The coceptions of two element α-concave convex and mixed α-concave convex operators are introduced. The fixed point theorems of the two type operators are obtained. By these theorems,the existence and uniquence of s...The coceptions of two element α-concave convex and mixed α-concave convex operators are introduced. The fixed point theorems of the two type operators are obtained. By these theorems,the existence and uniquence of solution of three type nonlinear integral equations is studied.展开更多
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-...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.展开更多
文摘The coceptions of two element α-concave convex and mixed α-concave convex operators are introduced. The fixed point theorems of the two type operators are obtained. By these theorems,the existence and uniquence of solution of three type nonlinear integral equations is studied.
基金supported by the National Natural Science Foundation of China(Nos.61432003,61572105,11171052,and 61328206)
文摘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.
