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// 3D Cube Rotation
// Created by Simon Speich
var Q = new Array();
var MTrans = new Array(); // transformation matrix
var MQube = new Array(); // position information of qube
var I = new Array(); // entity matrix
var Origin = new Object();
var Testing = new Object();
var LoopTimer;
var DisplArea = new Object();
DisplArea.Width = 300;
DisplArea.Height = 300;
function DrawLine(From, To) {
var x1 = From.V[0];
var x2 = To.V[0];
var y1 = From.V[1];
var y2 = To.V[1];
var dx = Math.abs(x2 - x1);
var dy = Math.abs(y2 - y1);
var x = x1;
var y = y1;
var IncX1, IncY1;
var IncX2, IncY2;
var Den;
var Num;
var NumAdd;
var NumPix;
if (x2 >= x1) { IncX1 = 1; IncX2 = 1; }
else { IncX1 = -1; IncX2 = -1; }
if (y2 >= y1) { IncY1 = 1; IncY2 = 1; }
else { IncY1 = -1; IncY2 = -1; }
if (dx >= dy) {
IncX1 = 0;
IncY2 = 0;
Den = dx;
Num = dx / 2;
NumAdd = dy;
NumPix = dx;
}
else {
IncX2 = 0;
IncY1 = 0;
Den = dy;
Num = dy / 2;
NumAdd = dx;
NumPix = dy;
}
NumPix = Math.round(Q.LastPx + NumPix);
var i = Q.LastPx;
for (; i < NumPix; i++) {
Num += NumAdd;
if (Num >= Den) {
Num -= Den;
x += IncX1;
y += IncY1;
}
x += IncX2;
y += IncY2;
}
Q.LastPx = NumPix;
}
function CalcCross(V0, V1) {
var Cross = new Array();
Cross[0] = V0[1]*V1[2] - V0[2]*V1[1];
Cross[1] = V0[2]*V1[0] - V0[0]*V1[2];
Cross[2] = V0[0]*V1[1] - V0[1]*V1[0];
return Cross;
}
function CalcNormal(V0, V1, V2) {
var A = new Array(); var B = new Array();
for (var i = 0; i < 3; i++) {
A[i] = V0[i] - V1[i];
B[i] = V2[i] - V1[i];
}
A = CalcCross(A, B);
var Length = Math.sqrt(A[0]*A[0] + A[1]*A[1] + A[2]*A[2]);
for (var i = 0; i < 3; i++) A[i] = A[i] / Length;
A[3] = 1;
return A;
}
function CreateP(X,Y,Z) {
this.V = [X,Y,Z,1];
}
// multiplies two matrices
function MMulti(M1, M2) {
var M = [[],[],[],[]];
var i = 0;
var j = 0;
for (; i < 4; i++) {
j = 0;
for (; j < 4; j++) M[i][j] = M1[i][0] * M2[0][j] + M1[i][1] * M2[1][j] + M1[i][2] * M2[2][j] + M1[i][3] * M2[3][j];
}
return M;
}
//multiplies matrix with vector
function VMulti(M, V) {
var Vect = new Array();
var i = 0;
for (;i < 4; i++) Vect[i] = M[i][0] * V[0] + M[i][1] * V[1] + M[i][2] * V[2] + M[i][3] * V[3];
return Vect;
}
function VMulti2(M, V) {
var Vect = new Array();
var i = 0;
for (;i < 3; i++) Vect[i] = M[i][0] * V[0] + M[i][1] * V[1] + M[i][2] * V[2];
return Vect;
}
// add to matrices
function MAdd(M1, M2) {
var M = [[],[],[],[]];
var i = 0;
var j = 0;
for (; i < 4; i++) {
j = 0;
for (; j < 4; j++) M[i][j] = M1[i][j] + M2[i][j];
}
return M;
}
function Translate(M, Dx, Dy, Dz) {
var T = [
[1,0,0,Dx],
[0,1,0,Dy],
[0,0,1,Dz],
[0,0,0,1]
];
return MMulti(T, M);
}
function RotateX(M, Phi) {
var a = Phi;
a *= Math.PI / 180;
var Cos = Math.cos(a);
var Sin = Math.sin(a);
var R = [
[1,0,0,0],
[0,Cos,-Sin,0],
[0,Sin,Cos,0],
[0,0,0,1]
];
return MMulti(R, M);
}
function RotateY(M, Phi) {
var a = Phi;
a *= Math.PI / 180;
var Cos = Math.cos(a);
var Sin = Math.sin(a);
var R = [
[Cos,0,Sin,0],
[0,1,0,0],
[-Sin,0,Cos,0],
[0,0,0,1]
];
return MMulti(R, M);
}
function RotateZ(M, Phi) {
var a = Phi;
a *= Math.PI / 180;
var Cos = Math.cos(a);
var Sin = Math.sin(a);
var R = [
[Cos,-Sin,0,0],
[Sin,Cos,0,0],
[0,0,1,0],
[0,0,0,1]
];
return MMulti(R, M);
}
function DrawQube() {
// calc current normals
var CurN = new Array();
var i = 5;
Q.LastPx = 0;
for (; i > -1; i--) CurN[i] = VMulti2(MQube, Q.Normal[i]);
if (CurN[0][2] < 0) {
if (!Q.Line[0]) { DrawLine(Q[0], Q[1]); Q.Line[0] = true; };
if (!Q.Line[1]) { DrawLine(Q[1], Q[2]); Q.Line[1] = true; };
if (!Q.Line[2]) { DrawLine(Q[2], Q[3]); Q.Line[2] = true; };
if (!Q.Line[3]) { DrawLine(Q[3], Q[0]); Q.Line[3] = true; };
}
if (CurN[1][2] < 0) {
if (!Q.Line[2]) { DrawLine(Q[3], Q[2]); Q.Line[2] = true; };
if (!Q.Line[9]) { DrawLine(Q[2], Q[6]); Q.Line[9] = true; };
if (!Q.Line[6]) { DrawLine(Q[6], Q[7]); Q.Line[6] = true; };
if (!Q.Line[10]) { DrawLine(Q[7], Q[3]); Q.Line[10] = true; };
}
if (CurN[2][2] < 0) {
if (!Q.Line[4]) { DrawLine(Q[4], Q[5]); Q.Line[4] = true; };
if (!Q.Line[5]) { DrawLine(Q[5], Q[6]); Q.Line[5] = true; };
if (!Q.Line[6]) { DrawLine(Q[6], Q[7]); Q.Line[6] = true; };
if (!Q.Line[7]) { DrawLine(Q[7], Q[4]); Q.Line[7] = true; };
}
if (CurN[3][2] < 0) {
if (!Q.Line[4]) { DrawLine(Q[4], Q[5]); Q.Line[4] = true; };
if (!Q.Line[8]) { DrawLine(Q[5], Q[1]); Q.Line[8] = true; };
if (!Q.Line[0]) { DrawLine(Q[1], Q[0]); Q.Line[0] = true; };
if (!Q.Line[11]) { DrawLine(Q[0], Q[4]); Q.Line[11] = true; };
}
if (CurN[4][2] < 0) {
if (!Q.Line[11]) { DrawLine(Q[4], Q[0]); Q.Line[11] = true; };
if (!Q.Line[3]) { DrawLine(Q[0], Q[3]); Q.Line[3] = true; };
if (!Q.Line[10]) { DrawLine(Q[3], Q[7]); Q.Line[10] = true; };
if (!Q.Line[7]) { DrawLine(Q[7], Q[4]); Q.Line[7] = true; };
}
if (CurN[5][2] < 0) {
if (!Q.Line[8]) { DrawLine(Q[1], Q[5]); Q.Line[8] = true; };
if (!Q.Line[5]) { DrawLine(Q[5], Q[6]); Q.Line[5] = true; };
if (!Q.Line[9]) { DrawLine(Q[6], Q[2]); Q.Line[9] = true; };
if (!Q.Line[1]) { DrawLine(Q[2], Q[1]); Q.Line[1] = true; };
}
Q.Line = [false,false,false,false,false,false,false,false,false,false,false,false];
Q.LastPx = 0;
}
function Loop() {
if (Testing.LoopCount > Testing.LoopMax) return;
var TestingStr = String(Testing.LoopCount);
while (TestingStr.length < 3) TestingStr = "0" + TestingStr;
MTrans = Translate(I, -Q[8].V[0], -Q[8].V[1], -Q[8].V[2]);
MTrans = RotateX(MTrans, 1);
MTrans = RotateY(MTrans, 3);
MTrans = RotateZ(MTrans, 5);
MTrans = Translate(MTrans, Q[8].V[0], Q[8].V[1], Q[8].V[2]);
MQube = MMulti(MTrans, MQube);
var i = 8;
for (; i > -1; i--) {
Q[i].V = VMulti(MTrans, Q[i].V);
}
DrawQube();
Testing.LoopCount++;
Loop();
}
function Init(CubeSize) {
// init/reset vars
Origin.V = [150,150,20,1];
Testing.LoopCount = 0;
Testing.LoopMax = 50;
Testing.TimeMax = 0;
Testing.TimeAvg = 0;
Testing.TimeMin = 0;
Testing.TimeTemp = 0;
Testing.TimeTotal = 0;
Testing.Init = false;
// transformation matrix
MTrans = [
[1,0,0,0],
[0,1,0,0],
[0,0,1,0],
[0,0,0,1]
];
// position information of qube
MQube = [
[1,0,0,0],
[0,1,0,0],
[0,0,1,0],
[0,0,0,1]
];
// entity matrix
I = [
[1,0,0,0],
[0,1,0,0],
[0,0,1,0],
[0,0,0,1]
];
// create qube
Q[0] = new CreateP(-CubeSize,-CubeSize, CubeSize);
Q[1] = new CreateP(-CubeSize, CubeSize, CubeSize);
Q[2] = new CreateP( CubeSize, CubeSize, CubeSize);
Q[3] = new CreateP( CubeSize,-CubeSize, CubeSize);
Q[4] = new CreateP(-CubeSize,-CubeSize,-CubeSize);
Q[5] = new CreateP(-CubeSize, CubeSize,-CubeSize);
Q[6] = new CreateP( CubeSize, CubeSize,-CubeSize);
Q[7] = new CreateP( CubeSize,-CubeSize,-CubeSize);
// center of gravity
Q[8] = new CreateP(0, 0, 0);
// anti-clockwise edge check
Q.Edge = [[0,1,2],[3,2,6],[7,6,5],[4,5,1],[4,0,3],[1,5,6]];
// calculate squad normals
Q.Normal = new Array();
for (var i = 0; i < Q.Edge.length; i++) Q.Normal[i] = CalcNormal(Q[Q.Edge[i][0]].V, Q[Q.Edge[i][1]].V, Q[Q.Edge[i][2]].V);
// line drawn ?
Q.Line = [false,false,false,false,false,false,false,false,false,false,false,false];
// create line pixels
Q.NumPx = 9 * 2 * CubeSize;
for (var i = 0; i < Q.NumPx; i++) CreateP(0,0,0);
MTrans = Translate(MTrans, Origin.V[0], Origin.V[1], Origin.V[2]);
MQube = MMulti(MTrans, MQube);
var i = 0;
for (; i < 9; i++) {
Q[i].V = VMulti(MTrans, Q[i].V);
}
DrawQube();
Testing.Init = true;
Loop();
}
for ( var i = 20; i <= 160; i *= 2 ) {
Init(i);
}
var actual = '';
for (var i = 0; i < Q.length; ++i) {
actual += Q[i].V + ';';
}
var expected = "-116.618229186398,212.51135212951073,62.5094191967962,1;127.83701023614447,417.11611179082263,90.41153816299942,1;293.9570894432935,196.58093046570656,252.17789153139591,1;49.501850020750915,-8.02382919560505,224.275772565193,1;6.042910556709444,103.41906953429206,-212.1778915313964,1;250.49814997925202,308.02382919560387,-184.27577256519325,1;416.61822918640064,87.48864787048812,-22.509419196796493,1;172.1629897638581,-117.1161117908236,-50.41153816299975,1;150.0000000000007,149.99999999999952,20,1;";
assertEq(actual, expected);
Q = null;
MTrans = null;
MQube = null;
I = null;
Origin = null;
Testing = null;
LoopTime = null;
DisplArea = null;