Offset of curves on tessellated surfaces

Abstract

Geodesic offset of curves on surfaces is an important and useful tool of computer aided design for applications such as generation of tool paths for NC machining and simulation of fibre path on tool surfaces in composites manufacturing. For many industrial and graphic applications, tessellation representation is used for curves and surfaces because of its simplicity in representation and for simpler and faster geometric operations. The paper presents an algorithm for computing offset of curves on tessellated surfaces. A curve on tessellation (COT) is represented as a sequence of 3D points, with each line segment of every two consecutive points lying exactly on the tessellation. With an incremental approach of the algorithm to compute offset COT, the final offset curve position is obtained through several intermediate offset curve positions. Each offset curve position is obtained by offsetting all the points of COT along the tessellation in such a way that all the line segments gets offset exactly along the faces of tessellation in which the line segments are contained. The algorithm, based entirely on tessellation representation, completely eliminates the formation of local self-intersections. Global self-intersections if any, are detected and corrected explicitly. Offset of both open and closed tessellated curves, either in a plane or on a tessellated surface, can be generated using the proposed approach. The computation of offset COT is very accurate within the tessellation tolerance.