Fast and intuitive generation of geometric shape transitions

We describe a novel method for continuously transforming two triangulated models of arbitrary topology into each other. Equal global topology for both objects is assumed. However, extensions for genus changes during metamorphosis are provided. The proposed method addresses the major challenge in 3D metamorphosis, namely, specifying the morphing process intuitively with minimal user interaction and sufficient detail. Corresponding regions and point features are interactively identified. These regions are parametrized automatically and consistently, providing a basis for smooth interpolation. Suitable 3D interaction techniques offer a simple and intuitive control over the whole morphing process.     

物体渐变技术现状与发展

物体渐变技术在虚拟现实、工业模拟、科学计算可视化、动画生成等领域有着广泛的应用，具有十分重要的意义，近年来，有许多研究者提出了一些效果不错的算法，对这些算法进行了分析，并对物体渐变的基本原理、物体的表示方法与渐变技术间的紧密联系、二维物体渐变技术和三维物体渐变技术做了较全面的综述，探讨了现有物体渐变技术中需要改进的关键问题，并给出了渐变技术在未来的发展方向。     

A novel constrained texture mapping method based on harmonic map

In this paper, we present a novel constrained texture mapping method based on the harmonic map. We first project the surface of a 3D model on a planar domain by an angle-based-flattening technique and perform a parametrization. The user then specifies interactively the constraints between the selected feature points on the parametric domain of the 3D model and the corresponding pixels on the texture image; the texture coordinates of other sample points on the 3D model are determined based on harmonic mapping between the parametric domain of the model and the texture image; finally we apply an adaptive local mapping refinement to improve the rendering result in real-time. Compared with other interactive methods, our method provides an analytically accurate solution to the problem, and the energy minimization characteristic of the harmonic map reduces the potential distortion that may result in the constrained texture mapping. Experimental data demonstrate good rendering effects generated by the presented algorithm.     

Variable-radius blending of parametric surfaces

The radius blend is a popular surface blending because of its geometric simplicity. A radius blend can be seen as the envelope of a rolling sphere or sweeping circle that centers on a spine curve and touches the surface to be blended along the linkage curves. For a given pair of base surfaces in parametric form, a reference curve, and a radius function of the rolling sphere, we present an exact representation for the variable-radius spine curve and propose a marching procedure. We describe methods that use the derived spine curve and linkage curves to compute a parametric form of the variable-radius sphearical and circular blends.     

Direct manipulation of FFD: efficient explicit solutions and decomposible multiple point constraints

Published online: 25 July 2001     

A note on harmonic subgraphs in labelled geometric graphs

Let S be a set of n points in general position in the plane, labelled bijectively with the integers {0,1,…,n−1}. Each edge (the straight segment that joins two points) is labelled with the sum of the labels of its endpoints. In this note we investigate the maximum size of noncrossing matchings and paths on S, under the requirement that no two edges have the same weight.