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Interactive mesh deformation using equality-constrained least squares
Authors:H. Masuda   Y. Yoshioka  Y. Furukawa
Affiliation:

aThe University of Tokyo, Graduate School of Engineering, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan

bNational Institute of Advanced Industrial Science and Technology, Digital Manufacturing Research Center, Namiki, Tsukuba-shi, Ibaraki 305-8561, Japan

Abstract:Mesh deformation techniques that preserve the differential properties have been intensively studied. In this paper, we propose an equality-constrained least squares approach for stably deforming mesh models while approximately preserving mean curvature normals and strictly satisfying other constraints such as positional constraints. We solve the combination of hard and soft constraints by constructing a typical least squares system using QR decomposition. A well-known problem of hard constraints is over-constraints. We show that the equality-constrained least squares approach is useful for resolving such over-constrained situations. In our framework, the rotations of mean curvature normals are treated using the logarithms of unit quaternions in . During deformation, mean curvature normals can be rotated while preserving their magnitudes. In addition, we introduce a new modeling constraints called rigidity constraints and show that rigidity constraints can effectively preserve the shapes of feature regions during deformation. Our framework achieves good performance for interactive deformation of mesh models.
Keywords:Equality-constrained least squares   Mesh deformation   Quaternion   Laplacian coordinate   Rigidity constraint
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