Simple Lighting(Soft3D 3)
Click:Switch lights
複数の平行光源(Directional light)によるライティングです。
Phongの反射モデルを利用し計算しています。
(最終的な色＝自己発光＋環境光＋拡散光＋鏡面光)
前回よりいろいろ最適化しました。
/**
* Copyright saharan ( http://wonderfl.net/user/saharan )
* MIT License ( http://www.opensource.org/licenses/mit-license.php )
* Downloaded from: http://wonderfl.net/c/v0ax
*/
package {
import flash.display.*;
import flash.events.*;
import flash.text.*;
import net.hires.debug.*;
[SWF(frameRate = "60", width="465", height="465")]
/**
* Software rendering in ActionScript3.0 #3
* @author saharan
*/
public class FlashSoft3D extends Sprite {
private var r:Renderer;
private var count:uint;
private var box:Model;
private var flag:Boolean;
public static var debug:TextField;
public function FlashSoft3D() {
if (stage) init();
else addEventListener(Event.ADDED_TO_STAGE, init);
}
private function init(e:Event = null):void {
removeEventListener(Event.ADDED_TO_STAGE, init);
r = new Renderer(465, 465);
// dirx, diry, dirz, red, green, blue
r.light(0).directional(2, 0, 1, 0.7, 0.2, 0.2);
r.light(1).directional(-2, 0, 1, 0.2, 0.7, 0.2);
r.light(2).directional(0, -2, 1, 0.2, 0.2, 0.7);
flag = true;
stage.addEventListener(MouseEvent.MOUSE_DOWN, function(e:MouseEvent = null):void {
if (flag) {
r.light(0).directional(0, 0, 1, 1, 1, 1);
r.light(1).disable();
r.light(2).disable();
} else {
r.light(0).directional(2, 0, 1, 0.7, 0.2, 0.2);
r.light(1).directional(-2, 0, 1, 0.2, 0.7, 0.2);
r.light(2).directional(0, -2, 1, 0.2, 0.2, 0.7);
}
flag = !flag;
} );
addChild(r.image);
// debug = new TextField();
// debug.x = 200;
// debug.textColor = 0xffffff;
// addChild(debug);
// addChild(new Stats());
box = new Model();
box.toBox(1, 1, 1);
addEventListener(Event.ENTER_FRAME, frame);
}
private function hsv(h:Number, s:Number, v:Number, dst:Vec3D):void {
h %= 360;
var i:int = h / 60;
var f:Number = h / 60 - i;
var p:Number = v * (1 - s);
var q:Number = v * (1 - f * s);
var t:Number = v * (1 - (1 - f) * s);
switch (i) {
case 0: dst.setVector(v, t, p);
break;
case 1: dst.setVector(q, v, p);
break;
case 2: dst.setVector(p, v, t);
break;
case 3: dst.setVector(p, q, v);
break;
case 4: dst.setVector(t, p, v);
break;
case 5: dst.setVector(v, p, q);
break;
default: dst.setVector(0, 0, 0);
break;
}
}
private function frame(e:Event = null):void {
count++;
r.beginScene(0x000000);
r.rotateY(count / 80);
r.rotateX(count / 100);
var num:int = 0;
var col:Vec3D = new Vec3D();
for (var i:int = -1; i <= 1; i++) {
for (var j:int = -1; j <= 1; j++) {
for (var k:int = -1; k <= 1; k++) {
r.push();
r.translate(i * 12, j * 12, k * 12);
r.rotateX(count / 40 * i);
r.rotateY(count / 40 * j);
r.rotateZ(count / 40 * k);
if (i == j && j == k && i == 0) {
r.rotateX(count / 30);
r.rotateY(count / 40);
r.scale(9, 9, 9);
col.setVector(1, 1, 1);
} else {
r.scale(2, 2, 2);
hsv(num += 8, 1, 1, col);
}
r.material(0.8, 0.8, 1, 16, 0, col.x, col.y, col.z);
box.render(r);
r.pop();
}
}
}
r.endScene();
}
}
}
import flash.display.*;
class Renderer {
private var img:BitmapData;
private var fBuffer:Vector.<uint>;
private var zBuffer:Vector.<Number>;
private var bitmap:Bitmap;
private var width:uint;
private var height:uint;
private var aspect:Number;
private var width2:uint;
private var height2:uint;
private var size:uint;
private var near:uint;
private var far:uint;
private var cameraPosition:Vec3D;
private var cameraTarget:Vec3D;
private var cameraUp:Vec3D;
private var worldMatrix:Mat4x4;
private var viewMatrix:Mat4x4;
private var projectionMatrix:Mat4x4;
private var numStacks:int;
private var stack:Vector.<Mat4x4>;
private var color:uint;
private var amb:Number;
private var dif:Number;
private var spc:Number;
private var shn:Number;
private var emi:Number;
private var r:Number;
private var g:Number;
private var b:Number;
private var lights:Vector.<Light>;
private var ambr:Number;
private var ambg:Number;
private var ambb:Number;
public function Renderer(width:uint, height:uint) {
img = new BitmapData(width, height, false, 0);
bitmap = new Bitmap(img);
this.width = width;
this.height = height;
aspect = height / width;
size = width * height;
width2 = width >> 1;
height2 = height >> 1;
numStacks = 0;
zBuffer = new Vector.<Number>(size, true);
fBuffer = new Vector.<uint>(size, true);
lights = new Vector.<Light>(8, true);
for (var i:int = 0; i < 8; i++) lights[i] = new Light();
stack = new Vector.<Mat4x4>(64, true);
worldMatrix = new Mat4x4();
viewMatrix = new Mat4x4();
projectionMatrix = new Mat4x4();
// system initialization
lookAt(new Vec3D(0, 0, 50), new Vec3D(0, 0, 0), new Vec3D(0, 1, 0));
perspective(60 * Math.PI / 180, 5, 5000);
ambient(0.2, 0.2, 0.2);
light(0).directional(0, 0, 1, 1, 1, 1);
material(0.8, 0.8, 0, 0, 0, 1, 1, 1);
}
public function get image():Bitmap {
return bitmap;
}
public function push():void {
if(numStacks < 32) {
stack[numStacks] = new Mat4x4(
worldMatrix.e00, worldMatrix.e01, worldMatrix.e02, worldMatrix.e03,
worldMatrix.e10, worldMatrix.e11, worldMatrix.e12, worldMatrix.e13,
worldMatrix.e20, worldMatrix.e21, worldMatrix.e22, worldMatrix.e23,
worldMatrix.e30, worldMatrix.e31, worldMatrix.e32, worldMatrix.e33);
numStacks++;
}
}
public function pop():void {
if (numStacks > 0) {
numStacks--;
worldMatrix = stack[numStacks];
}
}
public function rotateX(theta:Number):void {
var temp:Mat4x4 = new Mat4x4();
temp.rotateX(theta);
temp.mulEqualMatrix(worldMatrix);
worldMatrix = temp;
}
public function rotateY(theta:Number):void {
var temp:Mat4x4 = new Mat4x4();
temp.rotateY(theta);
temp.mulEqualMatrix(worldMatrix);
worldMatrix = temp;
}
public function rotateZ(theta:Number):void {
var temp:Mat4x4 = new Mat4x4();
temp.rotateZ(theta);
temp.mulEqualMatrix(worldMatrix);
worldMatrix = temp;
}
public function scale(sx:Number, sy:Number, sz:Number):void {
var temp:Mat4x4 = new Mat4x4();
temp.scale(sx, sy, sz);
temp.mulEqualMatrix(worldMatrix);
worldMatrix = temp;
}
public function translate(tx:Number, ty:Number, tz:Number):void {
var temp:Mat4x4 = new Mat4x4();
temp.translate(tx, ty, tz);
temp.mulEqualMatrix(worldMatrix);
worldMatrix = temp;
}
public function beginScene(background:uint):void {
for (var i:int = 0; i < size; i++) {
fBuffer[i] = background;
zBuffer[i] = 0;
}
worldMatrix.identity();
}
public function renderPolygon(v1:Vertex, v2:Vertex, v3:Vertex):void {
v1.worldPos.setVector(v1.pos.x, v1.pos.y, v1.pos.z);
worldMatrix.mulEqualVector(v1.worldPos);
v2.worldPos.setVector(v2.pos.x, v2.pos.y, v2.pos.z);
worldMatrix.mulEqualVector(v2.worldPos);
v3.worldPos.setVector(v3.pos.x, v3.pos.y, v3.pos.z);
worldMatrix.mulEqualVector(v3.worldPos);
lighting(v1, v2, v3);
v1.viewPos.setVector(v1.worldPos.x, v1.worldPos.y, v1.worldPos.z);
viewMatrix.mulEqualVector(v1.viewPos);
v2.viewPos.setVector(v2.worldPos.x, v2.worldPos.y, v2.worldPos.z);
viewMatrix.mulEqualVector(v2.viewPos);
v3.viewPos.setVector(v3.worldPos.x, v3.worldPos.y, v3.worldPos.z);
viewMatrix.mulEqualVector(v3.viewPos);
clipPolygonDepth(v1, v2, v3, 0);
}
public function light(id:uint):Light {
return lights[id];
}
public function ambient(r:Number, g:Number, b:Number):void {
ambr = r;
ambg = g;
ambb = b;
}
public function material(ambient:Number, diffuse:Number, specular:Number,
shininess:Number, emission:Number, r:Number, g:Number, b:Number):void {
amb = ambient;
dif = diffuse;
spc = specular;
shn = shininess;
emi = emission;
this.r = r;
this.g = g;
this.b = b;
}
private function lighting(v1:Vertex, v2:Vertex, v3:Vertex):void {
// simple lighting
var cr:Number = (amb * ambr + emi) * r;
var cg:Number = (amb * ambg + emi) * g;
var cb:Number = (amb * ambb + emi) * b;
const nor:Vec3D = v2.worldPos.sub(v1.worldPos).cross(v3.worldPos.sub(v2.worldPos));
nor.normalize();
const view:Vec3D = cameraTarget.sub(cameraPosition);
view.normalize();
const ref:Vec3D = new Vec3D();
for (var i:int = 0; i < 8; i++) {
const light:Light = lights[i];
if (light.type == Light.DISABLED) continue;
const lr:Number = light.r;
const lg:Number = light.g;
const lb:Number = light.b;
switch(light.type) {
case Light.DIRECTIONAL: // directional light
const dot:Number = light.dir.dot(nor) * dif;
if (dot > 0) {
cr += r * lr * dot;
cg += g * lg * dot;
cb += b * lb * dot;
}
if (spc > 0) {
// calc reflection vector and specular
// ref = vec - 2 * (nor * vec) * nor
var dots:Number = 2 * nor.dot(view);
ref.setVector(view.x - nor.x * dots, view.y - nor.y * dots, view.z - nor.z * dots);
dots = light.dir.dot(ref);
if (dots > 0) {
dots = Math.pow(dots, shn) * spc;
cr += lr * dots;
cg += lg * dots;
cb += lb * dots;
}
}
break;
}
}
if (cr > 1) cr = 1;
if (cg > 1) cg = 1;
if (cb > 1) cb = 1;
color = (cr * 0xff) << 16 | (cg * 0xff) << 8 | (cb * 0xff);
}
private function clipPolygonDepth(v1:Vertex, v2:Vertex, v3:Vertex, step:int):void {
var flag:int;
var c1:Vertex;
var c2:Vertex;
switch(step) {
case 0:// near
flag = 0;
if (v1.viewPos.z < near) flag |= 1;
if (v2.viewPos.z < near) flag |= 2;
if (v3.viewPos.z < near) flag |= 4;
if (flag != 0) {
switch (flag) {
case 1:// 1
c1 = interpolate(v1, v2, (near - v1.viewPos.z) / (v2.viewPos.z - v1.viewPos.z), false);
c2 = interpolate(v1, v3, (near - v1.viewPos.z) / (v3.viewPos.z - v1.viewPos.z), false);
c1.viewPos.z = near;
c2.viewPos.z = near;
clipPolygonDepth(c1, v2, v3, 1);
clipPolygonDepth(c1, v3, c2, 1);
return;
case 2:// 2
c1 = interpolate(v2, v3, (near - v2.viewPos.z) / (v3.viewPos.z - v2.viewPos.z), false);
c2 = interpolate(v2, v1, (near - v2.viewPos.z) / (v1.viewPos.z - v2.viewPos.z), false);
c1.viewPos.z = near;
c2.viewPos.z = near;
clipPolygonDepth(c1, v3, v1, 1);
clipPolygonDepth(c1, v1, c2, 1);
return;
case 3:// 1 2
c1 = interpolate(v1, v3, (near - v1.viewPos.z) / (v3.viewPos.z - v1.viewPos.z), false);
c2 = interpolate(v2, v3, (near - v2.viewPos.z) / (v3.viewPos.z - v2.viewPos.z), false);
c1.viewPos.z = near;
c2.viewPos.z = near;
clipPolygonDepth(c1, c2, v3, 1);
return;
case 4:// 3
c1 = interpolate(v3, v1, (near - v3.viewPos.z) / (v1.viewPos.z - v3.viewPos.z), false);
c2 = interpolate(v3, v2, (near - v3.viewPos.z) / (v2.viewPos.z - v3.viewPos.z), false);
c1.viewPos.z = near;
c2.viewPos.z = near;
clipPolygonDepth(c1, v1, v2, 1);
clipPolygonDepth(c1, v2, c2, 1);
return;
case 5:// 3 1
c1 = interpolate(v3, v2, (near - v3.viewPos.z) / (v2.viewPos.z - v3.viewPos.z), false);
c2 = interpolate(v1, v2, (near - v1.viewPos.z) / (v2.viewPos.z - v1.viewPos.z), false);
c1.viewPos.z = near;
c2.viewPos.z = near;
clipPolygonDepth(c1, c2, v2, 1);
return;
case 6:// 2 3
c1 = interpolate(v2, v1, (near - v2.viewPos.z) / (v1.viewPos.z - v2.viewPos.z), false);
c2 = interpolate(v3, v1, (near - v3.viewPos.z) / (v1.viewPos.z - v3.viewPos.z), false);
c1.viewPos.z = near;
c2.viewPos.z = near;
clipPolygonDepth(c1, c2, v1, 1);
return;
case 7:// 1 2 3
return;
}
}
case 1:// far
flag = 0;
if (v1.viewPos.z > far) flag |= 1;
if (v2.viewPos.z > far) flag |= 2;
if (v3.viewPos.z > far) flag |= 4;
if (flag != 0) {
switch (flag) {
case 1:// 1
c1 = interpolate(v1, v2, (far - v1.viewPos.z) / (v2.viewPos.z - v1.viewPos.z), false);
c2 = interpolate(v1, v3, (far - v1.viewPos.z) / (v3.viewPos.z - v1.viewPos.z), false);
c1.viewPos.z = far;
c2.viewPos.z = far;
clipPolygonScreen(c1, v2, v3, 0);
clipPolygonScreen(c1, v3, c2, 0);
return;
case 2:// 2
c1 = interpolate(v2, v3, (far - v2.viewPos.z) / (v3.viewPos.z - v2.viewPos.z), false);
c2 = interpolate(v2, v1, (far - v2.viewPos.z) / (v1.viewPos.z - v2.viewPos.z), false);
c1.viewPos.z = far;
c2.viewPos.z = far;
clipPolygonScreen(c1, v3, v1, 0);
clipPolygonScreen(c1, v1, c2, 0);
return;
case 3:// 1 2
c1 = interpolate(v1, v3, (far - v1.viewPos.z) / (v3.viewPos.z - v1.viewPos.z), false);
c2 = interpolate(v2, v3, (far - v2.viewPos.z) / (v3.viewPos.z - v2.viewPos.z), false);
c1.viewPos.z = far;
c2.viewPos.z = far;
clipPolygonScreen(c1, c2, v3, 0);
return;
case 4:// 3
c1 = interpolate(v3, v1, (far - v3.viewPos.z) / (v1.viewPos.z - v3.viewPos.z), false);
c2 = interpolate(v3, v2, (far - v3.viewPos.z) / (v2.viewPos.z - v3.viewPos.z), false);
c1.viewPos.z = far;
c2.viewPos.z = far;
clipPolygonScreen(c1, v1, v2, 0);
clipPolygonScreen(c1, v2, c2, 0);
return;
case 5:// 3 1
c1 = interpolate(v3, v2, (far - v3.viewPos.z) / (v2.viewPos.z - v3.viewPos.z), false);
c2 = interpolate(v1, v2, (far - v1.viewPos.z) / (v2.viewPos.z - v1.viewPos.z), false);
c1.viewPos.z = far;
c2.viewPos.z = far;
clipPolygonScreen(c1, c2, v2, 0);
return;
case 6:// 2 3
c1 = interpolate(v2, v1, (far - v2.viewPos.z) / (v1.viewPos.z - v2.viewPos.z), false);
c2 = interpolate(v3, v1, (far - v3.viewPos.z) / (v1.viewPos.z - v3.viewPos.z), false);
c1.viewPos.z = far;
c2.viewPos.z = far;
clipPolygonScreen(c1, c2, v1, 0);
return;
case 7:// 1 2 3
return;
}
}
}
clipPolygonScreen(v1, v2, v3, 0);
}
private function clipPolygonScreen(v1:Vertex, v2:Vertex, v3:Vertex, step:int):void {
var flag:int;
var c1:Vertex;
var c2:Vertex;
switch(step) {
case 0:// left
{ // transform
var invW:Number;
v1.projPos.setVector(v1.viewPos.x, v1.viewPos.y, v1.viewPos.z, 1);
projectionMatrix.mulEqualVector(v1.projPos);
invW = 1 / v1.projPos.w;
v1.projPos.x *= invW;
v1.projPos.y *= invW;
v1.projPos.z = invW;
v1.projPos.x = width2 + v1.projPos.x * width2 >> 0;
v1.projPos.y = height2 + v1.projPos.y * height2 >> 0;
v2.projPos.setVector(v2.viewPos.x, v2.viewPos.y, v2.viewPos.z);
projectionMatrix.mulEqualVector(v2.projPos);
invW = 1 / v2.projPos.w;
v2.projPos.x *= invW;
v2.projPos.y *= invW;
v2.projPos.z = invW;
v2.projPos.x = width2 + v2.projPos.x * width2 >> 0;
v2.projPos.y = height2 + v2.projPos.y * height2 >> 0;
v3.projPos.setVector(v3.viewPos.x, v3.viewPos.y, v3.viewPos.z);
projectionMatrix.mulEqualVector(v3.projPos);
invW = 1 / v3.projPos.w;
v3.projPos.x *= invW;
v3.projPos.y *= invW;
v3.projPos.z = invW;
v3.projPos.x = width2 + v3.projPos.x * width2 >> 0;
v3.projPos.y = height2 + v3.projPos.y * height2 >> 0;
// culling
if ((v3.projPos.x - v1.projPos.x) * (v2.projPos.y - v1.projPos.y) -
(v3.projPos.y - v1.projPos.y) * (v2.projPos.x - v1.projPos.x) < 0) return;
// TODO:Lighting
}
flag = 0;
if (v1.projPos.x < 0) flag |= 1;
if (v2.projPos.x < 0) flag |= 2;
if (v3.projPos.x < 0) flag |= 4;
if (flag != 0) {
switch (flag) {
case 1:// 1
c1 = interpolate(v1, v2, -v1.projPos.x / (v2.projPos.x - v1.projPos.x), true);
c2 = interpolate(v1, v3, -v1.projPos.x / (v3.projPos.x - v1.projPos.x), true);
c1.projPos.x = 0;
c2.projPos.x = 0;
clipPolygonScreen(c1, v2, v3, 1);
clipPolygonScreen(c1, v3, c2, 1);
return;
case 2:// 2
c1 = interpolate(v2, v3, -v2.projPos.x / (v3.projPos.x - v2.projPos.x), true);
c2 = interpolate(v2, v1, -v2.projPos.x / (v1.projPos.x - v2.projPos.x), true);
c1.projPos.x = 0;
c2.projPos.x = 0;
clipPolygonScreen(c1, v3, v1, 1);
clipPolygonScreen(c1, v1, c2, 1);
return;
case 3:// 1 2
c1 = interpolate(v1, v3, -v1.projPos.x / (v3.projPos.x - v1.projPos.x), true);
c2 = interpolate(v2, v3, -v2.projPos.x / (v3.projPos.x - v2.projPos.x), true);
c1.projPos.x = 0;
c2.projPos.x = 0;
clipPolygonScreen(c1, c2, v3, 1);
return;
case 4:// 3
c1 = interpolate(v3, v1, -v3.projPos.x / (v1.projPos.x - v3.projPos.x), true);
c2 = interpolate(v3, v2, -v3.projPos.x / (v2.projPos.x - v3.projPos.x), true);
c1.projPos.x = 0;
c2.projPos.x = 0;
clipPolygonScreen(c1, v1, v2, 1);
clipPolygonScreen(c1, v2, c2, 1);
return;
case 5:// 3 1
c1 = interpolate(v3, v2, -v3.projPos.x / (v2.projPos.x - v3.projPos.x), true);
c2 = interpolate(v1, v2, -v1.projPos.x / (v2.projPos.x - v1.projPos.x), true);
c1.projPos.x = 0;
c2.projPos.x = 0;
clipPolygonScreen(c1, c2, v2, 1);
return;
case 6:// 2 3
c1 = interpolate(v2, v1, -v2.projPos.x / (v1.projPos.x - v2.projPos.x), true);
c2 = interpolate(v3, v1, -v3.projPos.x / (v1.projPos.x - v3.projPos.x), true);
c1.projPos.x = 0;
c2.projPos.x = 0;
clipPolygonScreen(c1, c2, v1, 1);
return;
case 7:// 1 2 3
return;
}
}
case 1:// right
flag = 0;
if (v1.projPos.x > width) flag |= 1;
if (v2.projPos.x > width) flag |= 2;
if (v3.projPos.x > width) flag |= 4;
if (flag != 0) {
switch (flag) {
case 1:// 1
c1 = interpolate(v1, v2, (width - v1.projPos.x) / (v2.projPos.x - v1.projPos.x), true);
c2 = interpolate(v1, v3, (width - v1.projPos.x) / (v3.projPos.x - v1.projPos.x), true);
c1.projPos.x = width;
c2.projPos.x = width;
clipPolygonScreen(c1, v2, v3, 2);
clipPolygonScreen(c1, v3, c2, 2);
return;
case 2:// 2
c1 = interpolate(v2, v3, (width - v2.projPos.x) / (v3.projPos.x - v2.projPos.x), true);
c2 = interpolate(v2, v1, (width - v2.projPos.x) / (v1.projPos.x - v2.projPos.x), true);
c1.projPos.x = width;
c2.projPos.x = width;
clipPolygonScreen(c1, v3, v1, 2);
clipPolygonScreen(c1, v1, c2, 2);
return;
case 3:// 1 2
c1 = interpolate(v1, v3, (width - v1.projPos.x) / (v3.projPos.x - v1.projPos.x), true);
c2 = interpolate(v2, v3, (width - v2.projPos.x) / (v3.projPos.x - v2.projPos.x), true);
c1.projPos.x = width;
c2.projPos.x = width;
clipPolygonScreen(c1, c2, v3, 2);
return;
case 4:// 3
c1 = interpolate(v3, v1, (width - v3.projPos.x) / (v1.projPos.x - v3.projPos.x), true);
c2 = interpolate(v3, v2, (width - v3.projPos.x) / (v2.projPos.x - v3.projPos.x), true);
c1.projPos.x = width;
c2.projPos.x = width;
clipPolygonScreen(c1, v1, v2, 2);
clipPolygonScreen(c1, v2, c2, 2);
return;
case 5:// 3 1
c1 = interpolate(v3, v2, (width - v3.projPos.x) / (v2.projPos.x - v3.projPos.x), true);
c2 = interpolate(v1, v2, (width - v1.projPos.x) / (v2.projPos.x - v1.projPos.x), true);
c1.projPos.x = width;
c2.projPos.x = width;
clipPolygonScreen(c1, c2, v2, 2);
return;
case 6:// 2 3
c1 = interpolate(v2, v1, (width - v2.projPos.x) / (v1.projPos.x - v2.projPos.x), true);
c2 = interpolate(v3, v1, (width - v3.projPos.x) / (v1.projPos.x - v3.projPos.x), true);
c1.projPos.x = width;
c2.projPos.x = width;
clipPolygonScreen(c1, c2, v1, 2);
return;
case 7:// 1 2 3
return;
}
}
case 2:// top
flag = 0;
if (v1.projPos.y < 0) flag |= 1;
if (v2.projPos.y < 0) flag |= 2;
if (v3.projPos.y < 0) flag |= 4;
if (flag != 0) {
switch (flag) {
case 1:// 1
c1 = interpolate(v1, v2, -v1.projPos.y / (v2.projPos.y - v1.projPos.y), true);
c2 = interpolate(v1, v3, -v1.projPos.y / (v3.projPos.y - v1.projPos.y), true);
c1.projPos.y = 0;
c2.projPos.y = 0;
clipPolygonScreen(c1, v2, v3, 3);
clipPolygonScreen(c1, v3, c2, 3);
return;
case 2:// 2
c1 = interpolate(v2, v3, -v2.projPos.y / (v3.projPos.y - v2.projPos.y), true);
c2 = interpolate(v2, v1, -v2.projPos.y / (v1.projPos.y - v2.projPos.y), true);
c1.projPos.y = 0;
c2.projPos.y = 0;
clipPolygonScreen(c1, v3, v1, 3);
clipPolygonScreen(c1, v1, c2, 3);
return;
case 3:// 1 2
c1 = interpolate(v1, v3, -v1.projPos.y / (v3.projPos.y - v1.projPos.y), true);
c2 = interpolate(v2, v3, -v2.projPos.y / (v3.projPos.y - v2.projPos.y), true);
c1.projPos.y = 0;
c2.projPos.y = 0;
clipPolygonScreen(c1, c2, v3, 3);
return;
case 4:// 3
c1 = interpolate(v3, v1, -v3.projPos.y / (v1.projPos.y - v3.projPos.y), true);
c2 = interpolate(v3, v2, -v3.projPos.y / (v2.projPos.y - v3.projPos.y), true);
c1.projPos.y = 0;
c2.projPos.y = 0;
clipPolygonScreen(c1, v1, v2, 3);
clipPolygonScreen(c1, v2, c2, 3);
return;
case 5:// 3 1
c1 = interpolate(v3, v2, -v3.projPos.y / (v2.projPos.y - v3.projPos.y), true);
c2 = interpolate(v1, v2, -v1.projPos.y / (v2.projPos.y - v1.projPos.y), true);
c1.projPos.y = 0;
c2.projPos.y = 0;
clipPolygonScreen(c1, c2, v2, 3);
return;
case 6:// 2 3
c1 = interpolate(v2, v1, -v2.projPos.y / (v1.projPos.y - v2.projPos.y), true);
c2 = interpolate(v3, v1, -v3.projPos.y / (v1.projPos.y - v3.projPos.y), true);
c1.projPos.y = 0;
c2.projPos.y = 0;
clipPolygonScreen(c1, c2, v1, 3);
return;
case 7:// 1 2 3
return;
}
}
case 3:// bottom
flag = 0;
if (v1.projPos.y > height) flag |= 1;
if (v2.projPos.y > height) flag |= 2;
if (v3.projPos.y > height) flag |= 4;
if (flag != 0) {
switch (flag) {
case 1:// 1
c1 = interpolate(v1, v2, (height - v1.projPos.y) / (v2.projPos.y - v1.projPos.y), true);
c2 = interpolate(v1, v3, (height - v1.projPos.y) / (v3.projPos.y - v1.projPos.y), true);
c1.projPos.y = height;
c2.projPos.y = height;
renderTriangle(c1, v2, v3);
renderTriangle(c1, v3, c2);
return;
case 2:// 2
c1 = interpolate(v2, v3, (height - v2.projPos.y) / (v3.projPos.y - v2.projPos.y), true);
c2 = interpolate(v2, v1, (height - v2.projPos.y) / (v1.projPos.y - v2.projPos.y), true);
c1.projPos.y = height;
c2.projPos.y = height;
renderTriangle(c1, v3, v1);
renderTriangle(c1, v1, c2);
return;
case 3:// 1 2
c1 = interpolate(v1, v3, (height - v1.projPos.y) / (v3.projPos.y - v1.projPos.y), true);
c2 = interpolate(v2, v3, (height - v2.projPos.y) / (v3.projPos.y - v2.projPos.y), true);
c1.projPos.y = height;
c2.projPos.y = height;
renderTriangle(c1, c2, v3);
return;
case 4:// 3
c1 = interpolate(v3, v1, (height - v3.projPos.y) / (v1.projPos.y - v3.projPos.y), true);
c2 = interpolate(v3, v2, (height - v3.projPos.y) / (v2.projPos.y - v3.projPos.y), true);
c1.projPos.y = height;
c2.projPos.y = height;
renderTriangle(c1, v1, v2);
renderTriangle(c1, v2, c2);
return;
case 5:// 3 1
c1 = interpolate(v3, v2, (height - v3.projPos.y) / (v2.projPos.y - v3.projPos.y), true);
c2 = interpolate(v1, v2, (height - v1.projPos.y) / (v2.projPos.y - v1.projPos.y), true);
c1.projPos.y = height;
c2.projPos.y = height;
renderTriangle(c1, c2, v2);
return;
case 6:// 2 3
c1 = interpolate(v2, v1, (height - v2.projPos.y) / (v1.projPos.y - v2.projPos.y), true);
c2 = interpolate(v3, v1, (height - v3.projPos.y) / (v1.projPos.y - v3.projPos.y), true);
c1.projPos.y = height;
c2.projPos.y = height;
renderTriangle(c1, c2, v1);
return;
case 7:// 1 2 3
return;
}
}
}
renderTriangle(v1, v2, v3);
}
private function interpolate(v1:Vertex, v2:Vertex, t:Number, screen:Boolean):Vertex {
var v3:Vertex = new Vertex();
// v3.worldPos.x = v1.worldPos.x + (v2.worldPos.x - v1.worldPos.x) * t;
// v3.worldPos.y = v1.worldPos.y + (v2.worldPos.y - v1.worldPos.y) * t;
// v3.worldPos.z = v1.worldPos.z + (v2.worldPos.z - v1.worldPos.z) * t;
if(screen) {
v3.projPos.x = (v1.projPos.x + (v2.projPos.x - v1.projPos.x) * t) >> 0;
v3.projPos.y = (v1.projPos.y + (v2.projPos.y - v1.projPos.y) * t) >> 0;
v3.projPos.z = v1.projPos.z + (v2.projPos.z - v1.projPos.z) * t;
} else {
v3.viewPos.x = v1.viewPos.x + (v2.viewPos.x - v1.viewPos.x) * t;
v3.viewPos.y = v1.viewPos.y + (v2.viewPos.y - v1.viewPos.y) * t;
v3.viewPos.z = v1.viewPos.z + (v2.viewPos.z - v1.viewPos.z) * t;
}
return v3;
}
private function renderTriangle(v1:Vertex, v2:Vertex, v3:Vertex):void {
var top:Vec3D;
var left:Vec3D;
var right:Vec3D;
if (v1.projPos.y < v2.projPos.y) {
if (v2.projPos.y < v3.projPos.y) {
top = v1.projPos;
left = v2.projPos;
right = v3.projPos;
} else if (v1.projPos.y < v3.projPos.y) {
top = v1.projPos;
left = v3.projPos;
right = v2.projPos;
} else {
top = v3.projPos;
left = v1.projPos;
right = v2.projPos;
}
} else {
if (v2.projPos.y > v3.projPos.y) {
top = v3.projPos;
left = v2.projPos;
right = v1.projPos;
} else if (v1.projPos.y > v3.projPos.y) {
top = v2.projPos;
left = v3.projPos;
right = v1.projPos;
} else {
top = v2.projPos;
left = v1.projPos;
right = v3.projPos;
}
}
var min:int = top.y + 0.5;
var mid:int = left.y + 0.5;
var max:int = right.y + 0.5;
if ((left.x - top.x) / (left.y - top.y) > (right.x - top.x) / (right.y - top.y)) {
var temp:Vec3D = left;
left = right;
right = temp;
}
if (min == max) return;
renderFlat(top, left, right, min, mid, max);
}
private function renderFlat(top:Vec3D, left:Vec3D, right:Vec3D, min:int, mid:int, max:int):void {
var invLength:Number;
const zBuffer:Vector.<Number> = this.zBuffer;
const fBuffer:Vector.<uint> = this.fBuffer;
// thickness
var t:Number = (right.x - top.x) * (left.y - top.y) - (left.x - top.x) * (right.y - top.y);
if (t == 0) return;
t = 1 / t;
// in scanline
var lLength:int = left.y - top.y;
var rLength:int = right.y - top.y;
var lineZ:Number;
const addLineZ:Number = ((right.z - top.z) * lLength - (left.z - top.z) * rLength) * t * 0xffffff;
// left data
var lY:int = left.y;
invLength = 1 / lLength;
var lX:Number = top.x;
var lAddX:Number = (left.x - top.x) * invLength;
var lZ:Number = top.z;
var lAddZ:Number = (left.z - top.z) * invLength;
// right data
var rY:int = right.y;
invLength = 1 / rLength;
var rX:Number = top.x;
var rAddX:Number = (right.x - top.x) * invLength;
var rZ:Number = top.z;
var rAddZ:Number = (right.z - top.z) * invLength;
var y:int = min;
var offset:int = min * width;
while (y < max) {
if (y == mid) {
// flip left and right
if (lY == rY)
return;
if (y == lY) {
lLength = right.y - left.y;
invLength = 1 / lLength;
lX = left.x;
lAddX = (right.x - left.x) * invLength;
lZ = left.z;
lAddZ = (right.z - left.z) * invLength;
}
if (y == rY) {
rLength = left.y - right.y;
invLength = 1 / rLength;
rX = right.x;
rAddX = (left.x - right.x) * invLength;
rZ = right.z;
rAddZ = (left.z - right.z) * invLength;
}
}
const ilx:int = lX;
const irx:int = rX;
if (irx - ilx > 0) {
lineZ = lZ * 0xffffff;
var pix:int = offset + ilx;
const end:int = offset + irx;
while (pix < end) {
if (zBuffer[pix] < lineZ) {
fBuffer[pix] = color;
zBuffer[pix] = lineZ;
}
pix++;
lineZ += addLineZ;
}
}
lX += lAddX;
rX += rAddX;
lZ += lAddZ;
rZ += rAddZ;
offset += width;
y++;
}
}
public function renderPoint(vertex:Vec3D):void {
worldMatrix.mulEqualVector(vertex);
viewMatrix.mulEqualVector(vertex);
projectionMatrix.mulEqualVector(vertex);
var invW:Number = 1 / vertex.w;
vertex.x *= invW;
vertex.y *= invW;
vertex.z *= invW;
vertex.x = (width2 + vertex.x * width2) >> 0;
vertex.y = (height2 + vertex.y * height2) >> 0;
if (vertex.x >= 0 && vertex.x < width && vertex.y >= 0 && vertex.y < height) {
var index:uint = vertex.y * width + vertex.x;
fBuffer[index] = 0xffffff;
}
}
public function endScene():void {
img.setVector(img.rect, fBuffer);
}
public function lookAt(position:Vec3D, target:Vec3D, up:Vec3D):void {
cameraPosition = position;
cameraTarget = target;
cameraUp = up;
var axisZ:Vec3D = cameraTarget.sub(cameraPosition);
axisZ.normalize();
var axisX:Vec3D = cameraUp.cross(axisZ);
axisX.normalize();
var axisY:Vec3D = axisZ.cross(axisX);
viewMatrix.e00 = axisX.x;
viewMatrix.e01 = axisY.x;
viewMatrix.e02 = axisZ.x;
viewMatrix.e03 = 0;
viewMatrix.e10 = axisX.y;
viewMatrix.e11 = axisY.y;
viewMatrix.e12 = axisZ.y;
viewMatrix.e13 = 0;
viewMatrix.e20 = axisX.z;
viewMatrix.e21 = axisY.z;
viewMatrix.e22 = axisZ.z;
viewMatrix.e23 = 0;
viewMatrix.e30 = -axisX.dot(cameraPosition);
viewMatrix.e31 = -axisY.dot(cameraPosition);
viewMatrix.e32 = -axisZ.dot(cameraPosition);
viewMatrix.e33 = 1;
}
public function perspective(fovY:Number, near:Number, far:Number):void {
this.near = near;
this.far = far;
var h:Number = Math.cos(fovY * 0.5) / Math.sin(fovY * 0.5);
var w:Number = h * aspect;
var ffn:Number = far / (far - near);
projectionMatrix.e00 = w;
projectionMatrix.e01 = 0;
projectionMatrix.e02 = 0;
projectionMatrix.e03 = 0;
projectionMatrix.e10 = 0;
projectionMatrix.e11 = h;
projectionMatrix.e12 = 0;
projectionMatrix.e13 = 0;
projectionMatrix.e20 = 0;
projectionMatrix.e21 = 0;
projectionMatrix.e22 = ffn;
projectionMatrix.e23 = 1;
projectionMatrix.e30 = 0;
projectionMatrix.e31 = 0;
projectionMatrix.e32 = -near * ffn;
projectionMatrix.e33 = 0;
}
}
class Light {
public static const DISABLED:uint = 0;
public static const DIRECTIONAL:uint = 1;
public var dir:Vec3D;
public var pos:Vec3D;
public var r:Number;
public var g:Number;
public var b:Number;
public var type:uint;
public function Light() {
type = DISABLED;
dir = new Vec3D();
pos = new Vec3D();
}
public function directional(dx:Number, dy:Number, dz:Number, r:Number, g:Number, b:Number):void {
type = DIRECTIONAL;
dir.setVector(dx, dy, dz);
dir.normalize();
this.r = r;
this.g = g;
this.b = b;
}
public function disable():void {
type = DISABLED;
}
}
class Model {
public var vertices:Vector.<Vertex>;
public var faces:Vector.<Vector.<uint>>;
public function Model() {
vertices = new Vector.<Vertex>();
faces = new Vector.<Vector.<uint>>();
}
public function toBox(w:Number, h:Number, d:Number):void {
vertices[0] = new Vertex(-w, -h, -d);
vertices[1] = new Vertex(w, -h, -d);
vertices[2] = new Vertex(w, -h, d);
vertices[3] = new Vertex(-w, -h, d);
vertices[4] = new Vertex(-w, h, -d);
vertices[5] = new Vertex(w, h, -d);
vertices[6] = new Vertex(w, h, d);
vertices[7] = new Vertex( -w, h, d);
for (var i:int = 0; i < 12; i++)
faces[i] = new Vector.<uint>(3, true);
faces[0][0] = 0;
faces[0][1] = 1;
faces[0][2] = 2;
faces[1][0] = 0;
faces[1][1] = 2;
faces[1][2] = 3;
faces[2][0] = 7;
faces[2][1] = 6;
faces[2][2] = 5;
faces[3][0] = 7;
faces[3][1] = 5;
faces[3][2] = 4;
faces[4][0] = 4;
faces[4][1] = 5;
faces[4][2] = 1;
faces[5][0] = 4;
faces[5][1] = 1;
faces[5][2] = 0;
faces[6][0] = 6;
faces[6][1] = 7;
faces[6][2] = 3;
faces[7][0] = 6;
faces[7][1] = 3;
faces[7][2] = 2;
faces[8][0] = 5;
faces[8][1] = 6;
faces[8][2] = 2;
faces[9][0] = 5;
faces[9][1] = 2;
faces[9][2] = 1;
faces[10][0] = 7;
faces[10][1] = 4;
faces[10][2] = 0;
faces[11][0] = 7;
faces[11][1] = 0;
faces[11][2] = 3;
}
public function render(renderer:Renderer):void {
for (var i:int = 0; i < faces.length; i++)
renderer.renderPolygon(vertices[faces[i][0]], vertices[faces[i][1]], vertices[faces[i][2]]);
}
}
class Vertex {
public var pos:Vec3D;
public var worldPos:Vec3D;
public var viewPos:Vec3D;
public var projPos:Vec3D;
public function Vertex(x:Number = 0, y:Number = 0, z:Number = 0):void {
pos = new Vec3D(x, y, z);
worldPos = new Vec3D();
viewPos = new Vec3D();
projPos = new Vec3D();
}
}
class Vec3D {
/*
* [x y z w]
*/
public var x:Number;
public var y:Number;
public var z:Number;
public var w:Number;
public function Vec3D(x:Number = 0, y:Number = 0, z:Number = 0, w:Number = 0) {
setVector(x, y, z, w);
}
public function setVector(x:Number = 0, y:Number = 0, z:Number = 0, w:Number = 0):void {
this.x = x;
this.y = y;
this.z = z;
this.w = w;
}
public function add(v:Vec3D):Vec3D {
return new Vec3D(x + v.x, y + v.y, z + v.z);
}
public function addEqual(v:Vec3D):void {
x += v.x;
y += v.y;
z += v.z;
}
public function sub(v:Vec3D):Vec3D {
return new Vec3D(x - v.x, y - v.y, z - v.z);
}
public function subEqual(v:Vec3D):void {
x -= v.x;
y -= v.y;
z -= v.z;
}
public function mul(s:Number):Vec3D {
return new Vec3D(x * s, y * s, z * s);
}
public function mulEqual(s:Number):void {
x *= s;
y *= s;
z *= s;
}
public function dot(v:Vec3D):Number {
return x * v.x + y * v.y + z * v.z;
}
public function cross(v:Vec3D):Vec3D {
return new Vec3D(y * v.z - z * v.y, z * v.x - x * v.z, x * v.y - y * v.x);
}
public function length():Number {
return Math.sqrt(x * x + y * y + z * z);
}
public function normalize():void {
var length:Number = length();
if (length != 0 && length != 1) {
length = 1 / length;
x *= length;
y *= length;
z *= length;
}
}
}
class Mat4x4 {
/*
* [e00 e01 e02 e03]
* [e10 e11 e12 e13]
* [e20 e21 e22 e23]
* [e30 e31 e32 e33]
*/
public var e00:Number;
public var e01:Number;
public var e02:Number;
public var e03:Number;
public var e10:Number;
public var e11:Number;
public var e12:Number;
public var e13:Number;
public var e20:Number;
public var e21:Number;
public var e22:Number;
public var e23:Number;
public var e30:Number;
public var e31:Number;
public var e32:Number;
public var e33:Number;
public function Mat4x4(e00:Number = 1, e01:Number = 0, e02:Number = 0, e03:Number = 0,
e10:Number = 0, e11:Number = 1, e12:Number = 0, e13:Number = 0,
e20:Number = 0, e21:Number = 0, e22:Number = 1, e23:Number = 0,
e30:Number = 0, e31:Number = 0, e32:Number = 0, e33:Number = 1) {
setMatrix(e00, e01, e02, e03, e10, e11, e12, e13,
e20, e21, e22, e23, e30, e31, e32, e33);
}
public function identity():void {
setMatrix();
}
public function setMatrix(e00:Number = 1, e01:Number = 0, e02:Number = 0, e03:Number = 0,
e10:Number = 0, e11:Number = 1, e12:Number = 0, e13:Number = 0,
e20:Number = 0, e21:Number = 0, e22:Number = 1, e23:Number = 0,
e30:Number = 0, e31:Number = 0, e32:Number = 0, e33:Number = 1):void {
this.e00 = e00;
this.e01 = e01;
this.e02 = e02;
this.e03 = e03;
this.e10 = e10;
this.e11 = e11;
this.e12 = e12;
this.e13 = e13;
this.e20 = e20;
this.e21 = e21;
this.e22 = e22;
this.e23 = e23;
this.e30 = e30;
this.e31 = e31;
this.e32 = e32;
this.e33 = e33;
}
public function rotateX(theta:Number):void {
var sin:Number = Math.sin(theta);
var cos:Number = Math.cos(theta);
var m:Mat4x4 = new Mat4x4();
m.e11 = cos;
m.e12 = sin;
m.e21 = -sin;
m.e22 = cos;
mulEqualMatrix(m);
}
public function rotateY(theta:Number):void {
var sin:Number = Math.sin(theta);
var cos:Number = Math.cos(theta);
var m:Mat4x4 = new Mat4x4();
m.e00 = cos;
m.e02 = sin;
m.e20 = -sin;
m.e22 = cos;
mulEqualMatrix(m);
}
public function rotateZ(theta:Number):void {
var sin:Number = Math.sin(theta);
var cos:Number = Math.cos(theta);
var m:Mat4x4 = new Mat4x4();
m.e00 = cos;
m.e01 = -sin;
m.e10 = sin;
m.e11 = cos;
mulEqualMatrix(m);
}
public function translate(tx:Number, ty:Number, tz:Number):void {
var m:Mat4x4 = new Mat4x4();
m.e30 = tx;
m.e31 = ty;
m.e32 = tz;
mulEqualMatrix(m);
}
public function scale(sx:Number, sy:Number, sz:Number):void {
var m:Mat4x4 = new Mat4x4();
m.e00 = sx;
m.e11 = sy;
m.e22 = sz;
mulEqualMatrix(m);
}
public function mulMatrix(m:Mat4x4):Mat4x4 {
var t11:Number = e00 * m.e00 + e01 * m.e10 + e02 * m.e20 + e03 * m.e30;
var t12:Number = e00 * m.e01 + e01 * m.e11 + e02 * m.e21 + e03 * m.e31;
var t13:Number = e00 * m.e02 + e01 * m.e12 + e02 * m.e22 + e03 * m.e32;
var t14:Number = e00 * m.e03 + e01 * m.e13 + e02 * m.e23 + e03 * m.e33;
var t21:Number = e10 * m.e00 + e11 * m.e10 + e12 * m.e20 + e13 * m.e30;
var t22:Number = e10 * m.e01 + e11 * m.e11 + e12 * m.e21 + e13 * m.e31;
var t23:Number = e10 * m.e02 + e11 * m.e12 + e12 * m.e22 + e13 * m.e32;
var t24:Number = e10 * m.e03 + e11 * m.e13 + e12 * m.e23 + e13 * m.e33;
var t31:Number = e20 * m.e00 + e21 * m.e10 + e22 * m.e20 + e23 * m.e30;
var t32:Number = e20 * m.e01 + e21 * m.e11 + e22 * m.e21 + e23 * m.e31;
var t33:Number = e20 * m.e02 + e21 * m.e12 + e22 * m.e22 + e23 * m.e32;
var t34:Number = e20 * m.e03 + e21 * m.e13 + e22 * m.e23 + e23 * m.e33;
var t41:Number = e30 * m.e00 + e31 * m.e10 + e32 * m.e20 + e33 * m.e30;
var t42:Number = e30 * m.e01 + e31 * m.e11 + e32 * m.e21 + e33 * m.e31;
var t43:Number = e30 * m.e02 + e31 * m.e12 + e32 * m.e22 + e33 * m.e32;
var t44:Number = e30 * m.e03 + e31 * m.e13 + e32 * m.e23 + e33 * m.e33;
return new Mat4x4(t11, t12, t13, t14, t21, t22, t23, t24, t31, t32, t33, t34, t41,
t42, t43, t44);
}
public function mulEqualMatrix(m:Mat4x4):void {
var t11:Number = e00 * m.e00 + e01 * m.e10 + e02 * m.e20 + e03 * m.e30;
var t12:Number = e00 * m.e01 + e01 * m.e11 + e02 * m.e21 + e03 * m.e31;
var t13:Number = e00 * m.e02 + e01 * m.e12 + e02 * m.e22 + e03 * m.e32;
var t14:Number = e00 * m.e03 + e01 * m.e13 + e02 * m.e23 + e03 * m.e33;
var t21:Number = e10 * m.e00 + e11 * m.e10 + e12 * m.e20 + e13 * m.e30;
var t22:Number = e10 * m.e01 + e11 * m.e11 + e12 * m.e21 + e13 * m.e31;
var t23:Number = e10 * m.e02 + e11 * m.e12 + e12 * m.e22 + e13 * m.e32;
var t24:Number = e10 * m.e03 + e11 * m.e13 + e12 * m.e23 + e13 * m.e33;
var t31:Number = e20 * m.e00 + e21 * m.e10 + e22 * m.e20 + e23 * m.e30;
var t32:Number = e20 * m.e01 + e21 * m.e11 + e22 * m.e21 + e23 * m.e31;
var t33:Number = e20 * m.e02 + e21 * m.e12 + e22 * m.e22 + e23 * m.e32;
var t34:Number = e20 * m.e03 + e21 * m.e13 + e22 * m.e23 + e23 * m.e33;
var t41:Number = e30 * m.e00 + e31 * m.e10 + e32 * m.e20 + e33 * m.e30;
var t42:Number = e30 * m.e01 + e31 * m.e11 + e32 * m.e21 + e33 * m.e31;
var t43:Number = e30 * m.e02 + e31 * m.e12 + e32 * m.e22 + e33 * m.e32;
var t44:Number = e30 * m.e03 + e31 * m.e13 + e32 * m.e23 + e33 * m.e33;
setMatrix(t11, t12, t13, t14, t21, t22, t23, t24, t31, t32, t33, t34, t41,
t42, t43, t44);
}
public function mulVector(v:Vec3D):Vec3D {
return new Vec3D(e00 * v.x + e10 * v.y + e20 * v.z + e30,
e01 * v.x + e11 * v.y + e21 * v.z + e31,
e02 * v.x + e12 * v.y + e22 * v.z + e32,
e03 * v.x + e13 * v.y + e23 * v.z + e33);
}
public function mulEqualVector(v:Vec3D):void {
v.setVector(e00 * v.x + e10 * v.y + e20 * v.z + e30,
e01 * v.x + e11 * v.y + e21 * v.z + e31,
e02 * v.x + e12 * v.y + e22 * v.z + e32,
e03 * v.x + e13 * v.y + e23 * v.z + e33);
}
}