Showing papers in "Computer Aided Geometric Design in 2008"

TL;DR: Based on the roll parametrization the kinematics of a vehicle featured with Mecanum wheels are studied and an approximation of the roll surface by a torus is found for manufacture purposes.

TL;DR: Analysis and experiments show that iterative application of a one-step random walk in a progressive manner effectively preserves detailed features while denoising the mesh very well, and is faster than many other feature-preserving mesh Denoising algorithms.

TL;DR: The problem of specifying the two free parameters that arise in spatial Pythagorean-hodograph (PH) quintic interpolants to given first-order Hermite data is addressed and conditions on the data that identify when the ''ordinary'' cubic interpolant becomes a PH curve are formulated.

TL;DR: This paper determines how the support, the Holder regularity, the precision set, the degree of polynomials spanned by the limit curves, and the artifact behavior vary with the integer parameter that identifies the members of the family.

TL;DR: It is shown on examples that this algorithm is able to handle curves defined by high degree polynomials with large coefficients, to identify regions of interest and use the resulting structure for either efficient rendering of implicit curves, point localization or boolean operation computation.

TL;DR: This paper explores an alternative partitioning strategy that decomposes a given model into ''approximately convex'' pieces that may provide similar benefits as convex components, while the resulting decomposition is both significantly smaller (typically by orders of magnitude) and can be computed more efficiently.

TL;DR: It is demonstrated that the point-based representation of the Minkowski sum boundary can indeed provide similar functionality as the mesh-based representations can.

TL;DR: There is no rational rotation-minimizing frame (RMF) along any non-planar regular cubic polynomial curve and it is proved its nonexistence in the case of cubic curves.

TL;DR: It is shown that every continuous nonlinear averaging rule on a pair of real or complex numbers can be constructed by conjugating a linear averaging rule with an associated continuous locally invertible nonlinear map, so the averaging rules considered in this paper are actually the general case.

TL;DR: Fast, accurate, and reliable methods for detecting the crest lines on surfaces approximated by dense triangle meshes are developed and provided with an inherent level-of-detail control of the detected crest lines.

TL;DR: This paper takes the view that a good curve is one that does not deviate too far from the data polygon: the polygon formed by the data points, and studies periodic cubic spline interpolation to derive bounds on the deviation.

TL;DR: A general framework for surface modeling using geometric partial differential equations (PDEs) is presented and it is shown that the proposed approach can handle a large number of geometric PDEs and the numerical algorithm is efficient.

TL;DR: A topological approach to identifying the ''good'' interpolant among the four distinct solutions to the first-order Hermite interpolation problem for planar quintic Pythagorean-hodograph curves is presented and the existence theorem is proved.

TL;DR: This article will investigate how one can extract geometric curve features from the algebraic description of the curve by using a certain complex representation of polynomials introduced by (Tarel, J.-P., Cooper, D.B., 1998), which is very appropriate for the task of feature detection.

TL;DR: In this paper, a Riemannian manifold whose geodesics trace the edges of the mesh is defined, and a function @f, proportional to the logarithm of the cell size, is shown to obey the Poisson equation, with localized charges corresponding to irregular vertices.

TL;DR: This paper discovers that, in Farin (2006), the conditions Class A matrix satisfied cannot guarantee one of the two properties of the Class A Bezier curves, then the proof of the curvature and torsion monotonicity becomes incomplete.

TL;DR: It is shown that odd rational support functions correspond to those rational surfaces which can be equipped with a linear field of normal vectors, which were discussed by Sampoli et al. in 2006.

TL;DR: The proposed approach for computing sensitivities does not require solid's boundary to remain homeomorphic, and may be used with most types of constructive representations, including CSG and feature-based representations, where the defining Boolean expression may not be known.

TL;DR: Given a closed triangular mesh, a smooth free-form surface is constructed which is described as a collection of rational tensor-product and triangular surface patches which proceeds by blending together geometry functions for each vertex.

TL;DR: It is shown that a single quintic curve can be used for blending or for a transition curve between two circles, including the previously unsolved cases of concentric and tangential circles.

TL;DR: It is proved that the derivatives with any given degree of the Bezier curve sequence constructed this way would uniformly converge to the corresponding derivatives of the original rational Beziers curve.

TL;DR: It is proved that uniqueness of the minimal enclosing ellipsoid with respect to strictly eigenvalue convex size functions is unique.

TL;DR: It is proved that the polynomial quadratic triangular Bezier surfaces are LN-surfaces and it is demonstrated how to reparameterize the surfaces such that the normals obtain linear coordinate functions.

TL;DR: A new branching blend between two natural quadrics (circular cylinders/cones or spheres) in many positions is proposed, a ring shaped patch of a PN surface parametrized by rational bivariant functions of degree 6,3.

TL;DR: A large class of self-motions of Stewart-Gough type parallel manipulators is described, the spherical image of those motions is a planar curve of degree six in Euler parameters, to visualize trajectories of a space motion.

TL;DR: Three division algorithms are presented for univariate Bernstein polynomials: an algorithm for finding the quotient and remainder of two univariate polynmials, an algorithms for calculating the GCD of an arbitrary collection of univariatePolynomial, and an algorithm that converts each problem from the Bernstein basis to an equivalent problem in the monomial basis.

TL;DR: A new method of solving C^1 Hermite interpolation problems, which makes it possible to use a wider range of PH curves with potentially better shapes, and introduces PH curves of type K(t-c)^2^n^+^1+d.

TL;DR: The theory of the so-called PN surfaces and their PN parameterizations are brought in relation to the theory of SRC parameterizations and it is shown that this type of parameterizations can be further classified with respect to the degree of the construction of convolution surfaces.

TL;DR: An effort that aimed at the unification of the whole geometric preprocessing that preceded the wind tunnel readings with a realistic airplane wing model in a recent research project is given.

TL;DR: A new scheme based on quartic C^1-splines on type-1 triangulations approximating regularly distributed data yielding nearly-optimal approximation order for smooth functions is described.