Automatic Cage Building with Quadric Error Metrics

Abstract

Modern computer graphics applications usually require high resolution object models for realistic rendering. However, it is expensive and difficult to deform such models in real time. In order to reduce the computational cost during deformations, a dense model is often manipulated through a simplified structure, called cage, which envelops the model. However, cages are usually built interactively by users, which is tedious and time-consuming. In this paper, we introduce a novel method that can build cages automatically for both 2D polygons and 3D triangular meshes. The method consists of two steps: 1) simplifying the input model with quadric error metrics and quadratic programming to build a coarse cage; 2) removing the self-intersections of the coarse cage with Delaunay partitions. With this new method, a user can build a cage to envelop an input model either entirely or partially with the approximate vertex number the user specifies. Experimental results show that, compared to other cage building methods with the same number of vertex, cages built by our method are more similar to the input models. Thus, the dense models can be manipulated with higher accuracy through our cages.

Efficient and effective cage generation by region decomposition

“…Comparisons: we compare our method with , and . In Figure , we can see that our method can generate a more coarse cage, while the cages generated by the methods in and are too dense to manipulate.…”

“…In Figure , we can see that our method can generate a more coarse cage, while the cages generated by the methods in and are too dense to manipulate. For the woman model in Figure (see the the numerical results in Table ), it can be seen that our method is more efficient than those in and to get the comparable cages.…”

“…(d)The cage envelops the original woman model. (e)Cage generated by the method in , and it contains 200 vertices. The computation time is 5667.97s.…”

“…It is too dense for manipulation with 500 vertices. (b)Cage generated by the method in , and it contains 300 vertices. The computation time is 19.286s.…”

“…However, because the voxels are regular shapes, they can not catch many detail features of the model, and the generated cage is often too dense for cage‐based deformation. In , Deng et al build a cage with quadric error metrics, which decimates the input model with quadric error metrics and quadratic programming to build a coarse cage firstly, and then removes the self‐intersections of the coarse cage with Delaunay partitions. However, their method cannot deal with complex mesh models.…”