We present a shape representation, the multi-level partition of unity implicit surface, that allows us to construct surface models from very large sets of points. There are three key ingredients to our approach: 1) piecewise quadratic functions that capture the local shape of the surface, 2) weighting functions (the partitions of unity) that blend together these local shape functions, and 3) an...

This paper proposes a numerical method to the two-dimensional hyperbolic equations with nonlocal integral conditions. The nonlocal integral equation is of major challenge in the frame work of the numerical solutions of PDEs. The method benefits from collocation radial basis function method, the generalized thin plate splines radial basis functions are used.Therefore, it does not require any str...

Most 3D shape analysis methods use triangular meshes to discretize both the shape and functions on it as piecewise linear functions. With this representation, shape analysis requires fine meshes to represent smooth shapes and geometric operators like normals, curvatures, or LaplaceBeltrami eigenfunctions at large computational and memory costs. We avoid this bottleneck with a compression techni...

A shape invariant model for functions f1,...,fn specifies that each individual function fi can be related to a common shape function g through the relation fi(x)=aig(cix + di) + bi. We consider a flexible mixture model that allows multiple shape functions g1,...,gK, where each fi is a shape invariant transformation of one of those gk. We derive an MCMC algorithm for fitting the model using Baye...

A shape invariant model for functions f1, . . . , fn specifies that each individual function fi can be related to a common shape function g through the relation fi(x) = aig(cix + di) + bi. We consider a mixture model that allows multiple shape functions g1, . . . , gK , where each fi is a shape invariant transformation of one of those gk. We derive an MCMC algorithm for fitting the model using ...

a meshless method namely, discrete least square method (dlsm), is presented in the paper for the solution of free surface seepage problem. in this method computational domain is discredited by some nodes and then the set of simultaneous equations are built using moving least square (mls) shape functions and least square technique. the proposed method does not need any background mesh therefore ...