We consider the problem of finding a unit vector field (i.e., a direction field) over a domain that balances two competing objectives, smoothness and conformity to the shape of the domain. Common examples of this problem are finding normal directions along a curve and tangent directions over a surface. In a recent work, Jakob et al. observed that minimizing extrinsic variation of a tangent dire...

STATEMENT OF PROBLEM During the insertion appointment, the practitioner is often faced with the need to adjust ceramic surfaces to fit a restoration to the adjacent or opposing dentition and soft tissues. PURPOSE The purpose of this study was to assess the ceramic surface smoothness achieved with various commercially available ceramic polishing kits on different commonly used ceramic systems....

This paper proves that the welfare of the first price auction in Bayes-Nash equilibrium is at least a .743-fraction of the welfare of the optimal mechanism assuming agents’ values are independently distributed. The previous best bound was 1 − 1/e ≈ .63, derived in Syrgkanis and Tardos (2013) using smoothness, the standard technique for reasoning about welfare of games in equilibrium. In the wor...

We present a method of recovering shape from shading that solves directly for the surface height. By using a discrete formulation of the problem, we are able to achieve good convergence behavior by employing numerical solution techniques more powerful than gradient descent methods derived from variational calculus. Because we directly solve for height, we avoid the problem of nding an integrabl...

Subdivision surfaces are rapidly gaining popularity in computer graphics, modeling, simulation and animation. Existing of subdivision algorithms is suffer from the lack of precise definition of the schemes with guaranteed behavior for a sufficiently general type of control meshes, non-smoothness due to the existence of regular and nonregular face types during the subdivision process and incapab...