surfacewhere

Surfacewhere is a term used in computational geometry and computer graphics to describe a framework for locating and characterizing locations on one or more surfaces where a specified condition holds. It typically involves determining the locus of points that satisfy a set of surface equations or constraints, such as intersections of surfaces, tangency, or thresholded values of scalar fields defined on a surface.

In practice, surfacewhere can operate on implicit representations, parametric surfaces, or polygon meshes. It combines numerical methods such as root-finding and optimization with geometric predicates to identify candidate points and refine their positions. Depending on the implementation, it may also compute associated features like normals, curvatures, and contact directions to support further processing.

Applications include computer-aided design, visual effects, collision detection, mesh repair, and shape analysis. The concept helps automate the discovery of surface interactions, guide boolean operations, and extract meaningful features from complex models.

Origin and terminology: Surfacewhere is not a standardized term in core literature but appears as a descriptive label in academic discussions and software documentation. Its precise meaning is context dependent, ranging from locating surface intersections to finding regions where a scalar field on a surface meets a threshold. The term is sometimes used interchangeably with related notions such as isosurfaces, level sets, and contact curves, though with different emphases across tools.

See also: isosurface, level set, surface intersection, contact geometry.