Volume Representation by Gradient and Distance Fields - Spring ...

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CSG Operations with Voxelized Solids3.4 Special CSG Operationmay in certain cases significantly change shape of the object, but according to sampling theory,there is no other way how to solve this problem except of local or global increase of the gridresolution (Figure 3.9).Figure 3.9: The dependence of the object shape on the resolutionThe cube-sphere object. Operations from top: simple, advanced. Resolution from left: 32 3 , 64 3 ,128 3 , 256 3 .3.4 Special CSG OperationThe advanced CSG operation successfully solves voxelization of representable solids. However,sometimes we want to voxelize also objects which are beyond the limits of representability.In this case artifacts may appear (Figure 3.10a). With the special CSG operation we proposeheuristics improving such models by removing the most disturbing artifacts.An example of such problematic configuration is shown in Figure 3.11. We have two objectsA, B and we want to represent their union. If they are apart enough far, their surfaces are separated.If they intersect their surfaces are joined. It is clear that, when voxelized, there cannotexist a continuous transition between these two situations, because a thin gap or a thin bridgebetween the objects are not representable. This problem can be suppressed by either local orglobal increase of the grid resolution, but cannot be removed completely. Fortunately, the criticaldistance of two objects is in a narrow range of values—the advanced CSG operation gives correctresults outside of this critical range.The special CSG operation is an extension of the advanced CSG operation. Its goal is to detectregions, where the aforementioned problems can occur. It is based on the following heuristics:40
CSG Operations with Voxelized Solids3.4 Special CSG Operation(a)(b)Figure 3.10: Problems with representability of almost touching surfaces(a) advanced, (b) special CSG operation. Model: sphere minus cylinder.ABAB(a)(b)Figure 3.11: Problems with representabilityA smooth transition between configurations (a) and (b) is not possible in discrete grids.41
Page 1 and 2: FACULTY OF MATHEMATICS, PHYSICS AND
Page 3 and 4: Statutory Declaration:I do solemnly
Page 6 and 7: CONTENTSCONTENTS4.4.2 Rectification
Page 8 and 9: LIST OF FIGURESLIST OF FIGURES3.10
Page 10 and 11: Introduction1.1 Volume Graphics and
Page 12 and 13: Introduction1.3 Surface Normal Esti
Page 14 and 15: Introduction1.4 Object Representabi
Page 16 and 17: Introduction1.4 Object Representabi
Page 18 and 19: Representation of Volume Data Sets2
Page 34 and 35: Chapter 3CSG Operations with Voxeli
Page 36 and 37: CSG Operations with Voxelized Solid
Page 40 and 41: gCSG Operations with Voxelized Soli
Page 48 and 49: Sharp Details Correction Method4.1
Page 68 and 69: Implementation5.2 The vxtRL Library
Page 70 and 71: Implementation5.2 The vxtRL Library
Page 72 and 73: Bibliography[1] A. Kaufman, D. Cohe

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