We consider the problem of reconstructing a surface from scattered points sampled on a physical shape. The sampled shape is approximated as the zero level set of a function. This function is defined as a linear combination ...

We present a new algorithm to compute a topologically and geometrically accurate triangulation of an implicit surface. Our approach uses spatial subdivision techniques to decompose a manifold implicit surface into star-shaped ...

Geometry processing algorithms often require the robust extraction of curvature information. We propose to achieve this with principal component analysis (PCA) of local neighborhoods, defined via spherical kernels centered ...

Many applications in geometric modeling, computer graphics, visualization and computer vision benefit from a reduced representation called curve-skeletons of a shape. These are curves possibly with branches which compactly ...

We develop spherical barycentric coordinates. Analogous to classical, planar barycentric coordinates that describe the positions of points in a plane with respect to the vertices of a given planar polygon, spherical ...

In recent years, the moving least-square (MLS) method has been extensively studied for approximation and reconstruction of surfaces. The MLS method involves local weighted least-squares polynomial approximations, using a ...

We describe a subdivision scheme that acts on control nodes that each carry a vector of values. Each vector defines partial derivatives, referred to as jets in the following and subdivision computes new jets from old jets. ...

Priority-driven search is an algorithm for retrieving similar shapes from a large database of 3D objects. Given a query object and a database of target objects, all represented by sets of local 3D shape features, the ...

Meshes representing real world objects, both artist-created and scanned, contain a high level of redundancy due to (possibly approximate) planar reflection symmetries, either global or localized to different subregions. ...

Quality meshing in 2D and 3D domains is an important problem in geometric modeling and scientific computing. We are concerned with triangle meshes having only nonobtuse angles. Specifically, we propose a solution for ...