Abstract: Methods for defining smooth and continuous coordinate systems in a volume comprised of a lattice structure of guide columns derived from arbitrarily modeled surface topologies involving polygons, nurbs, linear segments, and subdivision surfaces. Applications of these techniques in computer graphics and computer animation include: (1) the definition of pseudo-coordinate systems for use in creating geometry which must grow from said surface (2) the creation of a highly stable coordinate system involving guide columns in which Cartesian physical simulations may be carried out and rendered as well as deformed and rerendered if desired.