Two Dimensional Hidden Surface Removal with Frame-to-frame Coherence

TL;DR

A hidden surface removal algorithm for two-dimensional layered scenes built from arbitrary primitives, particularly suited to interaction and animation in rich scenes, is described, which analyses and dramatically reduces the amount of rasterization and composition required to render a scene.

Abstract

We describe a hidden surface removal algorithm for two-dimensional layered scenes built from arbitrary primitives, particularly suited to interaction and animation in rich scenes (for example, in illustration). The method makes use of a set-based raster representation to implement a front-to-back rendering model which analyses and dramatically reduces the amount of rasterization and composition required to render a scene. The method is extended to add frame-to-frame coherence analysis and caching for interactive or animated scenes. A powerful system of primitive-combiners called filters is described, which preserves the efficiencies of the algorithm in highly complicated scenes. The set representation is extended to solve the problem of correlated mattes, leading to an efficient solution for high quality antialiasing. A prototype implementation has been prepared.

Figures (14)

• Figure 1: Possible raster set representation for shapes. For a sprite, the same structure is used, but with pixel data added to each horizontal span, possibly compressed with run length encoding.
• Figure 2: From left to right: A polygon in vector space and its shape, minshape and maxshape as sets of pixels (filled) when using an antialiasing filter with square footprint twice the interpixel spacing.
• Figure 3: Composing a line of two partially transparent sprites, preserving run-length encoded spans.
• Figure 4: A finite-width scanline and part of a polygon crossing it (shaded), together with the calculated shape scanline (marked as small circles around pixel centres for those pixels included in the shape). The large, dotted overlapping circles are antialiasing filter footprints, though we approximate them with squares for this process. If the left-most pixel here is pixel $0$, $spans(t)$ is {(1--3, 7--12}, $spans(b)$ is {0--3, 7--12} and $covered(e)$ is {0--4,7--12} so the result is {0--4, 7--12}.
• Figure 5: One stage of hidden surface removal front to back. The stages illustrated are repeated for each object in the stack or until the update shape is empty, starting with an update shape which covers the whole update region (a simple rectangle, here).