TL;DR: Extensions are made to the methods of Pratt (1990) for the use of cyclides in solid modelling, with particular regard to their application as blend surfaces and new insights are given into the geometry and Bezier representation of cyclide surface patches.

TL;DR: A rational cubic spline curve is described which has tension control parameters for manipulating the shape of the curve and the behaviour of the resulting representations is analysed with respect to variation of the control parameters.

TL;DR: This work reformulates the problem in a higher-dimensional space with more variables but simpler equations, thus avoiding complex symbolic manipulation and numerically delicate operations and considers the formation of offsets, spherical blends of fixed or variable radius, and Voronoi surfaces.

TL;DR: Sets of conditions are derived that are necessary and sufficient for tangent plane continuity between two polynomial or rational Bezier surfaces that are, in general, independent.

TL;DR: D Dupin's cyclides are useful in blending conventional solids in solid modeling and can easily be derived from a construction using an ellipse and a string as given 125 years ago by J. Clerk Maxwell.

TL;DR: This paper presents a classification of algorithms for local smooth surface interpolation with piecewise polynomials with the aim of determining whether these algorithms are suitable for interpolation on the surface of a discrete-time model.

TL;DR: Techniques for the construction and visualization of a function defined over a closed surface domain which depends on a discrete sample of measurements at arbitrary locations on the domain surface and transparent surface graphs projected from the domain are presented.

TL;DR: Given arbitrary points on a sphere and associated real values, the problem of constructing a smooth function defined over the sphere which interpolates the given data is addressed and several methods which are appropriate modifications of Hardy's planar multiquadric method are described.

TL;DR: In this paper, not only the common edge but also the position of the tangent planes at its points are considered to be given and a complete and explicit solution is derived for G2-continuity too.

TL;DR: A method for interpolating scattered data using C1 piecewise cubic surfaces based on data-dependent triangulations based on the Delaunay triangulation is discussed.

TL;DR: The introduced surfaces can be interpreted as functional splines, which fulfill geometric continuity conditions, and are used for interpolation, approximation, blending surfaces and solids, filling of surface holes and rounding solids.

TL;DR: It is shown how to apply this analysis to make the Oslo algorithm for knot insertion as efficient as Boehm's knot insertion algorithm.

TL;DR: The GC1 necessary and sufficient conditions between two adjacent rectangular or two triangular rational Bezier surface patches are presented and some practical and simple sufficient conditions are developed.

TL;DR: An algorithm is presented for finding the MPDs that minimizes a generalized energy integral over the entire surface that results in a surface design technique for interpolating over a network of curves by automatically selecting the optimal twist vectors at the grid points.

TL;DR: An algorithm for the interpolation of a ‘mesh of points’ in 3-space by a C1 surface is developed that generates a piecewise parametric surface such that the normal along patch boundaries varies linearly.

TL;DR: This paper develops a mathematical model of the blend generated by a ball shaped cutter, called the rolling ball blend, that provides closed form analytic solutions for most of the surfaces which are common in current solid modellers.

TL;DR: The generation of a fair, planar Bezier curve is approached as an approximation problem with constraints, which leads to a nonlinear system of equations, which is solved numerically.

TL;DR: A surface interpolation method with local control for meshes of cubic curves is described that gives extra control to the user while preserving first order geometric continuity between the patches.

TL;DR: The relationship between the polar form perspective of spline curves and the dual functional viewpoint and the explicit connection between these two formulations is derived, and this link is elaborated further through some examples ofSpline properties provable by both techniques.

TL;DR: It is shown that the limit of local corner cutting is a continously differentiable curve in case the corners of the iterates becomeincreasingly flat.

TL;DR: An algorithm which determines a bivariate smooth piecewise polynomial interpolant to function values given at points scattered in R 2fs so that the degree of the polynomials will be as small as possible for arbitrary triangulations and a high degree ofPolynomial precision is achieved.

TL;DR: A geometric construction is given for the Bezier points of two rational curves which join together with appropriate Frenet frame continuity of order m, for any m ⩽ n −1.

TL;DR: It is shown that the procedure for calculating intersection points converges quadratically and give error estimates.

TL;DR: All the conditions obtained can be served as the extension of the convexity preserving conditions of functional Bezier triangular patches.

TL;DR: This work considers the problem of contouring a bivariate quadratic polynomial, defined as a triangular Bezier patch, and develops a simple, yet completely robust algorithm for describing contours as piecewise rational quadRatic Beziers curves.

TL;DR: This paperconstructs the neutral set for the min-max criterion and this construction is compared to that of the max-min triangulation and the results are analyzed in order to attain a better understanding of the nature of the min -max criterion.

TL;DR: An efficient and robust algorithm for finding S ∩ P, an arbitrarily given bicubic Bezier patch and P, if non-empty, is described, and many interesting examples are shown.

TL;DR: Finite quadric segments bounded by four plane curves and smooth in the sense of differential geometry are considered, especially patches on ruled quadrics bounded byFour line segments.

TL;DR: A simple characterization of the de Boor algorithm by a symmetry property is obtained, which leads to the study of symmetric triangular algorithms.