Research On The Offsetting For Triangular Meshes And Curves On Them

Offset is an important operation in CAD/CAM, and had been widely used in various applications, such as numerical control machining, solid modeling, robotics etc. Lots of effective offsetting methods for single curve/surface have been proposed, but the study for compound curve/surface offsetting has just begun. For the triangular mesh is widely used in industry and computer graphics systems, this thesis focuses on the offset methods for triangular meshes and curves on them.Round offset for curves on triangular mesh has more applications than sharp offset, but there is no effective round offset method now. This thesis proposes a new round offset method. Firstly, compute offsetting trochoids for all ends of original curves, divide the original curves into more new line segments according to the offsetting trochoids so that every offsetting curve for new line segments is in a triangular face; Then, connect the gaps generated during offsetting using approximate arc segments, delete local invalid loops utilizing interference continuity; Finally, extend the sweep line method of polygonal chains intersection, delete global invalid loops by finding global intersections.The present offset methods for triangular mesh either use sharp offset to avoid gaps and local interferences or make use of feathers of 3-axis machining to delete interference in 2D CL-surface. A new offset method for triangular mesh is present in this thesis, using multiple normal vectors of a vertex to deal with gaps and continuity to delete local invalid areas. The characteristic of this method are using properties of vertexes and edges to connect gaps roundly and utilizing interference continuity to improve the efficiency of deleting local invalid areas.This thesis realized the new methods in the environment of VC++ 6.0 and ACIS. Experiments show that the proposed methods are effective; especially that deleting for local invalid areas is efficiently.