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Marching Cubes: A High Resolution Surface Construction Algorithm
Dr. Scott Schaefer
Polygon Models
AdvantagesAdvantagesExplicit connectivity informationExplicit connectivity informationEasy to renderEasy to render(Relatively) small storage(Relatively) small storage
DisadvantagesDisadvantagesTopology changes difficultTopology changes difficultInside/Outside test hardInside/Outside test hard
Implicit Representations of Shape
Shape described by solution to Shape described by solution to ff((xx)=)=cc9),( 22 −+= yxyxf
Implicit Representations of Shape
Shape described by solution to Shape described by solution to ff((xx)=)=cc9),( 22 −+= yxyxf
Implicit Representations of Shape
Shape described by solution to Shape described by solution to ff((xx)=)=cc9),( 22 −+= yxyxf
- --
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Implicit Representations of Shape
Shape described by solution to Shape described by solution to ff((xx)=)=cc9),( 22 −+= yxyxf
- --
-----
++ +
+
+++
+
Advantages
No topology to maintainNo topology to maintainAlways defines a closed surface!Always defines a closed surface!Inside/Outside testInside/Outside testCSG operationsCSG operations
Advantages
No topology to maintainNo topology to maintainAlways defines a closed surface!Always defines a closed surface!Inside/Outside testInside/Outside testCSG operationsCSG operations
- --
-----
++ +
+
+++
+
Advantages
No topology to maintainNo topology to maintainAlways defines a closed surface!Always defines a closed surface!Inside/Outside testInside/Outside testCSG operationsCSG operations
Advantages
No topology to maintainNo topology to maintainAlways defines a closed surface!Always defines a closed surface!Inside/Outside testInside/Outside testCSG operationsCSG operations
UnionUnion
Advantages
No topology to maintainNo topology to maintainAlways defines a closed surface!Always defines a closed surface!Inside/Outside testInside/Outside testCSG operationsCSG operations
UnionUnion
Advantages
No topology to maintainNo topology to maintainAlways defines a closed surface!Always defines a closed surface!Inside/Outside testInside/Outside testCSG operationsCSG operations
UnionUnion
--
--
-+
+
++
+
+
Advantages
No topology to maintainNo topology to maintainAlways defines a closed surface!Always defines a closed surface!Inside/Outside testInside/Outside testCSG operationsCSG operations
UnionUnion--
--
-+
+
++
+
+
Advantages
No topology to maintainNo topology to maintainAlways defines a closed surface!Always defines a closed surface!Inside/Outside testInside/Outside testCSG operationsCSG operations
UnionUnion
--
--
-+
+
++
+
+
--
--
-+
+
++
+
+
Advantages
No topology to maintainNo topology to maintainAlways defines a closed surface!Always defines a closed surface!Inside/Outside testInside/Outside testCSG operationsCSG operations
UnionUnion
--
--
-++
++
+
+
Advantages
No topology to maintainNo topology to maintainAlways defines a closed surface!Always defines a closed surface!Inside/Outside testInside/Outside testCSG operationsCSG operations
UnionUnionIntersectionIntersection
--
--
-+
+
++
+
+
--
--
-+
+
++
+
+
Advantages
No topology to maintainNo topology to maintainAlways defines a closed surface!Always defines a closed surface!Inside/Outside testInside/Outside testCSG operationsCSG operations
UnionUnionIntersectionIntersection - -
+ +
++
Advantages
No topology to maintainNo topology to maintainAlways defines a closed surface!Always defines a closed surface!Inside/Outside testInside/Outside testCSG operationsCSG operations
UnionUnionIntersectionIntersectionSubtractionSubtraction
--
--
-+
+
++
+
+
--
--
-+
+
++
+
+
Advantages
No topology to maintainNo topology to maintainAlways defines a closed surface!Always defines a closed surface!Inside/Outside testInside/Outside testCSG operationsCSG operations
UnionUnionIntersectionIntersectionSubtractionSubtraction
--
--
-+
+
++
+
+--
-
-
-+
+ +
+ ++
Advantages
No topology to maintainNo topology to maintainAlways defines a closed surface!Always defines a closed surface!Inside/Outside testInside/Outside testCSG operationsCSG operations
UnionUnionIntersectionIntersectionSubtractionSubtraction
-- -
+
+
+
+
+
Advantages
No topology to maintainNo topology to maintainAlways defines a closed surface!Always defines a closed surface!Inside/Outside testInside/Outside testCSG operationsCSG operations
UnionUnionIntersectionIntersectionSubtractionSubtraction
Disadvantages
Hard 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 difficult
Non-Analytic Implicit Functions
Sample functions over gridsSample functions over grids
Non-Analytic Implicit Functions
Sample functions over gridsSample functions over grids
Data Sources
Data Sources
Data Sources
Data Sources
Data Sources
Data Sources
2D Surface Reconstruction
2D Surface Reconstruction
2D Surface Reconstruction
2D Surface Reconstruction
2D Surface Reconstruction
3D Surface Reconstruction
3D Surface Reconstruction
Fun Examples
Fun Examples
Fun Examples
Fun Examples
![GPU-accelerated data expansion for the Marching Cubes ... · Extract iso-surface via Marching Cubes Scalar field is sampled over 3D grid Marching Cubes [Lorensen87] —Marches through](https://img.pdfslide.us/doc/110x75/5f59a4a397733378820cfae2/gpu-accelerated-data-expansion-for-the-marching-cubes-extract-iso-surface-via.jpg)
