Barycentric Coordinates
Radial blurring averages pixel values sampled at nearby points along an arc emanating from the target pixel (white dot in Figure 4). The sampling locations (black dots), however, are rarely centered on pixels. In our sample implementation, the pixel coordinates are simply truncated to integers, which can lead to visible artifacts in some images. A more accurate approach is to use barycentric coordinates. Barycentric coordinates account for the fact that the sampling location is not centered on a pixel by blending the values of neighboring pixels. Each neighbor contributes to the blended value in proportion to its overlap with a unit square centered on the sampling location. If truncation is used, the color value of the example pixel is green. With barycentric coordinates, the color value for the example pixel is a blend of green, blue, and plum. Blending pixel values increases accuracy but incurs an additional cost per pixel. However, this extra work increases the potential gain of multithreaded performance.
—H.G. and B.M.
