TL;DR: It is shown that the construction of classical hierarchical B-splines can be suitably modified in order to define locally supported basis functions that form a partition of unity by reducing the support of basis functions defined on coarse grids, according to finer levels in the hierarchy of splines.

TL;DR: This paper shows that, for any given T-spline, the linear independence of its blending functions can be determined by computing the nullity of the T- Spline-to-NURBS transform matrix.

TL;DR: In this article, the authors present parametric equations expressed in terms of incomplete gamma functions, which allow us to find an exact analytic representation of a curve segment for any real value of the shape parameter.

TL;DR: It is shown that certain triples of circle families may be arranged as so-called hexagonal webs, and the classical approach to these surfaces based on the spherical model of 3D Mobius geometry is revisited, providing computational tools for the identification ofcircle families on a given cyclide and for the direct design of those.

TL;DR: This work uses Bernstein-Bezier methods to get precise conditions on the geometry of the meshes which lead to local and stable bases in polynomial spline spaces defined on T-meshes.

TL;DR: The superspirals are generalizations of log-aesthetic curves, as well as other curves whose radius of curvature is a particular case of a completely monotonic Gauss hypergeometric function.

TL;DR: This work designs a quadratic energy such that its Hessian equals the Laplace operator if the surface is a part of the Euclidean plane, and, on the other hand, the Hessian eigenfunctions are sensitive to the extrinsic curvature on curved surfaces, and derives two shape signatures that can be used to identify features of surfaces.

TL;DR: It is proved that any compact-support function that reproduces a subspace of the exponential polynomials can be expressed as the convolution of an exponential B-spline with a compact- support distribution, and it is shown that the minimal-support basis functions of that subspace are linear combinations of derivatives of exponential A-splines.

TL;DR: It is shown that a few simple geometric tests are sufficient to guarantee the convergence of numerical methods to the closest point in an efficient algorithm for projecting a given point to its closest point on a family of freeform curves and surfaces.

TL;DR: Enough conditions are derived for a convergent interpolatory planar subdivision scheme to produce tangent continuous limit curves and these conditions as well as the proofs are purely geometric and do not rely on any parameterization.

TL;DR: This novel reconstruction method adapts a level set method to capture the topology of the point clouds in a robust manner and then employs an iterative geometric fitting algorithm to generate high-quality Catmull-Clark subdivision surfaces.

TL;DR: This paper makes use of some generalized matrix based representations of parameterized surfaces to represent the intersection curve of two such surfaces as the zero set of a matrix determinant, allowing to reduce some geometric operations on such curves to matrix operations using results from linear algebra.

TL;DR: Based on a measure defined in an extended Gaussian image, an efficient least squares solution is proposed to achieve an optimal quasi-developable mesh patch and it is shown that this linear system can be efficiently solved by a least squares direct matrix solver.

TL;DR: An efficient algorithm for trimming both local and global self-intersections in planar offset curves based on a G^1-continuous biarc approximation of the given planar curves is presented.

TL;DR: This paper presents a feature-based approach to 3D morphing of arbitrary genus-0 polyhedral objects that is appropriate for CAD editing and is based on a sphere parameterization process built on an optimization technique that uses a target function to maintain the correspondence between the initial polygons and the mapped ones.

TL;DR: An algorithm to compute a certified approximation to a given parametric space curve with cubic B-spline curves and a novel optimization method is proposed to select proper weights in the cubic rational Bezier curve to approximate the given curve.

TL;DR: Close formulas are presented for computing the differential geometry properties of the intersection curve of n-1 implicit hypersurfaces in R^n and first geodesic torsion for implicit curves in n-dimensions are presented.

TL;DR: This work proposes a geometrical reduction allowing a much simpler and more stable formulae, and compares the results by incorporating the proposed estimators for the local affine structure of an implicit surface in Marching Cubes based algorithms.

TL;DR: In this paper, the authors prove a result similar to the conjecture of Chen et al. concerning how to calculate the parameter values corresponding to all the singularities including the infinitely near singularities, of rational planar curves from the Smith normal forms of certain Bezout resultant matrices derived from @m-bases.

TL;DR: An algorithm which is capable of globally solving a well-constrained transcendental system over some sub-domain [email protected]?R^n, isolating all roots, which is compared to interval arithmetic.

TL;DR: This work classifies all configurations where this kind of rational parametrization is possible, and describes a general algorithm for parametrizing fixed radius rolling ball blends of pairs of natural quadrics.

TL;DR: The new perspective shows a link between those classic approximating and interpolatory subdivision algorithms such as cubic B-spline curve subdivision and the four-point interpolatory subdivisions, Catmull-Clark subdivision and [email protected]?s interpolatory scheme, and Loop subdivisions and the butterfly algorithm.

TL;DR: The main result in the paper is an algorithm for computing the (finitely many) real values of the parameter where the topology of the family may change.

TL;DR: Here it is proved the existence of an additional, more subtle constraint that governs the admissibility of curve networks for G^2 interpolation, and gives a sufficient geometric, G ^2 Euler condition on the curve network.

TL;DR: In this article, the intersection curve of two rational parametric surfaces S"1(u,s) and S"2(v,t), one being projectable and hence can be easily implicitized, is computed.

TL;DR: A biarc-based subdivision scheme is proposed that can generate a planar spiral matching an arbitrary set of given admissible G^2 Hermite data, including the case that the curvature at one end is zero.

TL;DR: It is shown that under some natural conditions the solution of the interpolation problem exists and is unique and it is given in a simple closed form which makes it attractive for practical applications.

TL;DR: An accurate and efficient method for computing the distance between two canal surfaces using a set of cone-spheres as bounding volumes and the distances between their bounding cone-Spheres to approximate their distance is presented.

TL;DR: This paper considers methods to compute tight bounds for polynomials in n variables by solving two linear programming problems over a polytope defined as the convex hull of the coefficients with respect to the tensorial Bernstein basis.