Polygon Clipping(Soft3D 2.5)
ポリゴンを視錘台でクリッピングします。
前後はスクリーン変換前、
上下左右はスクリーン変換後クリッピングを行っています。
クリッピングには線形補間を使用しました。
誤差によるズレをなくすためクリッピングされた頂点は明示的に座標を代入しています。
※完成した物は随時ここにまとめています http://el-ement.com/labs/fl3d/
/**
* Copyright saharan ( http://wonderfl.net/user/saharan )
* MIT License ( http://www.opensource.org/licenses/mit-license.php )
* Downloaded from: http://wonderfl.net/c/cAxB
*/
package {
import flash.display.*;
import flash.events.*;
import flash.text.*;
import net.hires.debug.*;
[SWF(frameRate = "50", width="465", height="465")]
/**
* Software rendering in ActionScript3.0 #2.5
* @author saharan
*/
public class FlashSoft3D extends Sprite {
private var r:Renderer;
private var count:uint;
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);
addChild(r.image);
debug = new TextField();
debug.x = 200;
debug.textColor = 0xffffff;
// addChild(new Stats());
addChild(debug);
addEventListener(Event.ENTER_FRAME, frame);
}
private function hsv(h:Number, s:Number, v:Number):uint {
h %= 360;
var i:int = h / 60;
var f:Number = h / 60 - i;
var b:int = v * 255;
var p:int = b * (1 - s);
var q:int = b * (1 - f * s);
var t:int = b * (1 - (1 - f) * s);
switch (i) {
case 0: return b << 16 | t << 8 | p;
case 1: return q << 16 | b << 8 | p;
case 2: return p << 16 | b << 8 | t;
case 3: return p << 16 | q << 8 | b;
case 4: return t << 16 | p << 8 | b;
case 5: return b << 16 | p << 8 | q;
}
return 0;
}
private function frame(e:Event = null):void {
count++;
r.beginScene(0x000000);
r.rotateY(count / 50);
r.rotateX(count / 100);
var i:int;
var j:int;
for (i = -3; i <= 3; i++) {
for (j = -3; j <= 3; j++) {
r.push();
r.translate(i * 16, j * 16, 0);
r.rotateY(count / 50 + i * 0.2);
r.rotateX(count / 100 + j * 0.2);
Renderer.color = hsv(((j + 5) * 10 + i + 5) * 365 / 100, 1, 1);
box(2, 3, 4);
r.pop();
}
}
r.endScene();
}
private function box(w:Number, h:Number, d:Number):void {
polygon(new Vertex(-w, -h, d), new Vertex(w, -h, d),
new Vertex(w, h, d), new Vertex(-w, h, d));
polygon(new Vertex(-w, h, -d), new Vertex(w, h, -d),
new Vertex(w, -h, -d), new Vertex(-w, -h, -d));
polygon(new Vertex(w, -h, -d), new Vertex(w, h, -d),
new Vertex(w, h, d), new Vertex(w, -h, d));
polygon(new Vertex(-w, h, -d), new Vertex(-w, -h, -d),
new Vertex(-w, -h, d), new Vertex(-w, h, d));
polygon(new Vertex(-w, -h, -d), new Vertex(w, -h, -d),
new Vertex(w, -h, d), new Vertex(-w, -h, d));
polygon(new Vertex(-w, h, d), new Vertex(w, h, d),
new Vertex(w, h, -d), new Vertex(-w, h, -d));
}
private function polygon(v1:Vertex, v2:Vertex, v3:Vertex, v4:Vertex):void {
r.renderPolygon(v1, v2, v3);
r.renderPolygon(v1, v3, v4);
}
}
}
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>;
public static var color:uint;
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);
stack = new Vector.<Mat4x4>();
worldMatrix = new Mat4x4();
viewMatrix = new Mat4x4();
projectionMatrix = new Mat4x4();
lookAt(new Vec3D(0, 0, 50), new Vec3D(0, 0, 0), new Vec3D(0, 1, 0));
perspective(60 * Math.PI / 180, 5, 5000);
}
public function get image():Bitmap {
return bitmap;
}
public function push():void {
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 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 {
fBuffer = img.getVector(img.rect);
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);
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);
// TODO:Lighting
}
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));
c2 = interpolate(v1, v3, (near - v1.viewPos.z) / (v3.viewPos.z - v1.viewPos.z));
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));
c2 = interpolate(v2, v1, (near - v2.viewPos.z) / (v1.viewPos.z - v2.viewPos.z));
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));
c2 = interpolate(v2, v3, (near - v2.viewPos.z) / (v3.viewPos.z - v2.viewPos.z));
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));
c2 = interpolate(v3, v2, (near - v3.viewPos.z) / (v2.viewPos.z - v3.viewPos.z));
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));
c2 = interpolate(v1, v2, (near - v1.viewPos.z) / (v2.viewPos.z - v1.viewPos.z));
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));
c2 = interpolate(v3, v1, (near - v3.viewPos.z) / (v1.viewPos.z - v3.viewPos.z));
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));
c2 = interpolate(v1, v3, (far - v1.viewPos.z) / (v3.viewPos.z - v1.viewPos.z));
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));
c2 = interpolate(v2, v1, (far - v2.viewPos.z) / (v1.viewPos.z - v2.viewPos.z));
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));
c2 = interpolate(v2, v3, (far - v2.viewPos.z) / (v3.viewPos.z - v2.viewPos.z));
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));
c2 = interpolate(v3, v2, (far - v3.viewPos.z) / (v2.viewPos.z - v3.viewPos.z));
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));
c2 = interpolate(v1, v2, (far - v1.viewPos.z) / (v2.viewPos.z - v1.viewPos.z));
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));
c2 = interpolate(v3, v1, (far - v3.viewPos.z) / (v1.viewPos.z - v3.viewPos.z));
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;
}
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));
c2 = interpolate(v1, v3, -v1.projPos.x / (v3.projPos.x - v1.projPos.x));
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));
c2 = interpolate(v2, v1, -v2.projPos.x / (v1.projPos.x - v2.projPos.x));
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));
c2 = interpolate(v2, v3, -v2.projPos.x / (v3.projPos.x - v2.projPos.x));
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));
c2 = interpolate(v3, v2, -v3.projPos.x / (v2.projPos.x - v3.projPos.x));
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));
c2 = interpolate(v1, v2, -v1.projPos.x / (v2.projPos.x - v1.projPos.x));
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));
c2 = interpolate(v3, v1, -v3.projPos.x / (v1.projPos.x - v3.projPos.x));
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));
c2 = interpolate(v1, v3, (width - v1.projPos.x) / (v3.projPos.x - v1.projPos.x));
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));
c2 = interpolate(v2, v1, (width - v2.projPos.x) / (v1.projPos.x - v2.projPos.x));
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));
c2 = interpolate(v2, v3, (width - v2.projPos.x) / (v3.projPos.x - v2.projPos.x));
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));
c2 = interpolate(v3, v2, (width - v3.projPos.x) / (v2.projPos.x - v3.projPos.x));
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));
c2 = interpolate(v1, v2, (width - v1.projPos.x) / (v2.projPos.x - v1.projPos.x));
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));
c2 = interpolate(v3, v1, (width - v3.projPos.x) / (v1.projPos.x - v3.projPos.x));
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));
c2 = interpolate(v1, v3, -v1.projPos.y / (v3.projPos.y - v1.projPos.y));
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));
c2 = interpolate(v2, v1, -v2.projPos.y / (v1.projPos.y - v2.projPos.y));
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));
c2 = interpolate(v2, v3, -v2.projPos.y / (v3.projPos.y - v2.projPos.y));
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));
c2 = interpolate(v3, v2, -v3.projPos.y / (v2.projPos.y - v3.projPos.y));
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));
c2 = interpolate(v1, v2, -v1.projPos.y / (v2.projPos.y - v1.projPos.y));
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));
c2 = interpolate(v3, v1, -v3.projPos.y / (v1.projPos.y - v3.projPos.y));
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));
c2 = interpolate(v1, v3, (height - v1.projPos.y) / (v3.projPos.y - v1.projPos.y));
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));
c2 = interpolate(v2, v1, (height - v2.projPos.y) / (v1.projPos.y - v2.projPos.y));
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));
c2 = interpolate(v2, v3, (height - v2.projPos.y) / (v3.projPos.y - v2.projPos.y));
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));
c2 = interpolate(v3, v2, (height - v3.projPos.y) / (v2.projPos.y - v3.projPos.y));
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));
c2 = interpolate(v1, v2, (height - v1.projPos.y) / (v2.projPos.y - v1.projPos.y));
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));
c2 = interpolate(v3, v1, (height - v3.projPos.y) / (v1.projPos.y - v3.projPos.y));
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):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;
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;
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;
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 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;
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 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);
}
}