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**1 - 2**of**2**### Converting CSG models into Meshed B-Rep Abstract Models Using Euler Operators and Propagation Based Marching Cubes

"... The purpose of this work is to define a new algorithm for converting a CSG repre-sentation into a B-Rep representation. Usually this conversion is done determining the union, intersection or difference from two B-Rep represented solids. Due to the lack of explicit representation of surface boundarie ..."

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The purpose of this work is to define a new algorithm for converting a CSG repre-sentation into a B-Rep representation. Usually this conversion is done determining the union, intersection or difference from two B-Rep represented solids. Due to the lack of explicit representation of surface boundaries, CSG models must be converted into B-Rep solid models when a description based on polygonal mesh is required. A potential solution is to convert a CSG model into a voxel based volume rep-resentation and then construct a B-Rep solid model. This method is called CSG voxelization, conceptually it is a set membership classification problem with respect to the CSG object for all sampling points in a volume space. Marching cubes al-gorithms create a simple mesh that is enough for visualization purposes. However, when engineering processes are involved, a solid model is necessary. A solid ensures that all triangles in the mesh are consistently oriented and define a closed surface. It is proposed in this work an algorithm for converting CSG models into triangulated solid models through a propagation based marching cubes algorithm. Three main new concepts are used in the algorithm: open boundary, B–Rep/CSG Voxelization mapping and constructive triangulation of active cells. The triangles supplied by the marching cubes algorithm need not be coherently oriented, the algorithm itself finds the correct orientation for the supplied triangles. The proposed algorithm re-stricts the exploration to the space occupied by the solid’s boundary. Differently from normal marching cubes algorithms that explore the complete sampled space. Preprint submitted to J. of the Braz. Soc. of Mech. Sc. and Eng. 13 December 2006 Key words: Solid model, marching cubes algorithm, triangular meshes. 1

### Converting CSG models into Meshed B-Rep Models Using Euler Operators and Propagation Based Marching Cubes

"... The purpose of this work is to define a new algorithm for converting a CSG representation into a B-Rep representation. Usually this conversion is done determining the union, intersection or difference from two B-Rep represented solids. Due to the lack of explicit representation of surface boundaries ..."

Abstract
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The purpose of this work is to define a new algorithm for converting a CSG representation into a B-Rep representation. Usually this conversion is done determining the union, intersection or difference from two B-Rep represented solids. Due to the lack of explicit representation of surface boundaries, CSG models must be converted into B-Rep solid models when a description based on polygonal mesh is required. A potential solution is to convert a CSG model into a voxel based volume representation and then construct a B-Rep solid model. This method is called CSG voxelization, conceptually it is a set membership classification problem with respect to the CSG object for all sampling points in a volume space. Marching cubes algorithms create a simple mesh that is enough for visualization purposes. However, when engineering processes are involved, a solid model is necessary. A solid ensures that all triangles in the mesh are consistently oriented and define a closed surface. It is proposed in this work an algorithm for converting CSG models into triangulated solid models through propagation based marching cubes algorithm. Three main new concepts are used in the algorithm: open boundary, B-Rep/CSG Voxelization mapping and constructive triangulation of active cells. The triangles supplied by the marching cubes algorithm need not be coherently oriented; the algorithm itself finds the correct orientation for the supplied triangles. The proposed algorithm restricts the exploration to the space occupied by the solid's boundary. Differently from normal marching cubes algorithms that explore the complete sampled space.