255 lines
7.1 KiB
Lua
255 lines
7.1 KiB
Lua
--!strict
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local bench = script and require(script.Parent.bench_support) or require("bench_support")
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function test()
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type Vertex = {
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pX: number, pY: number, pZ: number,
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uvX: number, uvY: number, uvZ: number,
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nX: number, nY: number, nZ: number,
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tX: number, tY: number, tZ: number,
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bX: number, bY: number, bZ: number,
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h: number
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}
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local grid_size = 100
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local mesh: {
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vertices: {Vertex},
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indices: {number},
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triangle_cone_p: {{x: number, y: number, z: number}},
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triangle_cone_n: {{x: number, y: number, z: number}}
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} = {
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vertices = table.create(grid_size * grid_size),
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indices = table.create((grid_size - 1) * (grid_size - 1) * 6),
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triangle_cone_p = table.create((grid_size - 1) * (grid_size - 1) * 2),
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triangle_cone_n = table.create((grid_size - 1) * (grid_size - 1) * 2)
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}
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local function init_vertices()
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local i = 1
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for y = 1,grid_size do
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for x = 1,grid_size do
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local v: Vertex = {}
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v.pX = x
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v.pY = y
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v.pZ = math.cos(x) + math.sin(y)
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v.uvX = (x-1)/(grid_size-1)
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v.uvY = (y-1)/(grid_size-1)
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v.uvZ = 0
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v.nX = 0
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v.nY = 0
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v.nZ = 0
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v.bX = 0
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v.bY = 0
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v.bZ = 0
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v.tX = 0
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v.tY = 0
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v.tZ = 0
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v.h = 0
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mesh.vertices[i] = v
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i += 1
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end
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end
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end
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local function init_indices()
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local i = 1
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for y = 1,grid_size-1 do
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for x = 1,grid_size-1 do
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mesh.indices[i] = x + (y-1)*grid_size
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i += 1
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mesh.indices[i] = x + y*grid_size
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i += 1
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mesh.indices[i] = (x+1) + (y-1)*grid_size
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i += 1
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mesh.indices[i] = (x+1) + (y-1)*grid_size
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i += 1
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mesh.indices[i] = x + y*grid_size
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i += 1
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mesh.indices[i] = (x+1) + y*grid_size
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i += 1
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end
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end
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end
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local function calculate_normals()
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local norm_sum = 0
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for i = 1,#mesh.indices,3 do
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local a = mesh.vertices[mesh.indices[i]]
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local b = mesh.vertices[mesh.indices[i + 1]]
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local c = mesh.vertices[mesh.indices[i + 2]]
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local abx = a.pX - b.pX
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local aby = a.pY - b.pY
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local abz = a.pZ - b.pZ
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local acx = a.pX - c.pX
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local acy = a.pY - c.pY
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local acz = a.pZ - c.pZ
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local nx = aby * acz - abz * acy;
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local ny = abz * acx - abx * acz;
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local nz = abx * acy - aby * acx;
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a.nX += nx
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a.nY += ny
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a.nZ += nz
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b.nX += nx
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b.nY += ny
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b.nZ += nz
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c.nX += nx
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c.nY += ny
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c.nZ += nz
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end
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for _,v in mesh.vertices do
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local magnitude = math.sqrt(v.nX * v.nX + v.nY * v.nY + v.nZ * v.nZ)
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v.nX /= magnitude
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v.nY /= magnitude
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v.nZ /= magnitude
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norm_sum += v.nX * v.nX + v.nY * v.nY + v.nZ * v.nZ
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end
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return norm_sum
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end
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local function compute_triangle_cones()
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local mesh_area = 0
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local pos = 1
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for i = 1,#mesh.indices,3 do
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local p0 = mesh.vertices[mesh.indices[i]]
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local p1 = mesh.vertices[mesh.indices[i + 1]]
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local p2 = mesh.vertices[mesh.indices[i + 2]]
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local p10x = p1.pX - p0.pX
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local p10y = p1.pY - p0.pY
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local p10z = p1.pZ - p0.pZ
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local p20x = p2.pX - p0.pX
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local p20y = p2.pY - p0.pY
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local p20z = p2.pZ - p0.pZ
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local normalx = p10y * p20z - p10z * p20y;
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local normaly = p10z * p20x - p10x * p20z;
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local normalz = p10x * p20y - p10y * p20x;
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local area = math.sqrt(normalx * normalx + normaly * normaly + normalz * normalz)
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local invarea = if area == 0 then 0 else 1 / area;
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local rx = (p0.pX + p1.pX + p2.pX) / 3
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local ry = (p0.pY + p1.pY + p2.pY) / 3
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local rz = (p0.pZ + p1.pZ + p2.pZ) / 3
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mesh.triangle_cone_p[pos] = { x = rx, y = ry, z = rz }
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mesh.triangle_cone_n[pos] = { x = normalx * invarea, y = normaly * invarea, z = normalz * invarea}
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pos += 1
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mesh_area += area
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end
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return mesh_area
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end
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local function compute_tangent_space()
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local checksum = 0
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for i = 1,#mesh.indices,3 do
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local a = mesh.vertices[mesh.indices[i]]
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local b = mesh.vertices[mesh.indices[i + 1]]
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local c = mesh.vertices[mesh.indices[i + 2]]
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local x1 = b.pX - a.pX
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local x2 = c.pX - a.pX
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local y1 = b.pY - a.pY
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local y2 = c.pY - a.pY
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local z1 = b.pZ - a.pZ
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local z2 = c.pZ - a.pZ
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local s1 = b.uvX - a.uvX
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local s2 = c.uvX - a.uvX
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local t1 = b.uvY - a.uvY
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local t2 = c.uvY - a.uvY
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local r = 1.0 / (s1 * t2 - s2 * t1);
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local sdirX = (t2 * x1 - t1 * x2) * r
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local sdirY = (t2 * y1 - t1 * y2) * r
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local sdirZ = (t2 * z1 - t1 * z2) * r
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local tdirX = (s1 * x2 - s2 * x1) * r
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local tdirY = (s1 * y2 - s2 * y1) * r
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local tdirZ = (s1 * z2 - s2 * z1) * r
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a.tX += sdirX
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a.tY += sdirY
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a.tZ += sdirZ
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b.tX += sdirX
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b.tY += sdirY
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b.tZ += sdirZ
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c.tX += sdirX
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c.tY += sdirY
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c.tZ += sdirZ
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a.bX += tdirX
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a.bY += tdirY
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a.bZ += tdirZ
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b.bX += tdirX
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b.bY += tdirY
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b.bZ += tdirZ
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c.bX += tdirX
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c.bY += tdirY
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c.bZ += tdirZ
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end
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for _,v in mesh.vertices do
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local tX = v.tX
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local tY = v.tY
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local tZ = v.tZ
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-- Gram-Schmidt orthogonalize
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local ndt = v.nX * tX + v.nY * tY + v.nZ * tZ
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local tmnsX = tX - v.nX * ndt
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local tmnsY = tY - v.nY * ndt
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local tmnsZ = tZ - v.nZ * ndt
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local l = math.sqrt(tmnsX * tmnsX + tmnsY * tmnsY + tmnsZ * tmnsZ)
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local invl = 1 / l
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v.tX = tmnsX * invl
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v.tY = tmnsY * invl
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v.tZ = tmnsZ * invl
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local normalx = v.nY * tZ - v.nZ * tY;
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local normaly = v.nZ * tX - v.nX * tZ;
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local normalz = v.nX * tY - v.nY * tX;
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local ht = normalx * v.bX + normaly * v.bY + normalz * v.bZ
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v.h = ht < 0 and -1 or 1
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checksum += v.tX + v.h
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end
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return checksum
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end
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init_vertices()
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init_indices()
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calculate_normals()
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compute_triangle_cones()
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compute_tangent_space()
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end
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bench.runCode(test, "mesh-normal-scalar")
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