A Constant Space Representation of Digital Cubic Parabolas
About the geometry of milling paths.
Ajustement spline le long d'un ensemble de courbes
All Bézier curves are attractors of iterated function systems.
Almost curvature continuous fitting of B-spline surfaces.
An algorithm based on rolling to generate smooth interpolating curves on ellipsoids
We present an algorithm to generate a smooth curve interpolating a set of data on an -dimensional ellipsoid, which is given in closed form. This is inspired by an algorithm based on a rolling and wrapping technique, described in [11] for data on a general manifold embedded in Euclidean space. Since the ellipsoid can be embedded in an Euclidean space, this algorithm can be implemented, at least theoretically. However, one of the basic steps of that algorithm consists in rolling the ellipsoid, over...
An example related to Whitney extension with almost minimal norm.
An iterative Clough-Tocher interpolant
Analogies from 2D to 3D Exercises in Disciplined Creativity
Approximation and/or construction of curves by minimization methods with or without constraints
Approximation de contours convexes par des splines paramétrées périodiques convexes , quadratiques ou cubiques
Approximation in the space of planes: applications to geometric modeling and reverse engineering.
Se estudia la aproximación en el espacio de planos. Se introduce una medida de la distancia en este espacio, con la que pueden resolverse problemas de modelado con superficies desarrollables mediante algoritmos de aproximación de curvas. Además, el reconocimiento y reconstrucción de caras planas en nubes de puntos aparecen como un problema "clustering" en el espacio de planos. La aplicabilidad práctica de estos resultados se muestra en varios ejemplos.
Approximation of discontinuous curves and surfaces by discrete splines with tangent conditions.
Approximation spline de surfaces de type explicite comportant des failles
B-spline bases and osculating flats : one result of H.-P. Seidel revisited
Along with the classical requirements on B-splines bases (minimal support, positivity, normalization) we show that it is natural to introduce an additional “end point property”. When dealing with multiple knots, this additional property is exactly the appropriate requirement to obtain the poles of nondegenerate splines as intersections of osculating flats at consecutive knots.
B-spline bases and osculating flats: One result of H.-P. Seidel revisited
Along with the classical requirements on B-splines bases (minimal support, positivity, normalization) we show that it is natural to introduce an additional “end point property". When dealing with multiple knots, this additional property is exactly the appropriate requirement to obtain the poles of nondegenerate splines as intersections of osculating flats at consecutive knots.
Closed spline curves bounding maximal area.
Closed-form expressions for the approximation of arclength parameterization for Bézier curves
In applications such as CNC machining, highway and railway design, manufacturing industry and animation, there is a need to systematically generate sets of reference points with prescribed arclengths along parametric curves, with sufficient accuracy and real-time performance. Thus, mechanisms to produce a parameter set that yields the coordinates of the reference points along the curve Q(t) = {x(t), y(t)} are sought. Arclength parameterizable expressions usually yield a parameter set that is necessary...
Computing homology.
Curvature computations on surfaces in -space