Optimal Polynomial Filters

TL;DR: Several contact-impact problems are modeled using various polygonal interpolation functions, including the Wachspress interpolation function, the metric coordinate shape functions, the natural neighbor based functions, and the mean value coordinate functions to demonstrate the efficiency of proposed technique in modeling contact- impact problems.

TL;DR: The combination of polytree meshes and adaptive filters not only clarifies the interfaces between material phases, but also decreases the computing time of the overall process in comparison to using the regular fine meshes.

TL;DR: The general construction of Floater's mean value coordinates is extended to a general form that is capable of constructing a family of coordinates in a convex 2D polygon, 3D triangular polyhedron, or higher-dimensional simplicial polytope, and the resulting family includes all possible coordinates in any convex simplicialpolytope.

TL;DR: An improved algorithm for prefiltering two-dimensional polygons is presented that removes the expensive clipping of the polygons against the filter mask and instead adds an integral to the accumulation buffer of the pixel according to whether the pixel center is outside the component region or not.

TL;DR: It is shown that reconstruction using derivative as well as amplitude values can greatly reduce aliasing, and a new family of piecewise cubic filters are investigated as a practical demonstration.

TL;DR: The theory of the multivariate polyhedral splines is applied to analytic antialiasing: a triangular simplex spline is used to represent surface intensity, while a box splines are used as a filter.

TL;DR: Though only slightly more complicated to implement than the widely used box prefiltering method, quadraturePrefiltering can generate images with much less visible aliasing artifacts, and renders very high quality images at reasonable cost.

TL;DR: This work presents a discrete pre-filtering technique for anti-aliasing Bezier curves using arbitrary filters which is numerically and geometrically robust and whose accuracy is controllable.