--- author: Stéphane Laurent date: '2018-06-25' highlighter: 'pandoc-solarized' output: html_document: highlight: kate keep_md: False md_document: preserve_yaml: True variant: markdown prettify: True prettifycss: minimal tags: 'javascript, graphics, maths' title: Marching cubes with Javascript --- In [this gist of mine](https://gist.github.com/stla/69bbbd59fab9d46cc5f49860eaf9f052), there is a Javascript implementation of the marching cubes algorithm. The code is an adaptation of the algorithm implemented in misc3d, a R package written by Dai Feng and Luke Tierney. The algorithm returns a triangulation of an isosurface, that is to say the surface defined by an implicit equation $$f(x,y,z) = \ell.$$ The triangulation is returned by  {.javascript} marchingCubes(f, l, xmin, xmax, ymin, ymax, zmin, zmax, nx, ny, nz)  where xmin and xmax are the bounds of the $x$ variable and nx is the number of subdivisions between xmin and xmax, and similarly for the $y$ and $z$ variables. The output is a $(n \times 3)$-array of vertices. Grouping the rows by chunks of three provides the triangles. As an illustration, below is a Dupin cyclide triangulated by the marching cubes algorithm and rendered with three.js. The full code is available in the source. Go [here](https://laustep.github.io/stlahblog/frames/threejs_cyclide.html) for a full-page rendering. Below is another triangulation of the Dupin cyclide. This one has less triangles, but the rendering is smooth because I included the surface normals at each vertex.