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