Need some math help with dodecahedron surface finding script

Help and Feedback Scripting Support
#1

Hello guys. I’m trying to implement rocks and ores in my game. And to do so, I have chosen to work with dodecahedrons. It’s 3D figure which consists out of 12 pentagons. But I have got some problems with it:
Ore pieces should cover dodecahedrone’s surface, but they do this not perfectly - they may float in air sometimes.

Screenshot of ores:
image
As you can see, some bits are deeper into the rock, some are more open. Code should place them on surface equally, which it fails for now. Sadly, after day spent, I was unable to find mistake myself, so I’m asking for your guys help.

local Angle = math.random(0, 360) * math.pi/180
local Depth = (20 - math.random(0, 400)^0.5)/20
--local Side = 0.6178910239805036
local Height = 0.7824446016137838
local Angle2 = math.pi/5 - math.abs(Angle % (math.pi/2.5) - math.pi/5)
local DepthMod = Height / math.cos(Angle2)

local X = math.cos(Angle) * Depth * DepthMod
local Y = math.sin(Angle) * Depth * DepthMod
local DotOnSurface = Vector3.new(X, 0, Y)
--Code above correctly makes point on pentagon. But IDK on which scale...

DotOnSurface *= 0.567917 / 1.56098 --tried to fix with blender measurement tool. I think I have failed.
		
local DodecahedronRadius = 0.405
local Side = math.random(1, 12)
--here it should to try select 1 surface and put ore dot relative to that surface.
--code fails with this too. (most likely)
if Side == 1 then
	return CFrame.new(0, -DodecahedronRadius, 0) * DotOnSurface
elseif Side == 12 then
	return CFrame.new(0, DodecahedronRadius, 0) * DotOnSurface
elseif Side <= 6 then
	return CFrame.fromEulerAngles(-math.pi/2.5, (Side - 1) * math.pi/2.5, 0, Enum.RotationOrder.YXZ) * CFrame.new(0, DodecahedronRadius, 0) * DotOnSurface
else
	return CFrame.fromEulerAngles(-math.pi/2.5, (Side - 6.5) * math.pi/2.5, 0, Enum.RotationOrder.YXZ) * CFrame.new(0, -DodecahedronRadius, 0) * DotOnSurface
end



--[==[
Some math.pi conversions:
math.pi = 180 degrees
math.pi/180 = used to convert degrees to radians
math.pi/5 = 72 degrees
math.pi/2.5 = 36 degrees
--]==]
1 Like