On local implicit approximation and its applications
ACM Transactions on Graphics (TOG) - Special issue on computer-aided design
Detecting cusps and inflection points in curves
Computer Aided Geometric Design
High accurate rational approximation of parametric curves
Selected papers of the international symposium on Free-form curves and free-form surfaces
Geometric Hermite interpolation
Computer Aided Geometric Design
Identification of inflection points and cusps on rational curves
Computer Aided Geometric Design
The NURBS book (2nd ed.)
The moving line ideal basis of planar rational curves
Computer Aided Geometric Design
Mathematical Methods for Curves and Surfaces
Approximation with Active B-Spline Curves and Surfaces
PG '02 Proceedings of the 10th Pacific Conference on Computer Graphics and Applications
Efficient isolation of polynomial's real roots
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on linear algebra and arithmetic, Rabat, Morocco, 28-31 May 2001
Computing μ-bases of rational curves and surfaces using polynomial matrix factorization
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Geometric Hermite interpolation: in memoriam Josef Hoschek
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
The Visual Computer: International Journal of Computer Graphics
Evolution-based least-squares fitting using Pythagorean hodograph spline curves
Computer Aided Geometric Design
Geometric Hermite interpolation with circular precision
Computer-Aided Design
On the computation of the topology of a non-reduced implicit space curve
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Axial moving planes and singularities of rational space curves
Computer Aided Geometric Design
Detecting real singularities of a space curve from a real rational parametrization
Journal of Symbolic Computation
Topology determination and isolation for implicit plane curves
Proceedings of the 2009 ACM symposium on Applied Computing
Complete numerical isolation of real roots in zero-dimensional triangular systems
Journal of Symbolic Computation
Shape preserving approximation by spatial cubic splines
Computer Aided Geometric Design
Shape-preserving interpolation by fair discrete G 3 space curves
Computer Aided Geometric Design
Rational quadratic approximation to real algebraic curves
Computer Aided Geometric Design
Computation of the topology of real algebraic space curves
Journal of Symbolic Computation
Cubic B-spline curve approximation by curve unclamping
Computer-Aided Design
Topology of 2D and 3D rational curves
Computer Aided Geometric Design
Collision and intersection detection of two ruled surfaces using bracket method
Computer Aided Geometric Design
Geometric Hermite interpolation for space curves
Computer Aided Geometric Design
Journal of Symbolic Computation
Rational Hausdorff divisors: A new approach to the approximate parametrization of curves
Journal of Computational and Applied Mathematics
| Hi-index | 0.00 |
Approximating complex curves with simple parametric curves is widely used in CAGD, CG, and CNC. This paper presents an algorithm to compute a certified approximation to a given parametric space curve with cubic B-spline curves. By certified, we mean that the approximation can approximate the given curve to any given precision and preserve the geometric features of the given curve such as the topology, singular points, etc. The approximated curve is divided into segments called quasi-cubic Bezier curve segments which have properties similar to a cubic rational Bezier curve. And the approximate curve is naturally constructed as the associated cubic rational Bezier curve of the control tetrahedron of a quasi-cubic curve. A novel optimization method is proposed to select proper weights in the cubic rational Bezier curve to approximate the given curve. The error of the approximation is controlled by the size of its tetrahedron, which converges to zero by subdividing the curve segments. As an application, approximate implicit equations of the approximated curves can be computed. Experiments show that the method can approximate space curves of high degrees with high precision and very few cubic Bezier curve segments.