Editing Isosurface (section)

== Implementation algorithms ==

=== Marching cubes ===
The [[marching cubes]] algorithm was first published in the 1987 SIGGRAPH proceedings by Lorensen and Cline,<ref>William E. Lorensen, Harvey E. Cline: [http://www.cs.sfu.ca/~haoz/teaching/cmpt464/references/87_Lorensen_MarchingCubes.pdf Marching Cubes: A high resolution 3D surface construction algorithm.] In: Computer Graphics, Vol. 21, Nr. 4, July 1987</ref> and it creates a surface by intersecting the edges of a [[Data (computing)|data]] volume grid with the volume contour. Where the surface intersects the edge the algorithm creates a vertex. By using a table of different triangles depending on different patterns of edge intersections the algorithm can create a surface. This algorithm has solutions for implementation both on the CPU and on the GPU.

=== Asymptotic decider ===
The [[asymptotic decider]] algorithm was developed as an extension to [[marching cubes]] in order to resolve the possibility of ambiguity in it.

=== Marching tetrahedra ===
The [[marching tetrahedra]] algorithm was developed as an extension to [[marching cubes]] in order to solve an ambiguity in that algorithm and to create higher quality output surface.

=== Surface nets ===
The Surface Nets algorithm places an intersecting vertex in the middle of a volume voxel instead of at the edges, leading to a smoother output surface.

=== Dual contouring ===
The [[dual contouring]] algorithm was first published in the 2002 SIGGRAPH proceedings by Ju and Losasso,<ref>Tao Ju, Frank Losasso, Scott Schaefer, Joe Warren: [http://www.frankpetterson.com/publications/dualcontour/dualcontour.pdf Dual Contouring of Hermite Data.] {{Webarchive|url=https://web.archive.org/web/20170918164804/http://www.frankpetterson.com/publications/dualcontour/dualcontour.pdf |date=2017-09-18 }} In: ACM Transactions on Graphics, Volume 21 Issue 3, July 2002</ref> developed as an extension to both [[surface nets]] and marching cubes. It retains a [[Dual polyhedron|dual]] vertex within the [[voxel]] but no longer at the center. Dual contouring leverages the position and [[normal (geometry)|normal]] of where the surface crosses the edges of a voxel to interpolate the position of the dual vertex within the voxel. This has the benefit of retaining sharp or smooth surfaces where surface nets often look blocky or incorrectly beveled.<ref>{{Cite web|url=https://0fps.net/2012/07/12/smooth-voxel-terrain-part-2/|title = Smooth Voxel Terrain (Part 2)|date = 12 July 2012}}</ref> Dual contouring often uses surface generation that leverages [[octree]]s as an optimization to adapt the number of triangles in output to the complexity of the surface.

=== Manifold dual contouring ===

Manifold [[dual contouring]] includes an analysis of the octree neighborhood to maintain continuity of the manifold surface <ref>{{cite web|author=Scott Schaefer, Tao Ju, Joe Warren|year=2006|title=Manifold Dual Contouring|url=http://faculty.cs.tamu.edu/schaefer/research/dualsimp_tvcg.pdf}}</ref><ref>{{cite AV media|date=30 Dec 2015|title=Manifold Dual Contouring|author=Lin X|url=https://www.youtube.com/watch?v=l3K-tD3TMqQ|access-date=28 April 2020|archive-date=11 September 2020|archive-url=https://web.archive.org/web/20200911201609/https://www.youtube.com/watch?v=l3K-tD3TMqQ&gl=US&hl=en|url-status=dead}}</ref><ref>{{cite web|title=Github Repository - isosurface|date=23 Oct 2016|author=Lin X|website=[[GitHub]] |url=https://github.com/Lin20/isosurface}}</ref>