Realistic behavior of deformable objects is essential for many applications in computer graphics, engineering, or medicine. Typical techniques are either based on mass-springdamper models, boundary element methods, finite difference methods, or finite element methods. These methods either lack accuracy or are computationally very expensive. If accuracy is required FEM computations use adaptive ...

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 implementation is nontrivial due to the computational, topological, and smoothness constraints, which should be satisfied by the underlying surface. The fundament...

Abstract The objective of this paper is to introduce a direct approach for generating local averaging rules for both the √ 3 and 1-to-4 vector subdivision schemes for computer-aided design of smooth surfaces. Our innovation is to directly construct refinable bivariate spline function vectors with minimum supports and highest approximation orders on the six-directional mesh, and to compute their...

In the implementation of subdivision scheme, three of the most important issues are smoothness, size of support, and approximation order. Our objective is to introduce an improved ternary 4-point approximating subdivision scheme derived from cubic polynomial interpolation, which has smaller support and higher smoothness, comparing to binary 4-point and 6-point schemes, ternary 3-point and 4-poi...

We present a new model for the representation of n-dimensional multiresolution meshes. It provides a robust topological representation of arbitrary meshes that are combined in closely interlinked levels of resolution. The proposed combinatorial model is formalized through the mathematical model of combinatorial maps allowing us to give a general formulation, in any dimensions, of the topologica...

Subdivision schemes are commonly used to obtain dense or smooth data representations from sparse discrete data. E. g., B-splines are smooth curves or surfaces that can be constructed by infinite subdivision of a polyline or polygon mesh of control points. New vertices are computed by linear combinations of the initial control points. We present a new non-linear subdivision scheme for the refine...

A totally odd H-subdivision means a subdivision of a graph H in which each edge of H corresponds to a path of odd length. Thus this concept is a generalization of a subdivision of H. In this paper, we give a structure theorem for graphs without a fixed graph H as a totally odd subdivision. Namely, every graph with no totally odd H-subdivision has a tree-decomposition such that each piece is eit...

Haptic rendering of meshes of arbitrary topology is a difficult and time-consuming process. This paper presents the use of subdivision surfaces in order to solve this problem. An overview of subdivision surfaces is given and the algorithms needed to calculate the surface contact point are discussed. We will show that this algorithm is faster than traditional algorithms. Introduction and Related...

We propose a wavelet based local subdivision of 3-D surfaces, which can be effectively applied to a mesh with complex and high curvature faces. This approach extends Lounsbery et al. works [1], which has been developed for regular triangular mesh subdivision. For such a purpose, a bi-orthogonal wavelet basis is constructed by defining a local inner product and using the lifting scheme [2]. As o...

The paper presents a new subdivision scheme, which constructs a surface approximating a given net of 3D-curves. Similar to the well known Chaikin algorithm for points, having a refinement step based on piecewise linear interpolation of the control points followed by evaluation at 1/4 and 3/4 of the local parameter value, the refinement step in the proposed subdivision scheme is based on piecewi...