Huawei Wang

√3-Subdivision-Based Biorthogonal Wavelets

A new efficient biorthogonal wavelet analysis based on the radic3 subdivision is proposed in the paper by using the lifting scheme. Since the radic3 subdivision is of the slowest topological refinement among the traditional triangular subdivisions, the multiresolution analysis based on the radic3 subdivision is more balanced than the existing wavelet analyses on triangular meshes and accordingly offers more levels of detail for processing polygonal models. In order to optimize the multiresolution analysis, the new wavelets, no matter whether they are interior or on boundaries, are orthogonalized with the local scaling functions based on a discrete inner product with subdivision masks. Because the wavelet analysis and synthesis algorithms are actually composed of a series of local lifting operations, they can be performed in linear time. The experiments demonstrate the efficiency and stability of the wavelet analysis for both closed and open triangular meshes with radic3 subdivision connectivity. The radic3-subdivision-based biorthogonal wavelets can be used in many applications such as progressive transmission, shape approximation, and multiresolution editing and rendering of 3D geometric models.

Estimating subdivision depth of Catmull-Clark surfaces

In this paper, both general and exponential bounds of the distance between a uniform Catmull-Clark surface and its control polyhedron are derived. The exponential bound is independent of the process of subdivision and can be evaluated without recursive subdivision. Based on the exponential bound, we can predict the depth of subdivision within a user-specified error tolerance. This is quite useful and important for pre-computing the subdivision depth of subdivision surfaces in many engineering applications such as surface/surface intersection, mesh generation, numerical control machining and surface rendering.

Eigenanalysis and continuity of non-uniform Doo-Sabin surfaces

In computer graphics and computer-aided geometric design, more and more subdivision schemes are being extensively used for free-form surfaces of arbitrary topology. The convergence and continuity analyses of uniform subdivision surfaces have been performed very well, but it is very difficult to prove the convergence and the continuity properties of non-uniform recursive subdivision surfaces (NURSSes, for short) because the subdivision matrix varies at each iteration step. This restricts widespread use of NURSSes, although NURSSes have a lot of advantages over uniform subdivision surfaces. In this paper, the concept of equivalent knot spacing is presented. A new technique for eigenanalysis, convergence and continuity analyses of non-uniform Doo-Sabin surfaces is proposed. Also, an interesting and important fact is found that the subdivision process of nonuniform Doo-Sabin surfaces may diverge sometime.

Improved ternary subdivision interpolation scheme

Abstract An improved ternary subdivision interpolation scheme was developed for computer graphics applications that can manipulate open control polygons unlike the previous ternary scheme, with the resulting curve proved to be still C 2 -continuous. Parameterizations of the limit curve near the two endpoints are given with expressions for the boundary derivatives. The split joint problem is handled with the interpolating ternary subdivision scheme. The improved scheme can be used for modeling interpolation curves in computer aided geometric design systems, and provides a method for joining two limit curves of interpolating ternary subdivisions.

Surface modeling with ternary interpolating subdivision

In this paper, a new interpolatory subdivision scheme, called ternary interpolating subdivision, for quadrilateral meshes with arbitrary topology is presented. It can be used to deal with not only extraordinary faces but also extraordinary vertices in polyhedral meshes of arbitrary topologies. It is shown that the ternary interpolating subdivision can generate a C1-continuous interpolatory surface. Some applications with open boundaries and curves to be interpolated are also discussed.

Touch-enabled haptic modeling of deformable multi-resolution surfaces

Currently, interactive data exploration in virtual environments is mainly focused on vision-based and non-contact sensory channels such as visual/auditory displays. The lack of tactile sensation in virtual environments removes an important source of information to be delivered to the users. In this paper, we propose the touch-enabled haptic modeling of deformable multi-resolution surfaces in real time. The 6-DOF haptic manipulation is based on a dynamic model of Loop surfaces, where the dynamic parameters are computed easily without subdividing the control mesh recursively. A local deforming scheme is developed to approximate the solution of the dynamics equations, thus the order of the linear equations is reduced greatly. During each of the haptic interaction loop, the contact point is traced and reflected to the rendering of updated graphics and haptics. The sense of touch against the deforming surface is calculated according to the surface properties and the damping-spring force profile. Our haptic system supports the dynamic modeling of deformable Loop surfaces intuitively through the touch-enabled interactive manipulation.

Physics-based subdivision surface modeling for medical imaging and simulation

In this paper a physics-based dynamic subdivision surface model based on Catmull-Clark surfaces is introduced and a new technique for exact evaluation of the dynamic model parameters, such as mass, damping and stiffness matrices, and dynamic forces etc. is presented for the dynamic subdivision surface. A closed-form analytic formula for thin-plate energy of Catmull-Clark surfaces of arbitrary topology is derived, which does not require recursive subdivision for calculating the dynamic parameters, so that it is more efficient and fast than the existing methods published for such dynamic models. This new strategy can be used for deformable surface modeling, medical imaging and simulation and so on.

EVALUATION OF NON-UNIFORM DOO-SABIN SURFACES

Parameterization approaches for non-uniform Doo-Sabin subdivision surfaces are developed in this paper using the eigenstructure of Doo-Sabin subdivision. New methods for evaluation of values and derivatives of Doo-Sabin surfaces at arbitrary parameters by means of non-iterative approaches are presented. Furthermore, generalized basis functions for non-uniform Doo-Sabin surfaces are derived. Thus, many algorithms and analysis techniques developed for parametric surfaces can be extended to Doo-Sabin surfaces.

Physics-based loop surface modeling

Strongly inspired by the research on physics-based dynamic models for surfaces, we propose a new method for precisely evaluating the dynamic parameters (mass, damping and stiffness matrices, and dynamic forces) for Loop surfaces without recursive subdivision regardless of regular or irregular faces. It is shown that the thin-plate energy of Loop surfaces can be evaluated precisely and efficiently, even though there are extraordinary points in the initial meshes, unlike the previous dynamic Loop surface scheme. Hence, the new method presented for Loop surfaces is much more efficient than the previous schemes.

Reflection and Refraction on Implicit Surfaces

Implicit surfaces are often used in computer graphics. They can be easily modeled and rendered, and many objects are composed of them in our daily life. In this paper, based on the concept of virtual objects, a novel method of real-time rendering is presented for reflection and refraction on implicit surface. The method is used to construct virtual objects from real objects quickly, and then render the virtual objects as if they were real objects except for one more step of merging their images with the real objects’ images. Characteristics of implicit surfaces are used to compute virtual objects effectively and quickly. GPUs (Graphics Processing Units) are used to compute virtual vertices quickly and further accelerate the computing and rendering processes. As a result, realistic effects of reflections and refractions on implicit surfaces are rendered in real time.