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fix doc warnings
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@ -57,14 +57,14 @@ A vertex is created for each grid edge with a sign change, i.e., where the edge
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More specifically, the vertex position is computed via linear interpolation of
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More specifically, the vertex position is computed via linear interpolation of
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the scalar field values evaluated at the cell corners forming the edge.
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the scalar field values evaluated at the cell corners forming the edge.
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These vertices are connected to form triangles within the cell, depending on the configuration
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These vertices are connected to form triangles within the cell, depending on the configuration
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of signs at the cell corners. Figure \ref Fig_IsosurfacingMCCases illustrates the configurations in 2D.
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of signs at the cell corners. Figure \cgalFigureRef{IsosurfacingMCCases} illustrates the configurations in 2D.
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In 3D, there is no less than 33 cases (not shown) \cgalCite{cgal:c-mcctci-95}.
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In 3D, there is no less than 33 cases (not shown) \cgalCite{cgal:c-mcctci-95}.
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\cgalFigureAnchor{Fig_IsosurfacingMCCases}
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\cgalFigureAnchor{IsosurfacingMCCases}
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<center>
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<center>
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<img src="MC_cases.png" style="max-width:70%;"/>
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<img src="MC_cases.png" style="max-width:70%;"/>
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</center>
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</center>
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\cgalFigureCaptionBegin{Fig_IsosurfacingMCCases}
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\cgalFigureCaptionBegin{IsosurfacingMCCases}
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Examples of some configurations for 2D Marching Cubes.
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Examples of some configurations for 2D Marching Cubes.
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\cgalFigureCaptionEnd
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\cgalFigureCaptionEnd
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@ -84,7 +84,7 @@ MC often generates more triangles, and more skinny triangles with small or large
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depicting the mesh edges in black in addition to the shaded facets.
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depicting the mesh edges in black in addition to the shaded facets.
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MC does not preserve the sharp features present in the isovalue of the input scalar field
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MC does not preserve the sharp features present in the isovalue of the input scalar field
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(see Figure \ref Fig_IsosurfacingMCDC).
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(see Figure \cgalFigureRef{IsosurfacingMCDC}).
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\subsection SubSecTMC Topologically Correct Marching Cubes (TMC)
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\subsection SubSecTMC Topologically Correct Marching Cubes (TMC)
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@ -97,11 +97,11 @@ To achieve this, the algorithm can insert additional vertices within cells.
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Furthermore, the mesh is guaranteed to be 2-manifold and watertight, as long as the isosurface
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Furthermore, the mesh is guaranteed to be 2-manifold and watertight, as long as the isosurface
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does not intersect the domain boundaries. [and the input is 2-manifold?]
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does not intersect the domain boundaries. [and the input is 2-manifold?]
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\cgalFigureAnchor{Fig_IsosurfacingMCTMC}
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\cgalFigureAnchor{IsosurfacingMCTMC}
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<center>
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<center>
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<img src="MC_TMC.png" style="max-width:70%;"/>
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<img src="MC_TMC.png" style="max-width:70%;"/>
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</center>
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</center>
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\cgalFigureCaptionBegin{Fig_IsosurfacingMCTMC}
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\cgalFigureCaptionBegin{IsosurfacingMCTMC}
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MC vs TMC [todo]
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MC vs TMC [todo]
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\cgalFigureCaptionEnd
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\cgalFigureCaptionEnd
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@ -114,11 +114,11 @@ of the incident cells. For a uniform hexahedral grid, this results into a quadri
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On the other hand it generates fewer faces and high quality faces than Marching Cubes, in general.
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On the other hand it generates fewer faces and high quality faces than Marching Cubes, in general.
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Finally, its main advantage over Marching Cubes is its ability to recover sharp creases and corners.
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Finally, its main advantage over Marching Cubes is its ability to recover sharp creases and corners.
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\cgalFigureAnchor{Fig_IsosurfacingMCDC}
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\cgalFigureAnchor{IsosurfacingMCDC}
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<center>
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<center>
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<img src="MC_DC.png" style="max-width:70%;"/>
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<img src="MC_DC.png" style="max-width:70%;"/>
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</center>
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</center>
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\cgalFigureCaptionBegin{Fig_IsosurfacingMCDC}
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\cgalFigureCaptionBegin{IsosurfacingMCDC}
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Comparison between a mesh of a CSG shape generated by Marching Cubes (left) and %Dual Contouring (right).
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Comparison between a mesh of a CSG shape generated by Marching Cubes (left) and %Dual Contouring (right).
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\cgalFigureCaptionEnd
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\cgalFigureCaptionEnd
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@ -153,13 +153,13 @@ of the output surface mesh.
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(** not guaranteed)
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(** not guaranteed)
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Note that the output mesh has boundaries when the isosurface intersects the domain boundaries,
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Note that the output mesh has boundaries when the isosurface intersects the domain boundaries,
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regardless of the method (see Figure \ref Fig_IsosurfacingOpen).
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regardless of the method (see Figure \cgalFigureRef{IsosurfacingOpen}).
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\cgalFigureAnchor{Fig_IsosurfacingOpen}
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\cgalFigureAnchor{IsosurfacingOpen}
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<center>
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<center>
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<img src="MC_DC_open.png" style="max-width:70%;"/>
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<img src="MC_DC_open.png" style="max-width:70%;"/>
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</center>
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</center>
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\cgalFigureCaptionBegin{Fig_IsosurfacingOpen}
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\cgalFigureCaptionBegin{IsosurfacingOpen}
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Output meshes can have boundaries when the isosurface intersects the domain boundary:
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Output meshes can have boundaries when the isosurface intersects the domain boundary:
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outputs of Marching Cubes (left) and %Dual Contouring (right) for an implicit sphere
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outputs of Marching Cubes (left) and %Dual Contouring (right) for an implicit sphere
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of radius 1.1 and a domain of size 2x2x2, both centered at the origin.
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of radius 1.1 and a domain of size 2x2x2, both centered at the origin.
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@ -240,11 +240,10 @@ Both these domain models possess template parameters to allow the user to custom
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Due to their cell-based nature, the isosurfacing algorithms are well-suited for parallel execution.
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Due to their cell-based nature, the isosurfacing algorithms are well-suited for parallel execution.
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\cgalFigureAnchor{fig_IsosurfacingPerf}
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\cgalFigureAnchor{IsosurfacingPerf}
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<center>
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<center>
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<img src="MC_DC_performance.png" style="max-width:70%;"/>
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<img src="MC_DC_performance.png" style="max-width:70%;"/>
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</center>
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</center>
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\cgalFigureCaptionEnd
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\section SecIsosurfacingExamples Examples
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\section SecIsosurfacingExamples Examples
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@ -268,11 +267,11 @@ that enable triangulating (or not) the output, and to constrain the vertex place
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\cgalExample{Isosurfacing_3/dual_contouring.cpp}
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\cgalExample{Isosurfacing_3/dual_contouring.cpp}
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\cgalFigureAnchor{Fig_IsosurfacingDC}
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\cgalFigureAnchor{IsosurfacingDC}
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<center>
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<center>
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<img src="DC.png" style="max-width:70%;"/>
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<img src="DC.png" style="max-width:70%;"/>
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</center>
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</center>
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\cgalFigureCaptionBegin{Fig_IsosurfacingDC}
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\cgalFigureCaptionBegin{IsosurfacingDC}
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Results of the %Dual Contouring algorithm: untriangulated (left column) or triangulated (right column),
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Results of the %Dual Contouring algorithm: untriangulated (left column) or triangulated (right column),
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unconstrained placement (top row) or constrained placement (bottom row).
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unconstrained placement (top row) or constrained placement (bottom row).
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\cgalFigureCaptionEnd
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\cgalFigureCaptionEnd
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@ -298,11 +297,11 @@ from this voxel data.
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\cgalExample{Isosurfacing_3/contouring_inrimage.cpp}
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\cgalExample{Isosurfacing_3/contouring_inrimage.cpp}
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\cgalFigureAnchor{Fig_IsosurfacingDC}
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\cgalFigureAnchor{IsosurfacingDCEx}
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<center>
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<center>
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<img src="isosurfacing_inrimage.png" style="max-width:70%;"/>
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<img src="isosurfacing_inrimage.png" style="max-width:70%;"/>
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</center>
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</center>
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\cgalFigureCaptionBegin{Fig_IsosurfacingDC}
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\cgalFigureCaptionBegin{IsosurfacingDCEx}
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Results of the Topologically Correct Marching Cubes algorithm for different isovalues (1, 2, and 2.9)
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Results of the Topologically Correct Marching Cubes algorithm for different isovalues (1, 2, and 2.9)
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on the skull model.
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on the skull model.
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\cgalFigureCaptionEnd
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\cgalFigureCaptionEnd
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