Flash/Flex学习笔记(44)：3D线条与填充

3D线条：把上一篇中的3D坐标旋转示例稍做修改，用线把各个小球连接起来即可。

var balls:Array;

var numBalls:uint=30;

 
var fl:Number=250;

 
var vpx:Number=stage.stageWidth/2;

 
var vpy:Number=stage.stageHeight/2;

 
function init():void {

 
balls=new Array(numBalls);

 
for (var i:uint=0; i<numBalls; i++) {

 
var ball:Ball3D=new Ball3D(0,0x000000);//注意：我们只需要线条，不需要小球，所以这里把小球的半径设置为0

 
balls[i]=ball;

ball.xpos = (Math.random()*2-1)*100;

 
ball.ypos = (Math.random()*2-1)*100;

 
ball.zpos = (Math.random()*2-1)*100;

 
addChild(ball);

 
}

 
addEventListener(Event.ENTER_FRAME,EnterFrameHandler);

 
}

 
function EnterFrameHandler(e:Event):void {

 
var dx:Number=mouseX-vpx;

 
var dy:Number=mouseY-vpy;

 
var angleY:Number=dx*0.0005;

 
var angleX:Number=dy*0.0005;

 
var angleZ:Number=Math.sqrt(dx*dx+dy*dy)*0.0005;

 
if (dx>0) {

 
angleZ*=-1;

 
}//以鼠标所在点的x坐标相对于消失点的位置为判断依据，左侧z轴正向旋转，右侧z轴反向旋转

 
for (var i:uint; i<numBalls; i++) {

 
var b:Ball3D=balls[i];

rotateX(b,angleX);

 
rotateY(b,angleY);

 
rotateZ(b,angleZ);

 
doPerspective(b);

 
}

 
//画线(注：画线处理，只能在所有旋转及透视完成之后再处理，否则如果先画好线，再处理旋转的话，因为小球的坐标已经变了，所以看上去线条的接头有可能不连续)

 
graphics.clear();

 
graphics.lineStyle(0);

 
graphics.moveTo(balls[0].x, balls[0].y);

 
for (i = 1; i < numBalls; i++) {     

 
graphics.lineTo(balls[i].x, balls[i].y);

}

 
graphics.lineTo(balls[0].x, balls[0].y);

 
//sortZ(); //注意:这里不能加z轴排序，因为z轴排序会不断修正小球的数组索引，导致上面的每跟线条的连接两端不断变化，在视觉上就产生了抖动

 
}

 
//x轴的坐标旋转

 
function rotateX(ball:Ball3D, angleX:Number):void {

 
var cosX:Number=Math.cos(angleX);

 
var sinX:Number=Math.sin(angleX);

 
var y1:Number=ball.ypos*cosX-ball.zpos*sinX;

 
var z1:Number=ball.zpos*cosX+ball.ypos*sinX;

 
ball.ypos=y1;

 
ball.zpos=z1;

 
}

 
//y轴的坐标旋转

 
function rotateY(ball:Ball3D, angleY:Number):void {

 
var cosY:Number=Math.cos(angleY);

 
var sinY:Number=Math.sin(angleY);

 
var x1:Number=ball.xpos*cosY-ball.zpos*sinY;

 
var z1:Number=ball.zpos*cosY+ball.xpos*sinY;

 
ball.xpos=x1;

ball.zpos=z1;

}

 
//z轴的坐标旋转

 
function rotateZ(ball:Ball3D, angleZ:Number):void {

var cosZ:Number=Math.cos(angleZ);

 
var sinZ:Number=Math.sin(angleZ);

 
var x1:Number=ball.xpos*cosZ-ball.ypos*sinZ;

 
var y1:Number=ball.ypos*cosZ+ball.xpos*sinZ;

 
ball.xpos=x1;

 
ball.ypos=y1;

 
}

 
//3D透视处理  
function doPerspective(ball:Ball3D):void {

 
if (ball.zpos>- fl) {

var scale:Number = fl / (fl + ball.zpos);

ball.scaleX=ball.scaleY=scale;

ball.x=vpx+ball.xpos*scale;

 
ball.y=vpy+ball.ypos*scale;

 
//ball.alpha = scale*0.65;

ball.visible=true;

 
} else {

 
ball.visible=false;

 
}

 
}

 
//z轴排序

function sortZ():void {

balls.sortOn("zpos",Array.DESCENDING|Array.NUMERIC);

 
for (var i:uint=0; i<numBalls; i++) {

 
setChildIndex(balls[i],i);

 
}

 
}

init();

如果从性能优化的角度考虑：Ball3D类用在这里比较浪费，Ball3D继承自Sprite，而我们在这里其实仅仅只要一个拥有少数几个属性(比如xpos,ypos,zpos之类)的点而已，对于Sprite默认的其它属性，包括事件支持，都是不需要的。

所以...我们又多出了一个新类Point3D

 
package {

 
public class Point3D {

public var fl:Number=250;

 
private var vpX:Number=0;

private var vpY:Number=0;

 
private var cX:Number=0;

 
private var cY:Number=0;

 
private var cZ:Number=0;

 
public var x:Number=0;

public var y:Number=0;

 
public var z:Number=0;      

 
public function Point3D(x:Number=0, y:Number=0, z:Number=0) {

 
this.x=x;

 
this.y=y;

 
this.z=z;

}

 
public function setVanishingPoint(vpX:Number, vpY:Number):void {

this.vpX=vpX;

 
this.vpY=vpY;

 
}

 
public function setCenter(cX:Number,cY:Number,cZ:Number=0):void {

 
this.cX=cX;

 
this.cY=cY;

 
this.cZ=cZ;

 
}

 
public function get screenX():Number {

 
var scale:Number = fl / (fl + z + cZ);

 
return vpX + cX + x * scale;

}

 
public function get screenY():Number {

 
var scale:Number = fl / (fl + z + cZ);

 
return vpY + cY + y * scale;

 
}

 
public function rotateX(angleX:Number):void {

var cosX:Number=Math.cos(angleX);

 
var sinX:Number=Math.sin(angleX);

var y1:Number=y*cosX-z*sinX;

 
var z1:Number=z*cosX+y*sinX;

 
y=y1;

z=z1;

}

public function rotateY(angleY:Number):void {

 
var cosY:Number=Math.cos(angleY);

var sinY:Number=Math.sin(angleY);

var x1:Number=x*cosY-z*sinY;

 
var z1:Number=z*cosY+x*sinY;

 
x=x1;

 
z=z1;

 
}

public function rotateZ(angleZ:Number):void {

 
var cosZ:Number=Math.cos(angleZ);

 
var sinZ:Number=Math.sin(angleZ);

 
var x1:Number=x*cosZ-y*sinZ;

 
var y1:Number=y*cosZ+x*sinZ;

 
x=x1;

y=y1;

}

}

}

利用这个类重写最开头的示例：

package {

 
import flash.display.Sprite;

 
import flash.events.Event;

public class Lines3D_B extends Sprite {

 
private var points:Array;

private var numPoints:uint=50;

 
private var fl:Number=250;

 
private var vpX:Number=stage.stageWidth/2;

 
private var vpY:Number=stage.stageHeight/2;

public function Lines3D_B() {

init();

 
}

 
private function init():void {

 
points = new Array();

 
for (var i:uint = 0; i < numPoints; i++) {

 
var point:Point3D=new Point3D(Math.random()*200-100,Math.random()*200-100,Math.random()*200-100);

 
point.setVanishingPoint(vpX, vpY);

points.push(point);

}

addEventListener(Event.ENTER_FRAME, onEnterFrame);

 
}

 
private function onEnterFrame(event:Event):void {

 
var angleX:Number = (mouseY - vpY) * .001;

 
var angleY:Number = (mouseX - vpX) * .001;

for (var i:uint = 0; i < numPoints; i++) {

 
var point:Point3D=points[i];

 
point.rotateX(angleX);

 
point.rotateY(angleY);

 
}

 
graphics.clear();

 
graphics.lineStyle(0);

 
graphics.moveTo(points[0].screenX, points[0].screenY);

 
for (i = 1; i < numPoints; i++) {

 
graphics.lineTo(points[i].screenX, points[i].screenY);

 
}

 
}

 
}

 
}

上面的示例各线条的节点都是随机分布在三维空间的，如果把这些点按一定的顺序排列好，结果会更有趣：

上图示意了一个z轴平面的正方形，其4个顶点的(x,y,z)坐标如图所示

package {

import flash.display.Sprite;

 
import flash.events.Event;

 
public class Square3D extends Sprite {

 
private var points:Array;

private var numPoints:uint=4;

private var fl:Number=250;

 
private var vpX:Number=stage.stageWidth/2;

 
private var vpY:Number=stage.stageHeight/2;

public function Square3D() {

init();

 
}

 
private function init():void {

 
points = new Array();

 
points[0]=new Point3D(-80,-80,50);

 
points[1]=new Point3D(80,-80,50);

 
points[2]=new Point3D(80,80,50);

 
points[3]=new Point3D(-80,80,50);

//设置每个点的消失点

for (var i:uint = 0; i < numPoints; i++) {

 
points[i].setVanishingPoint(vpX, vpY);

 
}

 
addEventListener(Event.ENTER_FRAME, EnterFrameHandler);

}

 
private function EnterFrameHandler(e:Event):void {

var dx:Number = mouseX - vpX;

 
var dy:Number = mouseY - vpY;

var angleX:Number = dy * 0.001;

 
var angleY:Number = dx * 0.001;

 
var angleZ:Number = Math.sqrt(dx*dx+dy*dy)*0.0005;

 
if (dx>0){angleZ*=-1;}

 
for (var i:uint = 0; i < numPoints; i++) {

 
var point:Point3D=points[i];

 
point.rotateX(angleX);

 
point.rotateY(angleY);

 
point.rotateZ(angleZ);

 
}

graphics.clear();

 
graphics.lineStyle(0);

graphics.moveTo(points[0].screenX, points[0].screenY);          

 
for (i = 1; i < numPoints; i++) {

 
graphics.lineTo(points[i].screenX, points[i].screenY);

 
}

 
graphics.lineTo(points[0].screenX, points[0].screenY);

 
}

 
}

 
}

ok，我们成功的搞出了一个在三维空间晃荡的正方形!

理解这种思路后，理论上可以做出任意的几何形状，比如下面这张图：

var pointNum:int=10;

var points:Array = new Array();

var vpX:Number=stage.stageWidth/2;

var vpY:Number=stage.stageHeight/2;

function Init():void {

points.push(new Point3D(-100,-140,0));

 
points.push(new Point3D(100,-140,0));

 
points.push(new Point3D(100,-90,0));

 
points.push(new Point3D(-40,-90,0));

 
points.push(new Point3D(-40,-40,0));

 
points.push(new Point3D(80,-40,0));

 
points.push(new Point3D(80,10,0));

 
points.push(new Point3D(-40,10,0));

 
points.push(new Point3D(-40,140,0));

 
points.push(new Point3D(-100,140,0));

for (var i:uint = 0; i < pointNum; i++) {

 
points[i].setVanishingPoint(vpX, vpY);

points[i].setCenter(0, 0, 100);

 
}

 
addEventListener(Event.ENTER_FRAME, EnterFrameHandler);

}

 
function EnterFrameHandler(e:Event):void {

var dx:Number=mouseX-vpX;

var dy:Number=mouseY-vpY;

 
var angleX:Number=dy*0.001;

 
var angleY:Number=dx*0.001;

 
var angleZ:Number=Math.sqrt(dx*dx+dy*dy)*0.0005;

 
if (dx>0) {

angleZ*=-1;

 
}

for (var i:uint = 0; i < pointNum; i++) {

 
var point:Point3D=points[i];

 
point.rotateX(angleX);

 
point.rotateY(angleY);

 
point.rotateZ(angleZ);

 
}

 
Draw();

 
}

 
function Draw():void {

 
graphics.clear();

 
graphics.lineStyle(1);

graphics.beginFill(0xff0000);

 
graphics.moveTo(points[0].screenX,points[0].screenY);

for (var i:uint=1; i<pointNum; i++) {

graphics.lineTo(points[i].screenX,points[i].screenY);

}

 
graphics.lineTo(points[0].screenX,points[0].screenY);

 
graphics.endFill();

}

 
Init();

如果形状是没有空洞的，上面的办法无疑是最方便的办法，但是如果形状本身上有“洞”，比如下面这样：

如果仍然套用上面的方法，至少还得多写段代码处理中间这个空洞的"画线"，再极端一点想象：如果形状中的空洞不止一个，有很多个的话，处理的代码就更复杂了。通常在3D编程中，业内更倾向于用“三角形”来处理这种复杂情况。如上图所示：整个A可以看作是0到10一共是11个小三角形组成的，可以先把三角形抽象成一个类

package

 
{

 
import flash.display.Graphics;

 
public class Triangle

 
{

private var pointA:Point3D;

 
private var pointB:Point3D;

 
private var pointC:Point3D;

 
private var color:uint;

public function Triangle(a:Point3D, b:Point3D, c:Point3D, color:uint)

 
{

 
pointA = a;

pointB = b;

 
pointC = c;

this.color = color;

 
}

 
public function draw(g:Graphics):void

 
{
g.beginFill(color);

 
g.moveTo(pointA.screenX, pointA.screenY);

 
g.lineTo(pointB.screenX, pointB.screenY);

 
g.lineTo(pointC.screenX, pointC.screenY);

 
g.lineTo(pointA.screenX, pointA.screenY);

 
g.endFill();

}

}

}

接下来的事情就比较简单了，定义一个三角形数组，然后根据顶点坐标初始化这个数组，然后各顶点的坐标该咋旋转就咋旋转，完事之后重新填充绘制三角形数组。

var pointNum:int = 11;

 
var points:Array = new Array(pointNum);

 
var triangles:Array;//三角形数组

 
var vpX:Number = stage.stageWidth / 2;

var vpY:Number = stage.stageHeight / 2;

function Init():void {

 
points[0] = new Point3D(-50,-250,100);

 
points[1] = new Point3D(50,-250,100);

 
points[2] = new Point3D(200,250,100);

 
points[3] = new Point3D(100,250,100);

 
points[4] = new Point3D(50,100,100);

 
points[5] = new Point3D(-50,100,100);

 
points[6] = new Point3D(-100,250,100);

 
points[7] = new Point3D(-200,250,100);

 
points[8] = new Point3D(0,-150,100);

 
points[9] = new Point3D(50,0,100);

 
points[10] = new Point3D(-50,0,100);

 
for (var i:uint = 0; i < pointNum; i++) {

 
points[i].setVanishingPoint(vpX, vpY);

 
points[i].setCenter(0, 0, 450);

}

 
//根据顶点赋值三角形数组

 
triangles = new Array();

 
triangles[0] = new Triangle(points[0],points[1],points[8],0xff0000);

 
triangles[1] = new Triangle(points[1],points[9],points[8],0xff0000);

 
triangles[2] = new Triangle(points[1],points[2],points[9],0xff0000);

 
triangles[3] = new Triangle(points[2],points[4],points[9],0xff0000);

 
triangles[4] = new Triangle(points[2],points[3],points[4],0xff0000);

 
triangles[5] = new Triangle(points[4],points[5],points[9],0xff0000);

 
triangles[6] = new Triangle(points[9],points[5],points[10],0xff0000);

 
triangles[7] = new Triangle(points[5],points[6],points[7],0xff0000);

 
triangles[8] = new Triangle(points[5],points[7],points[10],0xff0000);

 
triangles[9] = new Triangle(points[0],points[10],points[7],0xff0000);

triangles[10] = new Triangle(points[0],points[8],points[10],0xff0000);

addEventListener(Event.ENTER_FRAME, EnterFrameHandler);

 
}

 
function EnterFrameHandler(e:Event):void {

 
var dx:Number = mouseX - vpX;

 
var dy:Number = mouseY - vpY;

 
var angleX:Number = dy * 0.001;

var angleY:Number = dx * 0.001;

 
var angleZ:Number = Math.sqrt(dx * dx + dy * dy) * 0.0005;

 
if (dx > 0) {

 
angleZ *=  -1;

 
}

 
for (var i:uint = 0; i < pointNum; i++) {

 
var point:Point3D = points[i];

 
point.rotateX(angleX);

point.rotateY(angleY);

 
point.rotateZ(angleZ);

 
}

 
graphics.clear();

 
//画三角形

 
for (i=0; i<triangles.length; i++) {

 
triangles[i].draw(graphics);

 
}

}

 
Init();

旋转的立方体

示意图如下:

var pointNum:int = 8;

var points:Array = new Array(pointNum);

 
var triangles:Array;//三角形数组

 
var vpX:Number = stage.stageWidth / 2;

 
var vpY:Number = stage.stageHeight / 2;

 
function Init():void {

 
//前面四个角

 
points[0] = new Point3D(-100,-100,-100);

 
points[1] = new Point3D( 100,-100,-100);

 
points[2] = new Point3D( 100, 100,-100);

 
points[3] = new Point3D(-100, 100,-100);

 
//后面四个角

points[4] = new Point3D(-100,-100, 100);

 
points[5] = new Point3D( 100,-100, 100);

 
points[6] = new Point3D( 100, 100, 100);

 
points[7] = new Point3D(-100, 100, 100);    

 
for (var i:uint = 0; i < pointNum; i++) {

 
points[i].setVanishingPoint(vpX, vpY);

 
points[i].setCenter(0, 0, 100);

 
}

 
//根据顶点赋值三角形数组

 
triangles = new Array();

 
var _t:Number = Math.random() * 0xffffff;

 
triangles[0] = new Triangle(points[0],points[1],points[2],_t);

 
triangles[1] = new Triangle(points[0],points[2],points[3],_t);

 
_t = Math.random() * 0xffffff;

 
triangles[2] = new Triangle(points[0],points[5],points[1],_t);

 
triangles[3] = new Triangle(points[0],points[4],points[5],_t);

 
_t = Math.random() * 0xffffff;

triangles[4] = new Triangle(points[4],points[6],points[5],_t);

 
triangles[5] = new Triangle(points[4],points[7],points[6],_t);

 
_t = Math.random() * 0xffffff;

 
triangles[6] = new Triangle(points[3],points[2],points[6],_t);

triangles[7] = new Triangle(points[3],points[6],points[7],_t);

 
_t = Math.random() * 0xffffff;

 
triangles[8] = new Triangle(points[1],points[5],points[6],_t);

 
triangles[9] = new Triangle(points[1],points[6],points[2],_t);

 
_t = Math.random() * 0xffffff;

triangles[10] = new Triangle(points[4],points[0],points[3],_t);

 

triangles[11] = new Triangle(points[4],points[3],points[7],_t);

 
addEventListener(Event.ENTER_FRAME, EnterFrameHandler);

}

 
function EnterFrameHandler(e:Event):void {

 
var dx:Number = mouseX - vpX;

 
var dy:Number = mouseY - vpY;

var angleX:Number = dy * 0.001;

 
var angleY:Number = dx * 0.001;

var angleZ:Number = Math.sqrt(dx * dx + dy * dy) * 0.0005;

 
if (dx > 0) {

 
angleZ *=  -1;

}

 
for (var i:uint = 0; i < pointNum; i++) {

 
var point:Point3D = points[i];

 
point.rotateX(angleX);

 
point.rotateY(angleY);

 
point.rotateZ(angleZ);

 
}

 
graphics.clear();

 
//画三角形

 
for (i=0; i<triangles.length; i++) {

 
triangles[i].draw(graphics);

 
}

 
}

 
Init();

当然，在学习"背面剔除"前，为了防止六个面同时填充颜色相互遮挡，我们可以先把Triangle.cs中的draw方法临时修改一下

public function draw(g:Graphics):void

 
{

 
g.beginFill(color,0.4);//改成40%透明度填充

 
g.moveTo(pointA.screenX, pointA.screenY);

g.lineTo(pointB.screenX, pointB.screenY);

 
g.lineTo(pointC.screenX, pointC.screenY);

 
g.lineTo(pointA.screenX, pointA.screenY);

 
g.endFill();

}

利用这个原理，可以创建更多复杂的3D模型

3D金字塔型：

var pointNum:int = 5;

 
var points:Array = new Array(pointNum);

 
var triangles:Array;//三角形数组

 
var vpX:Number = stage.stageWidth / 2;

 
var vpY:Number = stage.stageHeight / 2;

 
function Init():void {

 
points[0] = new Point3D(0,-200,0);

 
points[1] = new Point3D(200,200,-200);

 
points[2] = new Point3D(-200,200,-200);

 
points[3] = new Point3D(-200,200,200);

 
points[4] = new Point3D(200,200,200);

 
for (var i:uint = 0; i < pointNum; i++) {

 
points[i].setVanishingPoint(vpX, vpY);

 
points[i].setCenter(0, 0, 450);

 
}

 
//根据顶点赋值三角形数组

triangles = new Array();

 
var _t:Number = Math.random() * 0xffffff;

triangles[0] = new Triangle(points[0],points[1],points[2],_t);

 
_t = Math.random() * 0xffffff;

 
triangles[1] = new Triangle(points[0],points[2],points[3],_t);

 
_t = Math.random() * 0xffffff;

 
triangles[2] = new Triangle(points[0],points[3],points[4],_t);

_t = Math.random() * 0xffffff;

 
triangles[3] = new Triangle(points[0],points[4],points[1],_t);

 
_t = Math.random() * 0xffffff;

 
triangles[4] = new Triangle(points[1],points[3],points[2],_t);

 
//_t = Math.random() * 0xffffff;

 
triangles[5] = new Triangle(points[1],points[4],points[3],_t);

addEventListener(Event.ENTER_FRAME, EnterFrameHandler);

 
}

 

function EnterFrameHandler(e:Event):void {

 
var dx:Number = mouseX - vpX;

 
var dy:Number = mouseY - vpY;

 
var angleX:Number = dy * 0.001;

 
var angleY:Number = dx * 0.001;

 
var angleZ:Number = Math.sqrt(dx * dx + dy * dy) * 0.0005;

 
if (dx > 0) {

 
angleZ *=  -1;

 
}

 
for (var i:uint = 0; i < pointNum; i++) {

 
var point:Point3D = points[i];

 
point.rotateX(angleX);

point.rotateY(angleY);

 
point.rotateZ(angleZ);

 
}

 
graphics.clear();

 
//画三角形;

 
for (i=0; i<triangles.length; i++) {

 
triangles[i].draw(graphics);

 
}

}

 
Init();

把前面示例中的A字型示例扩展一下，变成二层(即：再复制一层A，然后在z轴上推移若干距离，然后用线条连起来)

var pointNum:int = 22;