Metamorphosis of Polyhedral Surfaces using Decomposition

Abstract

This paper describes an algorithm for morphing polyhedral surfaces based on their decompositions into patches. The given surfaces need neither be genus‐zero nor two‐manifolds. We present a new algorithm for decomposing surfaces into patches. We also present a new projection scheme that handles topologically cylinder‐like polyhedral surfaces. We show how these two new techniques can be used within a general framework and result with morph sequences that maintain the distinctive features of the input models. Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computational Geometry and Object Modeling]: Boundary representations I.3.7 [Three‐Dimensional Graphics and Realism]: Animation

Mesh Decomposition Using Skeleton and Fuzzy Clustering

“…7, we can see that in a novel situation, as shown in Fig. 9, if a face f j belongs to patch i represented by edge (u 1 , v 1 ), the direction of its normal should be the same with 1 vc ( The result of final decomposition of the cow model is shown in Fig. 10.…”

“…With this method, we avoid using complex computing. For a mesh consists of n edges, it takes (log ) O n to find the lowest cost edge and (1) O to refresh the data. So the total runtime of the procedure is ( log ) O n n .…”

“…Shlafman et al [1] used decomposition in metamorphosis to give a correspondence between two models. Li et al [2] used decomposition in collision detection to build a hierarchical data structures.…”

“…Another problem is the result can easily be affected by noise of the mesh. Shalfman et al proposed a K-means clustering algorithm for mesh decomposition in [1]. The mesh is well segmented, but the boundaries are always too jaggy and always not correct.…”

A graph-based technique for semi-supervised segmentation of 3D surfaces

“…Some of them use standard clustering techniques or borrow segmentation procedures from the 2D domain, other exploit graph partitioning algorithms, shape fitting or even the distribution of symmetry planes over watertight objects. Shlafman et al propose to use a variation of K-means to group the triangles of the mesh into clusters (Shlafman et al, 2002). This is a quite direct adaptation: first the user specify the desired number of clusters (k), then the process starts by randomly selecting a set of k well spaced seed triangles and it iterates by alternating an assignment step (where each non-seed triangle is assigned to the nearest seed) and an adjustment step (where new seeds are selected by picking the triangle nearest to the center of each cluster).…”