Methods, systems, and apparatus for computer aided design of physical structures include: producing a quad parameterization computer model (including quad parameter domains) of a polygon mesh, where quad parameter domain(s) adjacent to a boundary curve interpolate the boundary curve; and forming a computer model of a three dimensional object by constructing locally refinable surface representation(s) from the quad parameterization computer model, refining a boundary of the locally refinable surface representation(s) to approximate the boundary curve within a first tolerance value set in accordance with a smallest dimension representable by a geometry modeling kernel, freezing control points of the locally refinable surface representation(s) at the boundary, and modifying remaining interior portions of the locally refinable surface representation(s) to approximate the polygon mesh within a second tolerance value that is at least an order of magnitude larger than the first tolerance value.