EnvelopeLayer

EnvelopeLayer is a data structure used in vector graphics and CAD applications to represent the envelope of a family of curves or shapes. The envelope is the locus where a member of the family is tangent to the envelope; the EnvelopeLayer stores this boundary as a separate, reusable layer for rendering, hit-testing, or analysis.

Construction and interpretation of an envelope can follow analytic or approximate methods. For analytic families defined by a constraint F(x,y,t)=0, the envelope is obtained by solving F(x,y,t)=0 together with ∂F/∂t=0 to eliminate t. In practice, many implementations approximate the envelope from a finite set of shapes by computing the outer boundary, performing a union, forming a convex hull, or sampling the family followed by curve fitting. The EnvelopeLayer can also support inner envelopes or multiple nested envelopes representing tangency with subfamilies.

Representation and operations: The EnvelopeLayer stores a path or polygon describing the envelope boundary. It supports operations such as union with other envelopes, offsetting, smoothing, and intersection tests. It also maintains metadata such as whether the boundary is open or closed, and whether it is filled or stroked. In editable systems, the envelope can be refined by adjusting control points or re-computing from the underlying shape set.

Applications: Used for fast hit-testing and culling, collision detection, outline rendering, shadow boundaries, and level-of-detail computation. It can also serve as a backing shape for selection tools in editors and as a concise summary of geometric complexity within a scene.

See also: envelope, boundary representation, convex hull, Minkowski sum, offset curve.