%D \module
%D   [       file=meta-imp-meshes-dodecahedron,
%D        version=2026.06.09,
%D          title=\METAPOST\ Graphics,
%D       subtitle=Docecahedron fractals,
%D         author=Hans Hagen,
%D           date=\currentdate,
%D      copyright={PRAGMA ADE \& \CONTEXT\ Development Team}]
%C
%C This module is part of the \CONTEXT\ macro||package and is
%C therefore copyrighted by \PRAGMA. See mreadme.pdf for
%C details.

%D See \type {meta-imp-mengersponge.mkxl} for some comments. Liek that file, we
%D added it because we needed (stl) examples for the manual and also wanted to
%D demonstrate the plug-in model. Both files are dedicated to Keith McKay who is
%D the one challenging us for such features.

\startluacode

local sqrt      = xmath.sqrt
local normalize = xmath.normalize

local p     <const> = (1 + sqrt(5)) / 2
local d     <const> = 1/p
local scale <const> = 1 / (2 + p)

local base_vertices = {
    {  1,  1, 1 }, { 1,  1, -1 }, {  1, -1, 1 }, {  1, -1, -1 },
    { -1,  1, 1 }, {-1,  1, -1 }, { -1, -1, 1 }, { -1, -1, -1 },
    {  0,  d, p }, { 0,  d, -p }, {  0, -d, p }, {  0, -d, -p },
    {  d,  p, 0 }, { d, -p,  0 }, { -d,  p, 0 }, { -d, -p,  0 },
    {  p,  0, d }, { p,  0, -d }, { -p,  0, d }, { -p,  0, -d },
}

for i=1,#base_vertices do
    local b = base_vertices[i]
    b[1], b[2], b[3] = normalize(b[1], b[2], b[3])
end

local base_faces = {
    { 1,  9, 11, 3, 17 }, { 2, 18, 4, 12, 10 }, { 5, 19, 7, 11,  9 }, { 6, 10, 12, 8, 20 },
    { 1, 13, 15, 5,  9 }, { 2, 10, 6, 15, 13 }, { 3, 11, 7, 16, 14 }, { 4, 14, 16, 8, 12 },
    { 1, 17, 18, 2, 13 }, { 3, 14, 4, 18, 17 }, { 5, 15, 6, 20, 19 }, { 7, 19, 20, 8, 16 },
}

local function generatefractal(level,cx,cy,cz,radius,vertices,triangles)
    if level == 0 then
        local nofvertices = #vertices
        local firstvertex = nofvertices
        for i=1,#base_vertices do
            local bv = base_vertices[i]
            local b1 = bv[1]
            local b2 = bv[2]
            local b3 = bv[3]
            nofvertices = nofvertices + 1
            vertices[nofvertices] = {
                cx + b1 * radius,
                cy + b2 * radius,
                cz + b3 * radius,
                b1, b2, b3
            }
        end
        local t = #triangles
        for i=1,#base_faces do
            local bf = base_faces[i]
            local a = firstvertex + bf[1]
            local b = firstvertex + bf[2]
            local c = firstvertex + bf[3]
            local d = firstvertex + bf[4]
            local e = firstvertex + bf[5]
            t = t + 1 triangles[t] = { a, b, c }
            t = t + 1 triangles[t] = { a, c, d }
            t = t + 1 triangles[t] = { a, d, e }
        end
        return
    end

    local distance = radius * (1 - scale)

    radius = radius * scale
    level  = level - 1

    for i=1,#base_vertices do
        local bv = base_vertices[i]
        generatefractal(
            level,
            cx + bv[1] * distance,
            cy + bv[2] * distance,
            cz + bv[3] * distance,
            radius,
            vertices,
            triangles
        )
    end
end

local function dodecahedron(iterations,radius)
    local vertices  = { }
    local triangles = { }
    generatefractal(iterations,0,0,0,radius,vertices,triangles)
    return vertices, triangles
end

metapost.registermesher("dodecahedron", function(specification)
    local vertices, triangles = dodecahedron(
        specification.level  or 3,
        specification.radius or 10
    )
    return {
        name      = "dodecahedron",
        id        = specification.id,
        vertices  = vertices,
        triangles = triangles,
    }
end)

\stopluacode

\continueifinputfile{meta-imp-meshes-dodecahedron.mkxl}

\setupbackgrounds
  [paper]
  [background=color,
   backgroundcolor=darkblue,
   backgroundcolor=,
   frame=on,
   framecolor=darkblue]

\starttext

\startMPpage

    lmt_scene_start [
        bytemap      = 34,
        width        = 20cm,
        crop         = true,
        supersample  = 2,
        projection   = "perspective",
        eye          = (10,10,10),
%         eye          = (20,20,20),
%         target       = (5,5,5),
        up           = (0,0,1),
        light        = (-1.5,-1,-2),
        intensity    = 1,
    ] ;

    lmt_scene_material [
        name      = "surface",
        diffuse   = (0,0.5,.5),
        specular  = (.40,.40,.40),
        shininess = 40,
%         opacity   = .15,
%         opacity   = .45,
% twosided = true,
    ] ;

    lmt_scene_internal [
        id        = "one",
        name      = "dodecahedron",
        level     = 3,
        radius    = 10,
        cache     = true,      % todo
        material  = "surface",
    ] ;

    lmt_scene_stop ;

\stopMPpage

\stoptext