Analytic Rasterization of Curves with Polynomial Filters. (6th May 2013)

• Record Type: Journal Article
• Authors: Manson, Josiah; Schaefer, Scott
• Is Part Of: Computer graphics forum. Volume 32:Number 2(2013)Part 4
• Page Start: 499
• Page End: 507
• Publication Date: 2013-05-06
• Subjects: I.3.7 [Computer Graphics]: Three‐Dimensional Graphics and Realism—Color, shading, shadowing, and texture; Computer graphics -- Periodicals; 006.605
• DOI: 10.1111/cgf.12070
• Languages: English
• ISSNs: 0167-7055

Abstract

Abstract: 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.