Any satisfiability problem in conjunctive normal form can be solved in polynomial time by reducing it to a 3-sat formulation and transforming this to a Linear Complementarity problem (LCP) which is then solved as a linear program (LP). Any instance in this problem class, reduced to a LCP may be solved, provided certain necessary and sufficient conditions hold. The proof that these conditions wi...

In this paper, we present a novel two-step, variational and feature preserving smoothing method for terrain data. The first step computes the field of 3D normal vectors from the height map and smoothes them by minimizing a robust penalty function of curvature. This penalty function favors piecewise planar surfaces; therefore, it is better suited for processing terrain data then previous methods...

Digital objects and digital surfaces are isothetic structures per se. Such surfaces are thus not adapted to direct visualization with isothetic quads, or to many geometry processing methods. We propose a new regularization technique to construct a piecewise smooth quadrangulated surface from a digital surface. More formally we propose a variational formulation which efficiently regularizes digi...

Computable general equilibrium models and other types of variational inequalities play a key role in computational economics. This paper describes the design and implementation of a pathsearch-damped Newton method for solving such problems. Our algorithm improves on the typical Newton method (which generates and solves a sequence of LCP's) in both speed and robustness. The underlying complement...

We are concerned with solving aane variational inequalities deened by a linear map A and a polyhedral set C. Most of the existing pivotal methods for such inequalities or mixed linear complementarity problems depend on the existence of extreme points in C or a certain non{singularity property of A with respect to the lineality of C. In this paper, we prove that if A is copositive{plus with resp...

We present a new method to measure specular free-form surfaces within seconds. We call the measuring principle ‘Phase Measuring Deflectometry’ (PMD). With a stereo based enhancement of PMD we are able to measure both the height and the slope of the surface. The basic principle is to project sinusoidal fringe patterns onto a screen located remotely from the surface under test and to observe the ...

A method is developed for using large-order perturbation theory to solve the systems of coupled diierential equations that result from variational solution of the Schrr odinger equation with wavefunctions of product form. This is a noniterative, computationally eecient way to solve self-consistent-eld (SCF) equations. Possible applications include electronic structure calculations using product...

We introduce a generative model of part-segmented 3D objects: the shape variational auto-encoder (ShapeVAE). The ShapeVAE describes a joint distribution over the existence of object parts, the locations of a dense set of surface points, and over surface normals associated with these points. Our model makes use of a deep encoder-decoder architecture that leverages the partdecomposability of 3D o...

where the potentials are given functions. Under various boundary conditions, Sturm and Liouville established that solutions of problem (1) can exist only for particular values of the real parameter λ, which is called an eigenvalue. Relevant examples of linear Sturm-Liouville problems are the Bessel equation and the Legendre equation. The classical Sturm-Liouville theory does not depend upon the...