376 lines
8.8 KiB
Lua
376 lines
8.8 KiB
Lua
-- 3D Cube Rotation
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-- http://www.speich.net/computer/moztesting/3d.htm
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-- Created by Simon Speich
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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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local Q = {}
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local MTrans = {}; -- transformation matrix
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local MQube = {} -- position information of qube
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local I = {} -- entity matrix
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local Origin = {}
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local Testing = {}
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local LoopTimer;
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local validation = {
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[20] = 2889,
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[40] = 2889,
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[80] = 2889,
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[160] = 2889
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};
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local DisplArea = {}
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DisplArea.Width = 300;
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DisplArea.Height = 300;
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local function DrawLine(From, To)
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local x1 = From.V[1];
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local x2 = To.V[1];
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local y1 = From.V[2];
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local y2 = To.V[2];
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local dx = math.abs(x2 - x1);
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local dy = math.abs(y2 - y1);
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local x = x1;
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local y = y1;
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local IncX1, IncY1;
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local IncX2, IncY2;
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local Den;
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local Num;
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local NumAdd;
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local NumPix;
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if (x2 >= x1) then IncX1 = 1; IncX2 = 1;
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else IncX1 = -1; IncX2 = -1; end
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if (y2 >= y1) then IncY1 = 1; IncY2 = 1;
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else IncY1 = -1; IncY2 = -1; end
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if (dx >= dy) then
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IncX1 = 0;
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IncY2 = 0;
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Den = dx;
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Num = dx / 2;
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NumAdd = dy;
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NumPix = dx;
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else
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IncX2 = 0;
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IncY1 = 0;
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Den = dy;
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Num = dy / 2;
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NumAdd = dx;
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NumPix = dy;
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end
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NumPix = math.floor(Q.LastPx + NumPix + 0.5);
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local i = Q.LastPx;
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while i < NumPix do
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Num = Num + NumAdd;
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if (Num >= Den) then
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Num = Num - Den;
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x = x + IncX1;
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y = y + IncY1;
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end
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x = x + IncX2;
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y = y + IncY2;
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i = i + 1;
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end
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Q.LastPx = NumPix;
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end
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local function CalcCross(V0, V1)
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local Cross = {};
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Cross[1] = V0[2]*V1[3] - V0[3]*V1[2];
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Cross[2] = V0[3]*V1[1] - V0[1]*V1[3];
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Cross[3] = V0[1]*V1[2] - V0[2]*V1[1];
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return Cross;
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end
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local function CalcNormal(V0, V1, V2)
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local A = {}; local B = {};
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for i = 1,3 do
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A[i] = V0[i] - V1[i];
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B[i] = V2[i] - V1[i];
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end
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A = CalcCross(A, B);
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local Length = math.sqrt(A[1]*A[1] + A[2]*A[2] + A[3]*A[3]);
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for i = 1,3 do A[i] = A[i] / Length; end
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A[4] = 1;
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return A;
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end
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local function CreateP(X,Y,Z)
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local result = {}
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result.V = {X,Y,Z,1};
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return result
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end
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-- multiplies two matrices
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local function MMulti(M1, M2)
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local M = {{},{},{},{}};
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for i = 1,4 do
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for j = 1,4 do
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M[i][j] = M1[i][1] * M2[1][j] + M1[i][2] * M2[2][j] + M1[i][3] * M2[3][j] + M1[i][4] * M2[4][j];
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end
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end
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return M;
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end
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-- multiplies matrix with vector
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local function VMulti(M, V)
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local Vect = {};
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for i = 1,4 do
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Vect[i] = M[i][1] * V[1] + M[i][2] * V[2] + M[i][3] * V[3] + M[i][4] * V[4];
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end
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return Vect;
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end
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local function VMulti2(M, V)
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local Vect = {};
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for i = 1,3 do
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Vect[i] = M[i][1] * V[1] + M[i][2] * V[2] + M[i][3] * V[3];
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end
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return Vect;
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end
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-- add to matrices
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local function MAdd(M1, M2)
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local M = {{},{},{},{}};
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for i = 1,4 do
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for j = 1,4 do
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M[i][j] = M1[i][j] + M2[i][j];
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end
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end
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return M;
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end
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local function Translate(M, Dx, Dy, Dz)
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local T = {
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{1,0,0,Dx},
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{0,1,0,Dy},
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{0,0,1,Dz},
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{0,0,0,1}
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};
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return MMulti(T, M);
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end
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local function RotateX(M, Phi)
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local a = Phi;
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a = a * math.pi / 180;
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local Cos = math.cos(a);
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local Sin = math.sin(a);
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local R = {
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{1,0,0,0},
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{0,Cos,-Sin,0},
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{0,Sin,Cos,0},
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{0,0,0,1}
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};
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return MMulti(R, M);
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end
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local function RotateY(M, Phi)
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local a = Phi;
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a = a * math.pi / 180;
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local Cos = math.cos(a);
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local Sin = math.sin(a);
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local R = {
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{Cos,0,Sin,0},
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{0,1,0,0},
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{-Sin,0,Cos,0},
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{0,0,0,1}
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};
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return MMulti(R, M);
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end
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local function RotateZ(M, Phi)
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local a = Phi;
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a = a * math.pi / 180;
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local Cos = math.cos(a);
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local Sin = math.sin(a);
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local R = {
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{Cos,-Sin,0,0},
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{Sin,Cos,0,0},
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{0,0,1,0},
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{0,0,0,1}
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};
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return MMulti(R, M);
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end
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local function DrawQube()
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-- calc current normals
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local CurN = {};
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local i = 5;
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Q.LastPx = 0;
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while i > -1 do CurN[i+1] = VMulti2(MQube, Q.Normal[i+1]); i = i - 1 end
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if (CurN[1][3] < 0) then
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if (not Q.Line[1]) then DrawLine(Q[1], Q[2]); Q.Line[1] = true; end
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if (not Q.Line[2]) then DrawLine(Q[2], Q[3]); Q.Line[2] = true; end
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if (not Q.Line[3]) then DrawLine(Q[3], Q[4]); Q.Line[3] = true; end
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if (not Q.Line[4]) then DrawLine(Q[4], Q[1]); Q.Line[4] = true; end
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end
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if (CurN[2][3] < 0) then
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if (not Q.Line[3]) then DrawLine(Q[4], Q[3]); Q.Line[3] = true; end
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if (not Q.Line[10]) then DrawLine(Q[3], Q[7]); Q.Line[10] = true; end
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if (not Q.Line[7]) then DrawLine(Q[7], Q[8]); Q.Line[7] = true; end
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if (not Q.Line[11]) then DrawLine(Q[8], Q[4]); Q.Line[11] = true; end
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end
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if (CurN[3][3] < 0) then
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if (not Q.Line[5]) then DrawLine(Q[5], Q[6]); Q.Line[6] = true; end
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if (not Q.Line[6]) then DrawLine(Q[6], Q[7]); Q.Line[6] = true; end
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if (not Q.Line[7]) then DrawLine(Q[7], Q[8]); Q.Line[7] = true; end
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if (not Q.Line[8]) then DrawLine(Q[8], Q[5]); Q.Line[8] = true; end
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end
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if (CurN[4][3] < 0) then
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if (not Q.Line[5]) then DrawLine(Q[5], Q[6]); Q.Line[5] = true; end
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if (not Q.Line[9]) then DrawLine(Q[6], Q[2]); Q.Line[9] = true; end
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if (not Q.Line[1]) then DrawLine(Q[2], Q[1]); Q.Line[1] = true; end
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if (not Q.Line[12]) then DrawLine(Q[1], Q[5]); Q.Line[12] = true; end
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end
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if (CurN[5][3] < 0) then
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if (not Q.Line[12]) then DrawLine(Q[5], Q[1]); Q.Line[12] = true; end
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if (not Q.Line[4]) then DrawLine(Q[1], Q[4]); Q.Line[4] = true; end
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if (not Q.Line[11]) then DrawLine(Q[4], Q[8]); Q.Line[11] = true; end
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if (not Q.Line[8]) then DrawLine(Q[8], Q[5]); Q.Line[8] = true; end
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end
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if (CurN[6][3] < 0) then
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if (not Q.Line[9]) then DrawLine(Q[2], Q[6]); Q.Line[9] = true; end
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if (not Q.Line[6]) then DrawLine(Q[6], Q[7]); Q.Line[6] = true; end
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if (not Q.Line[10]) then DrawLine(Q[7], Q[3]); Q.Line[10] = true; end
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if (not Q.Line[2]) then DrawLine(Q[3], Q[2]); Q.Line[2] = true; end
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end
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Q.Line = {false,false,false,false,false,false,false,false,false,false,false,false}
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Q.LastPx = 0;
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end
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local function Loop()
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if (Testing.LoopCount > Testing.LoopMax) then return; end
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local TestingStr = tostring(Testing.LoopCount);
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while (#TestingStr < 3) do TestingStr = "0" .. TestingStr; end
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MTrans = Translate(I, -Q[9].V[1], -Q[9].V[2], -Q[9].V[3]);
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MTrans = RotateX(MTrans, 1);
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MTrans = RotateY(MTrans, 3);
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MTrans = RotateZ(MTrans, 5);
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MTrans = Translate(MTrans, Q[9].V[1], Q[9].V[2], Q[9].V[3]);
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MQube = MMulti(MTrans, MQube);
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local i = 8;
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while i > -1 do
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Q[i+1].V = VMulti(MTrans, Q[i+1].V);
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i = i - 1
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end
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DrawQube();
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Testing.LoopCount = Testing.LoopCount + 1;
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Loop();
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end
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local function Init(CubeSize)
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-- init/reset vars
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Origin.V = {150,150,20,1};
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Testing.LoopCount = 0;
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Testing.LoopMax = 50;
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Testing.TimeMax = 0;
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Testing.TimeAvg = 0;
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Testing.TimeMin = 0;
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Testing.TimeTemp = 0;
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Testing.TimeTotal = 0;
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Testing.Init = false;
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-- transformation matrix
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MTrans = {
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{1,0,0,0},
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{0,1,0,0},
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{0,0,1,0},
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{0,0,0,1}
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};
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-- position information of qube
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MQube = {
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{1,0,0,0},
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{0,1,0,0},
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{0,0,1,0},
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{0,0,0,1}
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};
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-- entity matrix
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I = {
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{1,0,0,0},
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{0,1,0,0},
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{0,0,1,0},
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{0,0,0,1}
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};
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-- create qube
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Q[1] = CreateP(-CubeSize,-CubeSize, CubeSize);
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Q[2] = CreateP(-CubeSize, CubeSize, CubeSize);
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Q[3] = CreateP( CubeSize, CubeSize, CubeSize);
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Q[4] = CreateP( CubeSize,-CubeSize, CubeSize);
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Q[5] = CreateP(-CubeSize,-CubeSize,-CubeSize);
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Q[6] = CreateP(-CubeSize, CubeSize,-CubeSize);
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Q[7] = CreateP( CubeSize, CubeSize,-CubeSize);
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Q[8] = CreateP( CubeSize,-CubeSize,-CubeSize);
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-- center of gravity
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Q[9] = CreateP(0, 0, 0);
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-- anti-clockwise edge check
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Q.Edge = {{1,2,3},{4,5,7},{8,7,6},{5,6,2},{5,1,4},{2,6,7}};
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-- calculate squad normals
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Q.Normal = {};
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for i = 1,#Q.Edge do
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Q.Normal[i] = CalcNormal(Q[Q.Edge[i][1]].V, Q[Q.Edge[i][2]].V, Q[Q.Edge[i][3]].V);
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end
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-- line drawn ?
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Q.Line = {false,false,false,false,false,false,false,false,false,false,false,false};
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-- create line pixels
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Q.NumPx = 9 * 2 * CubeSize;
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for i = 1,Q.NumPx do CreateP(0,0,0); end
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MTrans = Translate(MTrans, Origin.V[1], Origin.V[2], Origin.V[3]);
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MQube = MMulti(MTrans, MQube);
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local i = 0;
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while i < 9 do
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Q[i+1].V = VMulti(MTrans, Q[i+1].V);
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i = i + 1
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end
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DrawQube();
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Testing.Init = true;
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Loop();
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-- Perform a simple sum-based verification.
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local sum = 0;
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for i = 1,#Q do
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local vector = Q[i].V;
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for j = 1,#vector do
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sum = sum + vector[j];
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end
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end
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if (math.floor(sum) ~= validation[CubeSize]) then
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assert(false, "Error: bad vector sum for CubeSize = " .. CubeSize .. "; expected " .. validation[CubeSize] .. " but got " .. math.floor(sum))
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end
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end
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local i = 20
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while i <= 160 do
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Init(i);
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i = i * 2
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end
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Q = nil;
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MTrans = nil;
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MQube = nil;
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I = nil;
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Origin = nil;
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Testing = nil;
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LoopTime = nil;
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DisplArea = nil;
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end
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bench.runCode(test, "3d-cube")
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