public static PlatonicSolid GetDodecahedron(double radius)
{
/// Dodecahedron: 12 faces, 30 edges, 20 vertices
/// inscribed / circumscribed = 0.7946544722498597 = 1.113516364 / 1.401258538
/// http://en.wikipedia.org/wiki/Dodecahedron#Cartesian_coordinates
/// (±1, ±1, ±1)
/// (0, ±1/φ, ±φ)
/// (±1/φ, ±φ, 0)
/// (±φ, 0, ±1/φ)
/// where φ = (1 + √5) / 2
double φ = (1.0 + Math.Sqrt(5)) / 2.0;
var obj = new PlatonicSolid
{
verts = new Vector[]
{
/// (±1, ±1, ±1)
new Vector(1, 1, 1), new Vector(1, 1, -1), new Vector(1, -1, 1), new Vector(1, -1, -1),
new Vector(-1, 1, 1), new Vector(-1, 1, -1), new Vector(-1, -1, 1), new Vector(-1, -1, -1),
/// (0, ±1/φ, ±φ)
new Vector(0, 1 / φ, φ), new Vector(0, 1 / φ, -φ), new Vector(0, -1 / φ, φ), new Vector(0, -1 / φ, -φ),
/// (±1/φ, ±φ, 0)
new Vector(1 / φ, φ, 0), new Vector(1 / φ, -φ, 0), new Vector(-1 / φ, φ, 0), new Vector(-1 / φ, -φ, 0),
/// (±φ, 0, ±1/φ)
new Vector(φ, 0, 1 / φ), new Vector(φ, 0, -1 / φ), new Vector(-φ, 0, 1 / φ), new Vector(-φ, 0, -1 / φ),
}
};
return(obj.CloneByRadius(radius));
}
public static PlatonicSolid Icosahedron(double radius)
{
/// Icosahedron: 20 faces, 30 edges, 12 vertices
/// inscribed / circumscribed = 0.7946544723127723 = 0.7557613141 / 0.9510565163
/// http://en.wikipedia.org/wiki/Icosahedron#Cartesian_coordinates
/// (0, ±1, ±φ)
/// (±1, ±φ, 0)
/// (±φ, 0, ±1)
/// where φ = (1 + √5) / 2
double φ = (1.0 + Math.Sqrt(5)) / 2.0;
var obj = new PlatonicSolid
{
verts = new Vector[]
{
/// (0, ±1, ±φ)
new Vector(0, 1, φ), new Vector(0, 1, -φ), new Vector(0, -1, φ), new Vector(0, -1, -φ),
/// (±1, ±φ, 0)
new Vector(1, φ, 0), new Vector(1, -φ, 0), new Vector(-1, φ, 0), new Vector(-1, -φ, 0),
/// (±φ, 0, ±1)
new Vector(φ, 0, 1), new Vector(φ, 0, -1), new Vector(-φ, 0, 1), new Vector(-φ, 0, -1),
}
};
return(obj.CloneByRadius(radius));
}
public static PlatonicSolid CloneByRadius(PlatonicSolid obj, double radius)
{
Vector[] verts = obj.verts.HCloneVectors().ToArray();
double rad = verts[0].Dist;
for (int i = 0; i < verts.Length; i++)
{
HDebug.AssertTolerance(0.00000001, rad - verts[i].Dist);
verts[i] = verts[i] * (radius / rad);
}
return(new PlatonicSolid
{
verts = verts
});
}
public static PlatonicSolid GetCuve(double radius)
{
/// Cuve: 6 faces, 12 edges, 8 vertices
/// inscribed / circumscribed = 0.5773502691896258 = 1 / sqrt(3)
/// http://en.wikipedia.org/wiki/Cube
var obj = new PlatonicSolid
{
verts = new Vector[]
{
new Vector(1, 1, 1), new Vector(1, 1, -1), new Vector(1, -1, 1), new Vector(1, -1, -1),
new Vector(-1, 1, 1), new Vector(-1, 1, -1), new Vector(-1, -1, 1), new Vector(-1, -1, -1),
}
};
return(obj.CloneByRadius(radius));
}
public static PlatonicSolid GetTetrahedon(double radius)
{
/// Tetrahedon: 4 faces, 6 edges, 4 vertices
/// inscribed / circumscribed = 0.33333333333333337 = sqrt(1/24) / sqrt(3/8)
/// http://en.wikipedia.org/wiki/Tetrahedron
var obj = new PlatonicSolid
{
verts = new Vector[]
{
new Vector(1, 1, 1), new Vector(1, -1, -1),
new Vector(-1, 1, -1), new Vector(-1, -1, 1),
}
};
return(obj.CloneByRadius(radius));
}
public static PlatonicSolid GetOctahedron(double radius)
{
/// Octahedron: 8 faces, 12 edges, 6 vertices
/// inscribed / circumscribed = 0.5773502075429352 = 0.4082482 / 0.7071067
/// http://en.wikipedia.org/wiki/Octahedron
///
/// Most efficient
/// * less vertices
/// * more faces
var obj = new PlatonicSolid
{
verts = new Vector[]
{
new Vector(0, 0, 1), new Vector(0, 0, -1),
new Vector(0, 1, 0), new Vector(0, -1, 0),
new Vector(1, 0, 0), new Vector(-1, 0, 0),
}
};
return(obj.CloneByRadius(radius));
}
