persurfaces

Persurfaces is a term found in some corners of geometric modeling and computer graphics. It is not a standardized concept, and definitions vary between authors. Broadly, persurfaces refer to surfaces designed or identified so that certain properties persist under perspective transformations or across different viewpoints.

In projective differential geometry, a persurface is a regular surface for which a chosen set of projective invariants remains unchanged under a family of perspective maps. In this interpretation, invariants might involve curvature-related quantities or the behavior of normals and tangent planes under projection, emphasizing persistence of geometric features through view changes.

In computer graphics, the term sometimes describes surfaces whose projected appearance remains stable when the camera moves within a specified range. This includes robustness of silhouettes, contour lines, and shading cues, aiming to reduce distortion and aliasing in rendered views while maintaining recognizable shape.

Construction and mathematics, when discussed, generally involve parameterizations X(u,v) of the surface and a family of perspective projections P_theta. A persurface satisfies invariance conditions for a chosen invariant I under theta in a given range, where I could denote a projected curvature sign, silhouette indicator, or another feature preserved by projection. In practice, designers may formulate an optimization problem to minimize the variance of projected invariants subject to smoothness constraints on the surface.

Applications include robust view-dependent modeling, architectural visualization, and CAD workflows where consistent visual communication across viewpoints is important. Limitations include potential trade-offs between invariant preservation and exact geometric fidelity, as well as increased computational cost and design complexity.

See also: surfaces, perspective projection, projective geometry, differential geometry, visual invariants.