Analytic Rasterization of Curves with Polynomial Filters
Article first published online: 6 MAY 2013
© 2013 The Author(s) Computer Graphics Forum © 2013 The Eurographics Association and Blackwell Publishing Ltd.
Computer Graphics Forum
Volume 32, Issue 2pt4, pages 499–507, May 2013
How to Cite
Manson, J. and Schaefer, S. (2013), Analytic Rasterization of Curves with Polynomial Filters. Computer Graphics Forum, 32: 499–507. doi: 10.1111/cgf.12070
- Issue published online: 6 MAY 2013
- Article first published online: 6 MAY 2013
- I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism—Color, shading, shadowing, and texture
We present a method of analytically rasterizing shapes that have curved boundaries and linear color gradients using piecewise polynomial prefilters. By transforming the convolution of filters with the image from an integral over area into a boundary integral, we find closed-form expressions for rasterizing shapes. We show that a polynomial expression can be used to rasterize any combination of polynomial curves and filters. Our rasterizer also handles rational quadratic boundaries, which allows us to evaluate circles and ellipses. We apply our technique to rasterizing vector graphics and show that our derivation gives an efficient implementation as a scanline rasterizer.