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In this paper, we present a new algorithm for quad-dominant meshing of unorganized point clouds based on periodic global parameterization. Our meshing method is guided by principal directions so as to preserve the intrinsic geometric properties. We use local Delaunay triangulation to smooth the initial principal directions and adapt the global parameterization to point clouds. By optimizing the fairness measure we can find the two scalar functions whose gradients best align with the guided principal directions. To handle the redundant vertices in the iso-lines due to overlapped triangles, an approach is specially designed to clean the iso-lines. Our approach is fully automatic and applicable to a surface of arbitrary genus. We also show an application of our method in curve skeleton extraction from incomplete point cloud data.

Subdivision is a convenient tool to construct objective curves and surfaces directly from given scattered points. Stationary p-subdivision schemes are highly efficient in the acquisitions of curve/surface points in shape modeling. The features of supported set of nonnegative mask of uniform convergent stationary subdivision schemes are important to their theoretic researches and applications. According to the properties of supported set of the nonnegative mask, a sufficient condition for uniform convergence of stationary p-subdivision scheme is presented. This condition is proved with two propositions and spline function. The contribution of this work is that the convergence of a stationary p-subdivision scheme can be judged directly. This direct judge is in favor of applications of this scheme.

Real-time and realistic rendering of forest is an impor- tant and a difficult work in computer graphics and digi- tal forestry. An image based real-time and realistic forest rendering software is developed in this paper. Three or- thogonal billboards are used to represent the geometry and material of a tree, so that the 3D perception is enhanced and weak parallax of usual images based approaches is avoided. Shadows of all trees on the plat ground are gen- erated through the stencil buffer, shadow projection and a mixture of the shadow with grass texture. Different bill- boards are chosen on the viewing direction and the lighting direction, so that the effect of object torsion due to poor im- age direction is avoided. Forest growth, forest rendering in different lighting conditions, navigation inside a forest, and flying over a forest are all simulated.