Ray tracing trimmed rational surface patches
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Curve intersection using Be´zier clipping
Computer-Aided Design - Special Issue: Be´zier Techniques
Computation of the solutions of nonlinear polynomial systems
Computer Aided Geometric Design
Degree reduction of Be´zier curves
Selected papers of the international symposium on Free-form curves and free-form surfaces
On the optimal stability of the Bernstein basis
Mathematics of Computation
Computer Aided Geometric Design - Special issue dedicated to Paul de Faget de Casteljau
Geometric constraint solver using multivariate rational spline functions
Proceedings of the sixth ACM symposium on Solid modeling and applications
Shape Interrogation for Computer Aided Design and Manufacturing
Shape Interrogation for Computer Aided Design and Manufacturing
Efficient topology determination of implicitly defined algebraic plane curves
Computer Aided Geometric Design
Computer Aided Geometric Design
Matrix representation for multi-degree reduction of Bézier curves
Computer Aided Geometric Design
Geometric computations in parameter space
Proceedings of the 21st spring conference on Computer graphics
Robust and numerically stable Bézier clipping method for ray tracing NURBS surfaces
Proceedings of the 21st spring conference on Computer graphics
Dual evolution of planar parametric spline curves and T-spline level sets
Computer-Aided Design
Bézier clipping is quadratically convergent
Computer Aided Geometric Design
Fast approach for computing roots of polynomials using cubic clipping
Computer Aided Geometric Design
Continued fraction expansion of real roots of polynomial systems
Proceedings of the 2009 conference on Symbolic numeric computation
Theoretical Computer Science
A hybrid parallel solver for systems of multivariate polynomials using CPUs and GPUs
Computer-Aided Design
Fat arcs for implicitly defined curves
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
SMI 2012: Full Curve intersection using hybrid clipping
Computers and Graphics
Journal of Computational and Applied Mathematics
A geometric strategy for computing intersections of two spatial parametric curves
The Visual Computer: International Journal of Computer Graphics
Construction of dual B-spline functions
Journal of Computational and Applied Mathematics
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We present an algorithm which is able to compute all roots of a given univariate polynomial within a given interval. In each step, we use degree reduction to generate a strip bounded by two quadratic polynomials which encloses the graph of the polynomial within the interval of interest. The new interval(s) containing the root(s) is (are) obtained by intersecting this strip with the abscissa axis. In the case of single roots, the sequence of the lengths of the intervals converging towards the root has the convergence rate 3. For double roots, the convergence rate is still superlinear (32). We show that the new technique compares favorably with the classical technique of Bezier clipping.