Related papers: General Midpoint Subdivision
Subdivision surfaces provide an elegant isogeometric analysis framework for geometric design and analysis of partial differential equations defined on surfaces. They are already a standard in high-end computer animation and graphics and are…
Midpoint subdivision generalizes the Lane-Riesenfeld algorithm for uniform tensor product splines and can also be applied to non regular meshes. For example, midpoint subdivision of degree 2 is a specific Doo-Sabin algorithm and midpoint…
This paper proposes to generalize linear subdivision schemes to nonlinear subdivision schemes for curve and surface modeling by refining vertex positions together with refinement of unit control normals at the vertices. For each round of…
In a previous paper [11] we introduced a weighted binary average of two 2D point-normal pairs, termed circle average, and investigated subdivision schemes based on it. These schemes refine point-normal pairs in 2D, and converge to limit…
Converting quad meshes to smooth manifolds, guided subdivision offers a way to combine the good highlight line distributions of recent G-spline constructions with the refinability of subdivision surfaces. Specifically, we present a C2…
Due to properties such as interpolation, smoothness, and spline connections, Hermite subdivision schemes employ fast iterative algorithms for geometrically modeling curves/surfaces in CAGD and for building Hermite wavelets in numerical…
This paper presents a hybrid algorithm that combines features form both Sqrt(3) and Loop Subdivision schemes. The algorithm aims at preserving sharp features and trim regions, during the surfaces subdivision, using a set of rules. The…
Any procedure applied to data, and any quantity derived from data, is required to respect the nature and symmetries of the data. This axiom applies to refinement procedures and multiresolution transforms as well as to more basic operations…
Subdivision surfaces are considered as an extension of splines to accommodate models with complex topologies, making them useful for addressing PDEs on models with complex topologies in isogeometric analysis. This has generated a lot of…
In this thesis, a new approach for constructing subdivision algorithms for generalized quadratic and cubic B-spline subdivision for subdivision surfaces and volumes is presented. First, a catalog of quality criteria for these subdivision…
This paper proposes a method for computing the visible occluding contours of subdivision surfaces. The paper first introduces new theory for contour visibility of smooth surfaces. Necessary and sufficient conditions are introduced for when…
In computed tomography, the approximation quality of a scan of a physical object is typically limited by the acquisition modalities, especially the hardware including X-ray detectors. To improve upon this, we experiment with a…
In this paper we extend the 2D circle average of [11] to a 3D binary average of point-normal pairs, and study its properties. We modify classical surface-generating linear subdivision schemes with this average obtaining surface-generating…
In this paper, we present a powerful differentiable surface fitting technique to derive a compact surface representation for a given dense point cloud or mesh, with application in the domains of graphics and CAD/CAM. We have chosen the Loop…
Convergence and normal continuity analysis of a bivariate non-stationary (level-dependent) subdivision scheme for 2-manifold meshes with arbitrary topology is still an open issue. Exploiting ideas from the theory of asymptotically…
Subdivision surfaces are proven to be a powerful tool in geometric modeling and computer graphics, due to the great flexibility they offer in capturing irregular topologies. This paper discusses the robust and efficient implementation of an…
Stationary subdivision schemes have been extensively studied and have numerous applications in CAGD and wavelet analysis. To have high-order smoothness of the scheme, it is usually inevitable to enlarge the support of the mask that is used,…
We establish convergence results for a spatial semidiscretization of Mean Curvature Flow (MCF) for surfaces with fixed boundaries. Our analysis is based on Huisken's evolution equations for the mean curvature and the normal vector, enabling…
We present a fast and efficient method for intersecting rays with Catmull-Clark subdivision surfaces. It takes advantage of the approximation democratized by OpenSubdiv, in which regular patches are represented by tensor product B\'ezier…
An isogeometric approach for solving the Laplace-Beltrami equation on a two-dimensional manifold embedded in three-dimensional space using a Galerkin method based on Catmull-Clark subdivision surfaces is presented and assessed. The…