Linear Map:

A mapping of a triangulated surface into space is linear if it maps each face into a plane triangle and each edge into a straight line segment.

This is what we naturally think of as a triangulated surface in space, or a polyhedron: all the faces and edges are flat, and there are no curved portions of the surface.

More technically, a map is linear if every point of a simplex is mapped as a convex linear combination of the images of its vertices.

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8/12/94 dpvc@geom.umn.edu -- The Geometry Center