A 3-D Contour Segmentation Scheme Based on Curvature and Torsion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Approximate conversion of rational splines
Computer Aided Geometric Design
An Adaptive Reduction Procedure for the Piecewise Linear Approximation of Digitized Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
Hierarchical segmentations of algebraic curves and some applications
Mathematical methods in computer aided geometric design
Approximate conversion of rational B-spline patches
Computer Aided Geometric Design
Offsets of polynomial Be´zier curves: Hermite approximation with error bounds
Mathematical methods in computer aided geometric design II
Piecewise linear approximations of digitized space curves with applications
Scientific visualization of physical phenomena
Degree reduction of Be´zier curves
Selected papers of the international symposium on Free-form curves and free-form surfaces
On rational parametric curve approximation
Selected papers of the international symposium on Free-form curves and free-form surfaces
Data point selection for piecewise linear curve approximation
Computer Aided Geometric Design
Approximation by Interval Bezier Curves
IEEE Computer Graphics and Applications
Computation of the solutions of nonlinear polynomial systems
Computer Aided Geometric Design
Computation of singularities and intersections of offsets of planar curves
Computer Aided Geometric Design
Efficient piecewise linear approximation of bézier curves with improved sharp error bound
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
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We present an efficient method of approximating a set of mutually nonintersecting simple composite planar and space Bezier curves within a prescribed tolerance using piecewise linear segments and ensuring the existence of a homeomorphism between the piecewise linear approximating segments and the actual nonlinear curves. Equations and a robust solution method relying on the interval projected polyhedron algorithm to determine significant points of planar and space curves are described. Preliminary approximation is obtained by computing those significant points on the input curves. This preliminary approximation, providing the most significant geometric information of input curves, is especially valuable when a coarse approximation of good quality is required such as in finite element meshing applications. The main approximation, which ensures that the approximation error is within a user specified tolerance, is next performed using adaptive subdivision. A convex hull method is effectively employed to compute the approximation error. We prove the existence of a homeomorphism between a set of mutually non-intersecting simple composite curves and the corresponding heap of linear approximating segments which do not have inappropriate intersections. For each pair of linear approximating segments, an intersection check is performed to identify possible inappropriate intersections. If these inappropriate intersections exist, further local refinement of the approximation is performed. A bucketing technique is used to identify the inappropriate intersections, which runs in O(n) time on the average where n is the number of linear approximating segments. Our approximation scheme is also applied to interval composite Bezier curves.