Parametric curves on meshes

In this paper, we propose a method for creating parametric curves on triangular meshes. A curve on a mesh is frequently used as a boundary curve of a specific region of a mesh in mesh modeling and applications such as texture mapping, remeshing or morphing. Although the curve defined in this paper is a piecewise linear approximation of a strict parametric curve, it is guaranteed that such a curve is just on a mesh. The basic idea is creating a curve on a spherical parameterization instead of direct definition on a mesh. The computation of this curve is done by using only the control points on a spherical parameterization which does not depend on the number of vertices in a mesh. This enables interactive creation/modification of curves even for dense meshes.