Curve network interpolation by C1C^1 quadratic B-spline surfaces

In this paper we investigate the problem of interpolating a B-spline curve network, in order to create a surface satisfying such a constraint and defined by blending functions spanning the space of bivariate $C^1$ quadratic splines on criss-cross triangulations. We prove the existence and uniqueness of the surface, providing a constructive algorithm for its generation. We also present numerical and graphical results and comparisons with other methods.Comment: With respect to the previous version, this version of the paper is improved. The results have been reorganized and it is more general since it deals with non uniform knot partitions. Accepted for publication in Computer Aided Geometric Design, October 201

Flexible G1 Interpolation of Quad Meshes

International audienceTransforming an arbitrary mesh into a smooth G1 surface has been the subject of intensive research works. To get a visual pleasing shape without any imperfection even in the presence of extraordinary mesh vertices is still a challenging problem in particular when interpolation of the mesh vertices is required. We present a new local method, which produces visually smooth shapes while solving the interpolation problem. It consists of combining low degree biquartic Bézier patches with minimum number of pieces per mesh face, assembled together with G1-continuity. All surface control points are given explicitly. The construction is local and free of zero-twists. We further show that within this economical class of surfaces it is however possible to derive a sufficient number of meaningful degrees of freedom so that standard optimization techniques result in high quality surfaces

Constrained Interpolation And Shape Preserving Approximation By Space Curves [QA297.6. K82 2006 f rb].

Dua jenis masalah rekabentuk lengkung telah ipertimbangkan. Terlebih dahulu kami mempertimbangkan interpolasi satu set titik data ruang yang bertertib dengan satu lengkung licin tertakluk kepada satu set satah kekangan yang berbentuk terhingga atau tak terhingga di mana garis cebis demi cebis yang menyambung titik data secara berturutan tidak bersilang dengan satah kekangan. Two types of curve designing problem have been considered. We first consider the interpolation of a given set of ordered spatial data points by a smooth curve in the presence of a set of finite or infinite constraint planes, where the polyline joining consecutive data points does not intersect with the constraint planes

A univariate rational quadratic trigonometric interpolating spline to visualize shaped data

This study was concerned with shape preserving interpolation of 2D data. A piecewise C1 univariate rational quadratic trigonometric spline including three positive parameters was devised to produce a shaped interpolant for given shaped data. Positive and monotone curve interpolation schemes were presented to sustain the respective shape features of data. Each scheme was tested for plentiful shaped data sets to substantiate the assertion made in their construction. Moreover, these schemes were compared with conventional shape preserving rational quadratic splines to demonstrate the usefulness of their construction

High-order adaptive methods for computing invariant manifolds of maps

The author presents efficient and accurate numerical methods for computing invariant manifolds of maps which arise in the study of dynamical systems. In order to decrease the number of points needed to compute a given curve/surface, he proposes using higher-order interpolation/approximation techniques from geometric modeling. He uses B´ezier curves/triangles, fundamental objects in curve/surface design, to create adaptive methods. The methods are based on tolerance conditions derived from properties of B´ezier curves/triangles. The author develops and tests the methods for an ordinary parametric curve; then he adapts these methods to invariant manifolds of planar maps. Next, he develops and tests the method for parametric surfaces and then he adapts this method to invariant manifolds of three-dimensional maps