Premium
Analytic Anti‐Aliasing of Linear Functions on Polytopes
Author(s) -
Auzinger T.,
Guthe M.,
Jeschke S.
Publication year - 2012
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/j.1467-8659.2012.03012.x
Subject(s) - polytope , polyhedron , vertex (graph theory) , computer science , tetrahedron , convolution (computer science) , anti aliasing , function (biology) , mathematics , filter (signal processing) , directx , algorithm , computer graphics (images) , combinatorics , geometry , computer vision , artificial intelligence , graph , audio signal processing , digital signal processing , evolutionary biology , artificial neural network , computer hardware , biology , audio signal
This paper presents an analytic formulation for anti‐aliased sampling of 2D polygons and 3D polyhedra. Our framework allows the exact evaluation of the convolution integral with a linear function defined on the polytopes. The filter is a spherically symmetric polynomial of any order, supporting approximations to refined variants such as the Mitchell‐Netravali filter family. This enables high‐quality rasterization of triangles and tetrahedra with linearly interpolated vertex values to regular and non‐regular grids. A closed form solution of the convolution is presented and an efficient implementation on the GPU using DirectX and CUDA C is described.