Vertex normal

Abstract: I propose a new equation to estimate the normal at a vertex of a polygonal approximation to a smooth surface, as a weighted sum of the normals to the facets surrounding the vertex. The equation accounts for the difference in size of these facets by assigning larger weights for smaller facets. When tested on random cubic polynomial surfaces, the equation is superior to other popular weighting methods.

Abstract: We present a new method for the recovery of a bivariate function H(x, y) that describes a “nice,” almost everywhere differentiable height profile, from shading information. The given shading data is assumed to be a result of diffuse, Lambertian reflection of light from the surface. This implies that, if the scene is uniformly illuminated from above, the shading yields information on the cosine of the angle between the vertical and the surface normal at each point. Given the shading information in the plane, the shape from shading problem is to determine all height profiles consistent with the data, and some boundary conditions, such as points of known height and surface orientation, or height profiles along continuous curves in the image plane. The new shape-from-shading method that we discuss is based on a recursive way of determining equal-height or level contours of the surface starting at a given level curve.

Abstract: The present invention smoothes a spherical graph signal composed of spherical signal points associated with graph vertices of a graph producing a smoothed spherical graph signal composed of smoothed spherical signal points. Each smoothed spherical signal point is computed by multiplying a vertex rotation matrix by the corresponding spherical signal point. The vertex rotation matrix is computed as a weighted average of neighbor rotation matrices using a local parameterization of the group of rotations. The present invention also filters anisotropically a graph signal composed signal points associated with graph vertices of a graph producing a filtered graph signal composed of filtered signal points. Each filtered signal point is computed as a weighted average of signal points corresponding to the corresponding graph vertices and neighbor graph vertices with neighbor weight matrices. The present invention also denoises the vertex positions of a polygon mesh without tangential drift. The face normals are smoothed on the dual graph of the polygon mesh. The smoothed face normals are used to construct neighbor weight matrices on the primal graph of the polygon mesh. The vertex positions are anisotropically filtered on the primal graph of the polygon mesh. The present invention also filters the vertex positions and face normals of a polygon mesh with interpolatory vertex positions and face normal constraints.

Abstract: We investigate current vertex normal computation algorithms and evaluate their effectiveness at approximating analytically computable (and thus comparable) normals for a variety of classes of model. We find that the most accurate algorithm depends on the class and that for some classes, none of the available algorithms is particularly good. We also compare the relative speeds of all algorithms.