dodecahedron(height:in:restitution:)
Creates a regular dodecahedron, a shape with 12 pentagonal faces, that the player tosses during gameplay.
Declaration
static func dodecahedron(height: Float, in unit: UnitLength = .meters, restitution: Float? = nil) -> TossableRepresentationParameters
- height:
The height of the dodecahedron.
- unit:
The unit of measurement for the height.
- restitution:
The coefficient of restitution, in the range [0, 1].
Discussion
The vertices for the simulated dodecahedron are oriented with one face toward +y with one vertex of that top face oriented toward -z. In this orientation, the height (h) is measured from face to opposing face, and the vertices have the following coordinates, which all lie on a circumscribed sphere of radius r = h/2 ⋅ sqrt(15)/(phi ⋅ sqrt(phi^2 + 1)), where phi = (sqrt(5) + 1)/2: ±Y face: ±{ 0, +1, -2/phi^2 } ⋅ h/2, ±{+2/phi ⋅ sin(72º), +1, -2/phi^2 ⋅ cos(72º) } ⋅ h/2, ±{+2/phi ⋅ sin(36º), +1, +2/phi^2 ⋅ cos(36º) } ⋅ h/2, ±{-2/phi ⋅ sin(36º), +1, +2/phi^2 ⋅ cos(36º) } ⋅ h/2, ±{-2/phi ⋅ sin(72º), +1, -2/phi^2 ⋅ cos(72º) } ⋅ h/2 Equator: ±{ 0, +1/phi^3, -2/phi } ⋅ h/2, ±{+2/phi^2 ⋅ sin(72º), +1/phi^3, -2/phi ⋅ cos(72º) } ⋅ h/2, ±{+2/phi^2 ⋅ sin(36º), +1/phi^3, +2/phi ⋅ cos(36º) } ⋅ h/2, ±{-2/phi^2 ⋅ sin(36º), +1/phi^3, +2/phi ⋅ cos(36º) } ⋅ h/2, ±{-2/phi^2 ⋅ sin(72º), +1/phi^3, -2/phi ⋅ cos(72º) } ⋅ h/2
Higher restitution values indicate materials that conserve kinetic energy during collisions, causing objects to bounce off each other elastically. Lower values suggest materials that absorb kinetic energy, resulting in less bounce and more energy loss upon impact.