normalheight

Normalheight is a term used in geometry and computer graphics to denote the height of a point above a reference plane measured along the plane’s normal direction. Formally, if a plane is defined by a fixed point p0 and a unit normal vector n, and p is any point in space, the normalheight h is the signed distance h = (p - p0) · n. The sign indicates which side of the plane the point lies on, while the magnitude gives the distance along the normal from the plane to the point. Normalheight is distinct from vertical height when the reference plane is not horizontal or when the space is oriented differently from gravity.

Usage and interpretation can vary by field. In 3D modeling and computer graphics, normalheight helps describe protrusions or recesses relative to a reference surface, or serves as a basis for directional shading and texturing effects that follow the plane’s orientation. In GIS and terrain analysis, it can represent elevation relative to a local datum plane, useful for analyses that require measurements perpendicular to a surface rather than along a global vertical axis. In manufacturing and quality control, normalheight can quantify deviations from a reference plane in a direction normal to that plane during inspection.

Practical considerations include the choice of the reference plane, the orientation of its normal, and the units involved. Numerical precision and the stability of the dot product are also important when dealing with nearly parallel planes or very small angle differences.

See also: signed distance, plane equation, projection (vector), orthogonal projection.