A new 3D morphing algorithm for polyhedral objects with the same genus is presented in the paper. Our main contribution is an efficient and general algorithm for setting up the vertex correspondence between the polyhedra. The proposed algorithm first interactively partitions the two original polyhedra into the same number of polygonal patches, the patch correspondence is also established during partitioning. Each pair of corresponding patches is then parametrized and resampled by using the harmonic maps. A feature polyhedron is finally constructed for each original polyhedron, and the vertex correspondence between each original polyhedron and its feature polyhedron is automatically established following a cluster scheme. The shape transition between the original polyhedral models is accomplished by composing three successive transformations using their feature polyhedra as the bridges. Experimental results demonstrate that our algorithm is very robust, and can deal with very general cases (non-zero genus polyhedral cases).

This paper proposes a new preprocessing method for interactive rendering of complex polygonal virtual environments. The approach divides the space that observer can reach into many rectangular viewpoint regions. For each region, an outer rectangular volume(ORV) is established to surround it. By adaptively partitioning the boundary of the ORV together with the viewpoint region, all the rays that originate from the viewpoint region are divided into the beams whose potentially visible polygon number is less than a preset threshold. If a resultant beam is the smallest and intersects many potentially visible polygons, the beam is simplified as a fixed number of rays and the averaged color of the hit polygons is recorded. For other beams, their potentially visible sets (PVS) of polygons are stored respectively. During an interactive walkthrough, the visual information related to the current viewpoint is retrieved from the storage. The view volume clipping, visibility culling and detail simplification are efficiently supported by these stored data. The rendering time is independent of the scene complexity.

In this paper, we present a novel fairing algorithm for the removal of noise from uniform triangular meshes without shrinkage and serious distortion. The key feature of this algorithm is to keep all triangle centers invariant at each smoothing step by including some constraints in the energy minimization functional. The constrained functional is then minimized efficiently using an iterative method. Further, we apply this smoothing technique to a multiresolution representation to remove arbitrary levels of detail. A volume-preserving decimation algorithm is presented to generate the multiresolution representation. The experimental results demonstrate the combined algorithm's stability and efficiency.

A new non-linear view interpolation algorithm is presented in this paper. Unlike the linear interpolation scheme, our method can exactly simulate the perspective viewing transformation during walkthrough. To accelerate the view interpolation, the algorithm employs a binary subdivision scheme to optimize the decomposition of the source image so that the number of resultant blocks is greatly reduced. Holes in the intermediate image are filled by two steps, namely enlarging the transferred blocks at the sides adjacent to holes and retrieving the local image within holes from the destination images by multidirectional interpolation. Experimental results demonstrate that our algorithm is much more accurate and efficient than the traditional one. Copyright.

Polygonal models have been widely applied in the community of CAD and computer graphics. Since a polygonal surface usually has no intrinsic parameterization, it is very difficult to map textures onto it with low distortion. In this paper, we present an efficient texture mapping algorithm for polygonal models. For each region to be mapped, the algorithm first constructs a B-spline patch with similar shape to surround the model. The mapped region is then projected onto the constructed B-spline patch to achieve a parameterization. By interactively controlling the B-spline patch, the user can conveniently decorate the surface of the model to meet his requirements. Both local and global texture mapping are discussed. The experimental results demonstrate that the algorithm has a great of potential applications in computer animation and virtual reality systems.

Methods for curve modeling with cubic algebraic curves based on geometric constraints are introduced in this paper. A 1-parameter family of cubic curves with four given points as well as two tangent lines at the endpoints is constructed in the first part of the paper. A 1-parameter family and 2-parameter family of cubic curve constructions are presented for interpolating two given endpoints and two given tangent lines as well as two given curvatures at the endpoints in the last part of the paper. 2001 Elsevier Science B.V. All rights reserved.

In general, mesh smoothing is performed by minimizing the discrete energy function for the surface. One of the major problems in mesh smoothing is to prevent the mesh from shrinking. In this paper, we propose a novel volume constraint to address the shrinking problem in mesh smoothing. Our key observation is that the mesh can be efficiently smoothed patch by patch in a signal processing manner, and then a local volume preserving constraint can be easily imposed to the energy minimization problem associated with the small patch, called the smoothing stencil, so as to effectively avoid the mesh shrinkage. In our implementation, the smoothing stencil is the 1-ring neighboring region of an edge or a triangle. And the constrained minimization problem is solved by a 2-step approximation method for efficiency. A series of examples demonstrate that the proposed smoothing method can be applied to remove noise from a mesh or remove rough detail from an original mesh to generate a smooth model in object reconstruction and geometry modeling. c 2002 Elsevier Science (USA)

There are many methods based on optimization technique for resolving the problem of deformation-minimization in texture mapping. Recently, a new optimization-based method for parameterizing polygonal meshes with minimum deformation has been developed to specifically address the problem of feature matching in texture mapping. However, these optimization-based methods achieve the result of high quality at the expense of long computation time. In this paper, we present a fast analytic texture mapping method based on radial basis function (RBF) interpolation to solve the problem of constrained texture mapping. The users control the mapping process by interactively defining and editing a set of constraints consisting of 3D points picked on the surface and the corresponding 2D points of the texture. RBF is invoked to interpolate the user-defined constraints to provide an analytic parameterization of the surface. The energy-minimization characteristic of RBF also ensures that the mapping function smoothly interpolates the constraints with satisfying non-deformation properties. This method has been applied to several data sets and excellent results have been produced. Our method is much faster than the optimization-based method for texture mapping with the same good effect achieved.

This paper presents a novel approach for 3D surface filtering over two-manifold meshes. A robust spherical parameterization algorithm is proposed to transform the input surface into a spherical vector function/signal. This signal is then decomposed into frequency domain using spherical harmonic transforms. Finally, traditional filtering techniques are generalized to process such spherical signals in either the frequency or spatial domain. Our major contribution is the two-phase spherical parameterization algorithm, which can handle meshes with complex shapes by incorporating local parameterization into the progressive mesh. A number of experimental examples demonstrate the potential of our algorithm.

This paper presents a √2subdivision scheme for quadrilateralmeshes that can be regarded as an extension of a 4-8 subdivision with new subdivision rules and improved capability and performance. The proposed scheme adopts a so-called √2split operator to refine a control mesh such that the face number of the refined mesh generally equals the edge number and is thus about twice the face number of the coarse mesh. Smooth rules are designed in reference to the 4-8 subdivision, while a new set of weights is developed to balance the flatness of surfaces at vertices of different valences. Compared to the 4-8 subdivision, the presented scheme can be naturally generalized for arbitrary control nets and is more efficient in both space and computing time management. Analysis shows that limit surfaces produced by the scheme are C4 continuous for regular control meshes and G1 continuous at extraordinary vertices.