Projective transformations of the parameter of a Bernstein-Bézier curve
ACM Transactions on Graphics (TOG)
Approximating a composite cubic curve by one with fewer pieces
Computer-Aided Design
Curve and surface constructions using rational B-splines
Computer-Aided Design
Mathematical elements for computer graphics (2nd ed.)
Mathematical elements for computer graphics (2nd ed.)
Choosing nodes in parametric curve interpolation
Computer-Aided Design
A technique for smoothing scattered data with conic sections
Computers in Industry
IEEE Computer Graphics and Applications
An integrated environment to visually construct 3D animations
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
3D Reconstruction of parametric curves: recovering the control points
Machine Graphics & Vision International Journal
A Newton-type method for constrained least-squares data-fitting with easy-to-control rational curves
Journal of Computational and Applied Mathematics
Capturing planar shapes by approximating their outlines
Journal of Computational and Applied Mathematics
Compressing the incompressible with ISABELA: in-situ reduction of spatio-temporal data
Euro-Par'11 Proceedings of the 17th international conference on Parallel processing - Volume Part I
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A geometric method for fitting rational cubic B-spline curves to data representing smooth curves, such as intersection curves or silhouette lines, is presented. The algorithm relies on the convex hull and on the variation diminishing properties of Bezier/B-spline curves. It is shown that the algorithm delivers fitting curves that approximate the data with high accuracy even in cases with large tolerances. The ways in which the algorithm computes the end tangent magnitudes and inner control points, fits cubic curves through intermediate points, checks the approximate error, obtains optimal segmentation using binary search, and obtains appropriate final curve form are discussed.