Premium
Wavelet Rasterization
Author(s) -
Manson J.,
Schaefer S.
Publication year - 2011
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.1467-8659.2011.01887.x
Subject(s) - wavelet , polygon mesh , quadratic equation , haar wavelet , bounded function , computer science , wavelet transform , mathematics , multiresolution analysis , line (geometry) , algorithm , wavelet packet decomposition , computer graphics (images) , discrete wavelet transform , geometry , artificial intelligence , mathematical analysis
We present a method for analytically calculating an anti‐aliased rasterization of arbitrary polygons or fonts bounded by Bézier curves in 2D as well as oriented triangle meshes in 3D. Our algorithm rasterizes multiple resolutions simultaneously using a hierarchical wavelet representation and is robust to degenerate inputs. We show that using the simplest wavelet, the Haar basis, is equivalent to performing a box‐filter to the rasterized image. Because we evaluate wavelet coefficients through line integrals in 2D, we are able to derive analytic solutions for polygons that have Bézier curve boundaries of any order, and we provide solutions for quadratic and cubic curves. In 3D, we compute the wavelet coefficients through analytic surface integrals over triangle meshes and show how to do so in a computationally efficient manner.