Marching Cubes: A High Resolution Surface Construction AlgorithmDr. Scott SchaeferPolygon ModelsAdvantagesAdvantagesExplicit connectivity informationExplicit connectivity informationEasy to renderEasy to render(Relatively) small storage(Relatively) small storageDisadvantagesDisadvantagesTopology changes difficultTopology changes difficultInside/Outside test hardInside/Outside test hardImplicit Representations of ShapeShape described by solution to Shape described by solution to ff((xx)=)=cc9),(22−+= yxyxfImplicit Representations of ShapeShape described by solution to Shape described by solution to ff((xx)=)=cc9),(22−+= yxyxfImplicit Representations of ShapeShape described by solution to Shape described by solution to ff((xx)=)=cc9),(22−+= yxyxf--------Implicit Representations of ShapeShape described by solution to Shape described by solution to ff((xx)=)=cc9),(22−+= yxyxf--------++++++++AdvantagesNo topology to maintainNo topology to maintainAlways defines a closed surface!Always defines a closed surface!Inside/Outside testInside/Outside testCSG operationsCSG operationsAdvantagesNo topology to maintainNo topology to maintainAlways defines a closed surface!Always defines a closed surface!Inside/Outside testInside/Outside testCSG operationsCSG operations--------++++++++AdvantagesNo topology to maintainNo topology to maintainAlways defines a closed surface!Always defines a closed surface!Inside/Outside testInside/Outside testCSG operationsCSG operationsAdvantagesNo topology to maintainNo topology to maintainAlways defines a closed surface!Always defines a closed surface!Inside/Outside testInside/Outside testCSG operationsCSG operationsUnionUnionAdvantagesNo topology to maintainNo topology to maintainAlways defines a closed surface!Always defines a closed surface!Inside/Outside testInside/Outside testCSG operationsCSG operationsUnionUnionAdvantagesNo topology to maintainNo topology to maintainAlways defines a closed surface!Always defines a closed surface!Inside/Outside testInside/Outside testCSG operationsCSG operationsUnionUnion-----++++++AdvantagesNo topology to maintainNo topology to maintainAlways defines a closed surface!Always defines a closed surface!Inside/Outside testInside/Outside testCSG operationsCSG operationsUnionUnion-----++++++AdvantagesNo topology to maintainNo topology to maintainAlways defines a closed surface!Always defines a closed surface!Inside/Outside testInside/Outside testCSG operationsCSG operationsUnionUnion-----++++++-----++++++AdvantagesNo topology to maintainNo topology to maintainAlways defines a closed surface!Always defines a closed surface!Inside/Outside testInside/Outside testCSG operationsCSG operationsUnionUnion-----++++++AdvantagesNo topology to maintainNo topology to maintainAlways defines a closed surface!Always defines a closed surface!Inside/Outside testInside/Outside testCSG operationsCSG operationsUnionUnionIntersectionIntersection-----++++++-----++++++AdvantagesNo topology to maintainNo topology to maintainAlways defines a closed surface!Always defines a closed surface!Inside/Outside testInside/Outside testCSG operationsCSG operationsUnionUnionIntersectionIntersection--++++AdvantagesNo topology to maintainNo topology to maintainAlways defines a closed surface!Always defines a closed surface!Inside/Outside testInside/Outside testCSG operationsCSG operationsUnionUnionIntersectionIntersectionSubtractionSubtraction-----++++++-----++++++AdvantagesNo topology to maintainNo topology to maintainAlways defines a closed surface!Always defines a closed surface!Inside/Outside testInside/Outside testCSG operationsCSG operationsUnionUnionIntersectionIntersectionSubtractionSubtraction-----++++++-----++++++AdvantagesNo topology to maintainNo topology to maintainAlways defines a closed surface!Always defines a closed surface!Inside/Outside testInside/Outside testCSG operationsCSG operationsUnionUnionIntersectionIntersectionSubtractionSubtraction---+++++AdvantagesNo topology to maintainNo topology to maintainAlways defines a closed surface!Always defines a closed surface!Inside/Outside testInside/Outside testCSG operationsCSG operationsUnionUnionIntersectionIntersectionSubtractionSubtractionDisadvantagesHard to render Hard to render --no polygonsno polygonsCreating polygons amounts to root finding Creating polygons amounts to root finding Arbitrary shapes hard to represent as an Arbitrary shapes hard to represent as an analytic functionanalytic functionCertain operations (like simplification) can Certain operations (like simplification) can be difficultbe difficultNon-Analytic Implicit FunctionsSample functions over gridsSample functions over gridsNon-Analytic Implicit FunctionsSample functions over gridsSample functions over gridsData SourcesData SourcesData SourcesData SourcesData SourcesData Sources2D Surface Reconstruction2D Surface Reconstruction2D Surface Reconstruction2D Surface Reconstruction2D Surface Reconstruction3D Surface Reconstruction3D Surface ReconstructionFun ExamplesFun ExamplesFun ExamplesFun
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