Smooth feature line detection for meshes

In this paper the authors present a novel semi-automatic feature line detection technique for meshes. Taking into account the distance and orientation between two vertices on meshes and the curvature information of vertices, they first find an initial feature line which connects some user-specified vertices on meshes; then parameterize the “feature strip” surrounding the feature line onto a planar domain using a vertex flattening technique; and refine the flattened feature strip using the 2D snakes approach to make the feature line smoother and more accurate; lastly they get the feature line by mapping the refined line back to the original meshes. Experimental results showed that their method can extract the feature line rapidly and precisely. As an ap- plication, they propose a mesh decomposition method based on the detected feature line.

ARAP++:an extension of the local/global approach to mesh parameterization

Mesh parameterization is one of the fundamental operations in computer graphics(CG) and computeraided design(CAD). In this paper, we propose a novel local/global parameterization approach, ARAP++, for singleand 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.

Measured boundary parameterization based on Poisson's equation

One major goal of mesh parameterization is to minimize the conformal distortion. Measured boundary parameteri-zations focus on lowering the distortion by setting the boundary free with the help of distance from a center vertex to all the boundary vertices. Hence these parameterizations strongly depend on the determination of the center vertex. In this paper,we introduce two methods to determine the center vertex automatically. Both of them can be used as necessary supplements to the existing measured boundary methods to minimize the common artifacts as a result of the obscure choice of the center vertex. In addition,we propose a simple and fast measured boundary parameterization method based on the Poisson's equation. Our new approach generates less conformal distortion than the fixed boundary methods. It also generates more regular domain boundaries than other measured boundary methods. Moreover,it offers a good tradeoff between computation costs and conformal distortion compared with the fast and robust angle based flattening (ABF++).