Showing papers in "Computer Aided Geometric Design in 1985"

TL;DR: 'Surfaces in Computer Aided Geometric Design' focuses on the representation and design of surfaces in a computer graphics environment and can be traced from its inception in rectangular Coons patches and Bezier patches to triangular patches which are current research topics.

TL;DR: A technique is presented that makes it possible to piece together two algebraic surface patches with any degree of cross-boundary derivative continuity.

TL;DR: A Newton-Raphson like method improves the placement of the segment endpoints on the two surfaces and serves to reduce evaluations and hence running time for the algorithm.

TL;DR: A new construction of Bezier points of curvature continuous cubic spline curves and surfaces from their B-spline control points allows the use of all results of the powerful Bernstein-Bezier technique in the realm of geometric splines.

TL;DR: This paper outlines exact offset procedures for three basic classes of solid primitive: (1) solids of revolution with simple profile curves; (2)solids of linear extrusion with simple Profile curves; and (3) convex planar polyhedra.

TL;DR: This paper presents a simple general method for treating such convergence questions which actually provides precise rates of convergence and illustrates the method by applying it to B-spline curves which are refined by increasing the degrees and/or refining the knot sequences.

TL;DR: A standard and a modified version of the Clough-Tocher interpolation scheme are described in terms of Bernstein-Bezier polynomials over triangles, compared by a method that simulates reflection lines.

TL;DR: The equation of an infinite thin plate under the influence of point loads and mid-plane forces is developed and this function is then used to interpolate scattered data, giving the user the parameter of tension to give some control over overshoot when the surface has large gradients.

TL;DR: Problems related to intersections are transformed to finding the zeroes of B-spline represented functions of one, two, three or four variables by using recursive subdivision techniques.

TL;DR: The v-splines are generalized to geometric spline curves and the computational equations of quintic splines curves with curvature and torsion continuity are given.

TL;DR: A set of methods are described in this paper, which are to be used in the context of data exchanges between surface modellers by means of the VDA/VDMA standard surface interface.

TL;DR: This paper develops a method of forming smooth closed surfaces from a discrete triangular interpolant by relaxing the C^1 property of an interpolant to 'Visually C ^1''.

TL;DR: The principal differences of knot insertion algorithms are discussed and their efficiencies are compared.

TL;DR: The aim of this paper is to show that the Bernstein-Bezier method for representing polynomials over triangles may be useful for the construction of bivariate spline approximants on regular or arbitrary triangulations of a planar domain.

TL;DR: Several refinement and subdivision algorithms for univariate B-spline curves are discussed in a tensor product setting and efficiency considerations lead to a different choice of algorithms than in the univariate case.

TL;DR: This contribution introduces a simple criterion for detecting undesired domains by using the k-orthotomics, the so called Bezout-method, in optics.

TL;DR: The paper raises a number of questions which could form the basis for useful research in this area and some suggestions for practical algorithms outlined.

TL;DR: Two problems of the tensor product description of spatial domains by the method of Bernstein-Bezier are discussed: the construction of a volume point together with the first derivatives in this point and the solution of the interpolation problem.

TL;DR: The results of these operations are applied to construct an optimal, robust, intersection algorithm for any two non-planar rational cubic curves, and it is shown that two such curves can intersect in at most five points.

TL;DR: In the present paper, a smoothing algorithm for bicubic spline surfaces is presented, having the piecewise cubic boundaries of the patches fixed, the algorithm chooses adequate twists factors in order to increase the smoothness.

TL;DR: A geometric construction for rational conic segments and quadric patches is presented here that provides elegent recipes for avoiding singularities and can easily be used to define quadric patch of different types.

TL;DR: An explicit representation of a finite dimensional Hermite interpolation polynomial for thesimplex in R^n is described and the basis functions of this scheme are used in the construction of a C^N transfinite blending function interpolant for the simplex.

TL;DR: The new algorithm allows the calculation and the display of boundaries and contour curves with high precision in a minimal way and can be displayed both on vector and raster devices and are invariant under image transformations.

TL;DR: A characterization theorem for visually C^2 (short: V^2) curves and a short derivation of v-spline interpolants is given.

TL;DR: A specific approach to this problem is described that is modeled after univariate spline interpolation and yields visually pleasing surfaces and is therefore suitable for design applications, but is less suitable for the approximation of derivatives of a given function.

TL;DR: It is shown that the refined control net, viewed as a piecewise linear approximation converges to the spline surface at the rate of 1/r^2 where r is the degree of refinement.

TL;DR: A new algorithm for piecewise bicubic interpolation to bivariate data on a rectangular mesh is described and the Hermite form is used to represent the resulting surface.

TL;DR: The purpose of this note is to describe and illustrate a simple algorithm for the interactive graphical generation of smooth surfaces.

TL;DR: Three simple algorithms for calculating bivariate box splines and their linear combinations are given: a Mansfield-like recursion formula, the refinement of the control net and the construction of the Bezier net.

TL;DR: As examples of application of the de Boor-Fix dual functionals, alternative proofs are given for the recurrence formula of discrete B-splines and the derivative formula of B- Splines.