which looks at do...

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

Algorithms for Complex Shapes with Certified Numerics and Topology A deterministic Bitstream Descartes Algorithm

We describe a variant of the Descartes algorithm for root isolation of polynomials with real coefficients. It is assumed that the coefficients of the polynomial can be approximated with arbitrary precision; exact computation in the field of coefficients is not required. We refer to such coefficients as bitstream coefficients. The algorithm is deterministic and has same asymptotic complexity as ...

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