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Abstract: mesh parameterization is one of the fundamental operations in computer graphics (CG) and computer-aided design (CAD). In this paper, we propose a novel local/global parameterization approach, ARAP++, for single- and multi-boundary triangular meshes. It is an extension of the as-rigid-as-possible (ARAP) approach, which stitches together 1-ring patches instead of individual triangles. To optimize the spring energy, we introduce a linear iterative scheme which employs convex combination weights and a fitting jacobian matrix corresponding to a prescribed family of transformations. Our algorithm is simple, efficient, and robust. The geometric properties (angle and area) of the original model can also be preserved by appropriately prescribing the singular values of the fitting matrix. To reduce the area and stretch distortions for high-curvature models, a stretch operator is introduced. Numerical results demonstrate that ARAP++ outperforms several state-of-the-art methods in terms of controlling the distortions of angle, area, and stretch. Furthermore, it achieves a better visualization performance for several applications, such as texture mapping and surface remeshing.

This paper proposes an extended local/global parameterization (ARAP++) method for single-boundary and multi-boundary triangular meshes. It suggests two main extensions in comparison with ARAP. 1) The current ARAP scheme combines a local mapping from a 3D triangle to the plane with a global ‘stitch’ operation for individual triangles, while the proposed ARAP++ adopts a global operation that stitches the 1-ring patches together; 2) Similar to energy minimization of mesh parameterization, the scheme of this paper is based on optimization of the spring energy, which can cover the ARAP approach (based on the optimization of Dirichlet energy) as a special case. The main interesting point is that each triangle is looked upon 3 different view points: those of the 3 vertices. An interesting property is that each angle can therefore be corrected is order to sum to Pi around each vertex.

ARAP++:一类推广的局部/全局参数化算法

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