# Offset Triangular Mesh Using the Multiple Normal Vectors of a Vertex

Topics: Orthogonality, Force, Surfaces Pages: 4 (1225 words) Published: November 14, 2011
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Offset Triangular Mesh Using the Multiple Normal Vectors of a Vertex Su-Jin Kim1, Dong-Yoon Lee2 and Min-Yang Yang3
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Korea Advanced Institute of Science and Technology, sujinkim@kaist.ac.kr 2 Korea Advanced Institute of Science and Technology, yunny@kaist.ac.kr 3 Korea Advanced Institute of Science and Technology, myyang@kaist.ac.kr

ABSTRACT This paper introduces and illustrates the results of a new method for offsetting triangular mesh by moving all vertices along the multiple normal vectors of a vertex. The multiple normal vectors of a vertex are set the same as the normal vectors of the faces surrounding the vertex, while the two vectors with the smallest difference are joined repeatedly until the difference is smaller than allowance. Offsetting with the multiple normal vectors of a vertex does not create a gap or overlap at the smooth edges, thereby making the mesh size uniform and the computation time short. In addition, this offsetting method is accurate at the sharp edges because the vertices are moved to the normal directions of faces and joined by the blend surface. The method is also useful for rapid prototyping and tool path generation if the triangular mesh is tessellated part of the solid models with curved surfaces and sharp edges. The suggested method and previous methods are implemented on a PC using C++ and illustrated using an OpenGL library. Keywords: Offset, Triangular mesh, Multiple normal vectors

1. INTRODUCTION Offsets are widely used in tool path generation for numerical control machining, rapid prototyping, hollow or shelled model generation, and access space representations in robotics. In a numerical control machining area, 2D and 3D offsets are particularly important and useful for gouge-free and collision-free tool paths [1,2]. In 2D milling, a contour is offset by the size of the cutter radius, and invalid loops are removed for a gouge-free tool path [1]. In 3D milling, a gouge can be removed by computing the cutter...