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Flash与3D编程探秘(六)- 全方位旋转摄像机

发布时间:2020-12-15 06:43:07 所属栏目:百科 来源:网络整理
导读:前面讨论过了如何横向旋转和移动摄像机,希望你已经完全理解,因为本文中的内容紧接着上一篇。回想一下,在前面制做的动画中,摄像机的旋转一直是围绕着y轴(竖直向上的轴)旋转,然而现实中我们可以上下旋转摄像机,甚至可以把摄像机倾斜一定角度,这就提醒

前面讨论过了如何横向旋转和移动摄像机,希望你已经完全理解,因为本文中的内容紧接着上一篇。回想一下,在前面制做的动画中,摄像机的旋转一直是围绕着y轴(竖直向上的轴)旋转,然而现实中我们可以上下旋转摄像机,甚至可以把摄像机倾斜一定角度,这就提醒了大家还需要更深入的研究旋转这个课题。下面几个动画演示了摄像机(简单的摄像机轮廓)3种旋转模式,从左到右分别是横向旋转,纵向旋转,倾斜。从3D空间角度来说,分别是沿y,x和z轴旋转。

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横向和纵向旋转摄像机



倾斜摄像机


再介绍一些三角函数方程

事情变得复杂起来了!不过请你还是保持头脑清醒,这一篇文章你的任务就是学会纵向旋转和倾斜摄像机。你也许会想,我已经学会了横向旋转摄像机,算法中使用了一个panning的变量代表旋转角度,那么我再加两个变量,然后按顺序先沿x旋转,然后再沿y,最后z旋转不就好了。Well,这种想法很接近但却是错的(不要把3D数学想的那么简单)。来看一下下面的两个图,还是以3D空间在2D平面上的投影举例,把线段OB沿着z轴(也就是2D平面上 的原点)旋转大约78度,可以看到OB的长度就是我们的旋转半径。那么接下来,把OB沿y轴旋转,看一下图中的旋转半径是多少?不难看出,旋转半径明显的变小了。继续,如果你沿y旋转后,再打算沿x轴旋转,你还是会有同样“半径变化”的问题。

先沿z轴旋转再试图沿y旋转

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在上面的例子中,如果想要保持旋转半径不变,那么一开始就不要有旋转角度。不过拿着摄像机左转右转,怎么可能保持角度不变!?因此你要在每一次摄像机旋转后,计算新的旋转半径。可是如果每一次都把旋转半径计算出来,那一定是很头疼!


于是人们聪明的想到了省力的方法。先来再看一下2D的三角函数(又是三角函数),根据旋转半径和旋转角度可以得到x和y:
<!--

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--> x? = ?Math.cos(angle) * radius;
y?
= ?Math.sin(angle) * radius;


需要注意一点,上面的方程式旋转点为原点,并且之前旋转角度为0。如果之前就有旋转角度a,再旋转b,那么方程式就成了:

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--> x? = ?Math.cos(a + b) * radius;
y?
= ?Math.sin(a + b) * radius;

看起来眼熟,但是不知道是什么了?别担心:
<!--

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--> cos(a + b)? = ?cos(a) * cos(b)? - ?sin(a) * sin(b);
sin(a
+ b)? = ?sin(a) * cos(b)? + ?sin(b) * cos(a);

把cos(a+b)和sin(a+b)带入上面的x和y求值方程我们就有:
<!--

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--> x? = ?radius * cos(a) * cos(b)? - ?radius * sin(a) * sin(b);
y?
= ?radius * sin(a) * cos(b)? + ?radius * sin(b) * cos(a);

化简一下得到:
<!--

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--> x? = ?x_before * cos(b)? - ?y_before * sin(b);
y?
= ?x_before * sin(b)? + ?y_before * cos(b);

这样,使用上面两个方程,不用担心你在其他平面(xz或者yz平面)的旋转角度,也不用每一次旋转后再去计算物体新的旋转半径了,只要关心旋转后的x和y,并且把它们作为下一次旋转的x_before和y_before,问题就解决了。下面我把相应的方程式写上:

围绕y轴旋转pan角度:
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--> x? = ?Math.cos(pan) * x_before? - ?Math.sin(pan) * z_before;
z?
= ?Math.sin(pan) * x_before? + ?Math.cos(pan) * z_before;

围绕x轴旋转pitch角度:
<!--

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--> y? = ?Math.cos(pitch) * y_before? - ?Math.sin(pitch) * z_before;
z?
= ?Math.sin(pitch) * y_before? + ?Math.cos(pitch) * z_before;

围绕z轴旋转tilt角度:
<!--

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--> x? = ?Math.cos(tilt) * x_before? - ?Math.sin(tilt) * y_before;
y?
= ?Math.sin(tilt) * x_before? + ?Math.cos(tilt) * y_before;


那么基本的知识已经说完了。总结一下,当你在使用这些方程式操作摄像机全方位旋转的时候,只要取得相应的变量,然后替换在方程里就可以了。是不是看起来有点难理解?不要担心,适应这些东西是需要花一点时间(特别是这些对你来说还是新课题的话),不过适应以后你应该就觉得很简单了。坦白的说,其实你并不需要知道到底这些是怎样得来的,你只要知道如何使用它们,得到想要得结果就可以了(当然完全理解会对你以后的学习有一些帮助)。这些方程你可以写成一个函数,然后命名它为“给我旋转”方程,当你需要摄像机旋转的时候,只要呼唤“给我旋转”就好了,至于“给我旋转”怎么做的工作,你就不需要担心了。

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全方位旋转摄像机?

只说这些理论的东西,你肯定会觉得乏味,那么我举个例子来说明。下面这个程序演示了摄像机的全方位旋转,运行程序你会看到你置身在一个巨大的正方体中,这个正方体是由很多我们的朋友小P组成的,不过这回用不同颜色的小P来代表不同的边。使用WS键控制纵向旋转,AD键控制横向旋转,QE控制倾斜角度,鼠标点击屏幕禁止或者允许鼠标移动控制纵向和横向旋转。



全方位旋转摄像机,使用WS纵向旋转,AD横向旋转,QE倾斜角度,鼠标点击禁止或者允许鼠标控制


制作步骤:

1. 首先定义几个常量,MAX_OBJ是每条边上的物体数量,CUBE_WIDTH是正方体的边长。

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--> // ?constants
var?MAX_OBJ? = 6 ;
var?PI?
= ? 3.1415926535897932384626433832795 ;
var?CUBE_WIDTH?
= ? 300 ;

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2. 下面还是设置原点,场景,焦距等。

<!--

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--> // ?same?as?usual
var?origin? = ? new ?Object();
origin.x?
= ?stage.stageWidth / 2 ;
origin.y?
= ?stage.stageHeight / 2 ;
origin.z?
= ? 0 ;

var?scene?
= ? new ?Sprite();
scene.x?
= ?origin.x;
scene.y?
= ?origin.y;
this .addChild(scene);

var?focal_length?
= 400 ;

?

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3. 设置摄像机,这回的摄像机多了几个新的属性,pitching是纵向旋转角度,tilt是倾斜的角度。

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--> var?camera? = ? new ?Object();
camera.x?
= ? 0 ;
camera.y?
= ? 0 ;
camera.z?
= ? 0 ;
camera.panning?
= ? - PI / 8 ;???????????????? // ?init?pan?angle?of?our?camera,?pan?left
camera.pitching? = ? - PI / 8 ;?????????????? // ?pitch?up
camera.tilt? = ? 0 ;?????????????????? ? ? ? ? // ?and?no?tilt

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4. 设置一些全局变量,在处理键盘和鼠标事件时会用到。

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--> // ?global?booleans?for?our?keyboard?control
var?pan_left;
var?pan_right;
var?pitch_up;
var?pitch_down;
var?mouse_ctl?
= ? true ;

?

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5. 下面布置一个正方体,你完全不必要明白我是怎么布置场景的,因为布置场景的方式并不唯一,所以如果你愿意的话,你可以自己动手布置3D场景,当然我也不介意直接拷贝我的设置场景的代码去用。总之,这些代码就是初始化一些小P,然后把它们摆放在合适位置(围绕着摄像机)。

<!--

Code highlighting produced by Actipro CodeHighlighter (freeware)
http://www.CodeHighlighter.com/

--> // ?ok,?here?you?don't?have?to?know?how?i?acutally?setup?the?cube
// ?cause?every?body?has?a?different?way?of?doing?that,?if?you?really
// ?interested?in?how?i?did?it,?then?you?may?have?a?look
// ?you?can?just?copy?my?code?and?it?will?set?it?up?for?you
var?len? = ?CUBE_WIDTH / 2 ;
for ?(var?seg? = ? 0 ;?seg? < ? 3 ;?seg ++ )
{
????var?line_h;
????var?line_v;????
????var?line_z;
????
????
switch ?(seg)
????{
????????
case ? 0 :
????????????line_h?
= ? true ;
????????????line_v?
= ? false ;
????????????line_z?
= ? false ;
????????????
break ;
????????
case ? 1 :
????????????line_h?
= ? false ;
????????????line_v?
= ? true ;
????????????line_z?
= ? false ;
????????????
break ;
????????
case ? 2 :
????????????line_h?
= ? false ;
????????????line_v?
= ? false ;
????????????line_z?
= ? true ;
????????????
break ;
????}
????
????
for ?(var?i? = ? 0 ;?i? < ?MAX_OBJ;?i ++ )
????{
????????
if ?(line_h? || ?(i? == ? 0 ? || ?i? == ?MAX_OBJ - 1 ))
????????{
????????????
for ?(var?j? = ? 0 ;?j? < ?MAX_OBJ;?j ++ )
????????????{
????????????????
if ?(line_v? || ?(j? == ? 0 ? || ?j? == ?MAX_OBJ - 1 ))
????????????????{
????????????????????
for ?(var?k? = ? 0 ;?k? < ?MAX_OBJ;?k ++ )
????????????????????{
????????????????????????
if ?(line_z? || ?(k? == ? 0 ? || ?k? == ?MAX_OBJ - 1 ))
????????????????????????{
????????????????????????????var?ball;
????????????????????????????
if ?(line_h)
????????????????????????????{
????????????????????????????????ball?
= ? new ?SphereHorizontal();
????????????????????????????????
if ?((i? == ? 0 ? || ?i? == ?MAX_OBJ - 1 ))
????????????????????????????????{
????????????????????????????????????ball?
= ? new ?SphereVertex();
????????????????????????????????}
????????????????????????????????
else
????????????????????????????????{
????????????????????????????????????ball?
= ? new ?SphereHorizontal();
????????????????????????????????}
????????????????????????????}
????????????????????????????
if ?(line_v)
????????????????????????????{
????????????????????????????????ball?
= ? new ?SphereVertical();
????????????????????????????????
if ?((j? == ? 0 ? || ?j? == ?MAX_OBJ - 1 ))
????????????????????????????????{
????????????????????????????????????
continue ;
????????????????????????????????}
????????????????????????????}
????????????????????????????
if ?(line_z)
????????????????????????????{
????????????????????????????????ball?
= ? new ?SphereStraight();
????????????????????????????????
if ?((k? == ? 0 ? || ?k? == ?MAX_OBJ - 1 ))
????????????????????????????????{
????????????????????????????????????
continue ;
????????????????????????????????}
????????????????????????????}
????????????????????????????ball.x_3d?
= ? - len? + ?(i) * (CUBE_WIDTH / MAX_OBJ);
????????????????????????????ball.y_3d?
= ? - len? + ?(j) * (CUBE_WIDTH / MAX_OBJ);
????????????????????????????ball.z_3d?
= ? - len? + ?(k) * (CUBE_WIDTH / MAX_OBJ);
????????????????????????????scene.addChild(ball);
????????????????????????}
????????????????????}
????????????????}
????????????}
????????}
????}
}

?

?

6. 下面的函数就是刷新小P位置和大小的函数,这也是这篇文章主要讲述的内容,所以,请集中。OK,首先要得出小P(其中一个小P)到摄像机的x,y和z 距离。对于横向旋转角度panning,使用本文前面讲述的方程,把相应的x距离和z距离带入,然后得出新的x距离和z距离。使用相同的方法得出 纵向旋转角度pitching后的y和z距离,对摄像机倾斜角度tilt再次使用上述方程。这样就得到围绕三个轴旋转后新的x,y和z距离,继而便可以使用老办法算出物体的缩放和移动。最后别忘记加一个z_near变量,存储小P到摄像机的距离,以便于对所有小P进行z排序。

<!--

Code highlighting produced by Actipro CodeHighlighter (freeware)
http://www.CodeHighlighter.com/

--> // ?update?ball?size?and?position
// ?here?is?what?we?really?care?about,?so?concentrate
function?display(obj)
{????
????var?x_distance?
= ?obj.x_3d? - ?camera.x;???????? // ?first?we?determine?x?distance?ball?to?camera
????var?y_distance? = ?obj.y_3d? - ?camera.y;???????? // ?y
????var?z_distance? = ?obj.z_3d? - ?camera.z;???????? // ?z?distance
????
????var?tempx,?tempy,?tempz;???????????????????????
// ?some?temporary?variables
????
????
// ?two?more?trig?you?need?to?know?about,?suppose?a?is?the?previous?angle
????
// ?cos(a+b)?=?cos(a)*cos(b)?-?sin(a)*sin(b)
????
// ?sin(a+b)?=?sin(a)*cos(b)?+?cos(a)*sin(b)
????
// ?thus?we?have?the?following
????var?angle? = ?camera.panning;
????tempx?
= ?Math.cos(angle) * x_distance? - ?Math.sin(angle) * z_distance;
????tempz?
= ?Math.sin(angle) * x_distance? + ?Math.cos(angle) * z_distance;
????x_distance?
= ?tempx;
????z_distance?
= ?tempz;
????
????angle?
= ?camera.pitching;???????????????????? // ?the?same?thing?we?have?for?pitch?angle
????tempy? = ?Math.cos(angle) * y_distance? - ?Math.sin(angle) * z_distance;
????tempz?
= ?Math.sin(angle) * y_distance? + ?Math.cos(angle) * z_distance;
????y_distance?
= ?tempy;
????z_distance?
= ?tempz;
????
????angle?
= ?camera.tilt;????????????????????????? // ?and?tilt?angle
????tempx? = ?Math.cos(angle) * x_distance? - ?Math.sin(angle) * y_distance;
????tempy?
= ?Math.sin(angle) * x_distance? + ?Math.cos(angle) * y_distance;
????x_distance?
= ?tempx;
????y_distance?
= ?tempy;
????
????
if ?(z_distance? > ? 0 )?????????????????????????????????????????? // ?if?the?ball?isin?front?of?the?camera
????{
????????
if ?( ! obj.visible)????????????????????????????????
????????????obj.visible?
= ? true ;???????????????????????????????????? // ?make?the?ball?visible?anyway
????????????
????????var?scale?
= ?focal_length / (focal_length + z_distance);?? // ?cal?the?scale?of?the?ball
????????obj.x? = ?x_distance * scale;???????????????????????????? // ?calcualte?the?x?position?in?a?camera?view?
????????obj.y? = ?y_distance * scale;??????????????????????????? // ?and?y?position
????????obj.scaleX? = ?obj.scaleY? = ?scale;??????????????????? // ?scale?the?ball?to?a?proper?state
????}
????
else
????{
????????obj.visible?
= ? false ;
????}
????
????obj.z_near?
= ?z_distance;???????????? // ?keep?track?of?z?distance?to?our?camera
}

?

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7. 写一个循环函数,不停的调用第6步的函数刷新所有的小P。如果你一直有看文章的话那么这些对你来说应该不难。

<!--

Code highlighting produced by Actipro CodeHighlighter (freeware)
http://www.CodeHighlighter.com/

--> // ?loop?to?update?the?screen
function?run(e:Event)
{
????
for ?(var?i? = ? 0 ;?i? < ?scene.numChildren;?i ++ )????????????????? // ?update?all?the?balls?on?the?screen
????{
????????display(scene.getChildAt(i));
????}
????
????swap_depth(scene);
}

// ?bubble?sort?algo
function?swap_depth(container:Sprite)
{
????
for ?(var?i? = ? 0 ;?i? < ?container.numChildren? - ? 1 ;?i ++ )
????{
????????
for ?(var?j? = ?container.numChildren? - ? 1 ;?j? > ? 0 ;?j -- )
????????{
????????????
if ?(Object(container.getChildAt(j - 1 )).z_near? < ?Object(container.getChildAt(j)).z_near)
????????????{
????????????????container.swapChildren(container.getChildAt(j
- 1 ),?container.getChildAt(j));
????????????}
????????}
????}
}

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8. 最后是设置一些键盘和鼠标事件响应函数,完成我们的程序。

<!--

Code highlighting produced by Actipro CodeHighlighter (freeware)
http://www.CodeHighlighter.com/

--> function?key_down(e:KeyboardEvent): void
{
????
if ?(e.keyCode? == ? 65 )???????????? // ?a
????????pan_left? = ? true ;
????
if ?(e.keyCode? == ? 68 )???????????? // ?d
????????pan_right? = ? true ;
????
if ?(e.keyCode? == ? 87 )???????????? // ?w
????????pitch_up? = ? true ;
????
if ?(e.keyCode? == ? 83 )???????????? // ?s
????????pitch_down? = ? true ;
}
function?key_up(e:KeyboardEvent):
void
{
????
????
if ?(e.keyCode? == ? 65 )
????????pan_left?
= ? false ;
????
if ?(e.keyCode? == ? 68 )
????????pan_right?
= ? false ;
????
if ?(e.keyCode? == ? 87 )
????????pitch_up?
= ? false ;
????
if ?(e.keyCode? == ? 83 )
????????pitch_down?
= ? false ;
}
function?key_response(e:Event):
void
{
????
if ?(pan_left)
????????camera.panning?
-= ? 0.01 ;
????
if ?(pan_right)
????????camera.panning?
+= ? 0.01 ;
????
if ?(pitch_up)
????????camera.pitching?
-= ? 0.01 ;
????
if ?(pitch_down)
????????camera.pitching?
+= ? 0.01 ;
????????
????
if ?(mouse_ctl)???????????????????????????????? // ?if?allow?mouse?control?pan?and?pitch
????{
????????camera.panning?
+= ?scene.mouseX / 22000 ;
????????camera.pitching?
+= ?scene.mouseY / 22000 ;
????}
????
????
// ?limit?the?pitch?and?tilt
???? if ?(camera.pitching? < ? - 1 * PI / 3 )
????????camera.pitching?
= ? - 1 * PI / 3 ;
????
if ?(camera.pitching? > ?PI / 3 )
????????camera.pitching?
= ?PI / 3 ;
}
function?clicked(e:Event)????????????????????????
// ?toggle?mouse?control
{
????mouse_ctl?
= ? ! mouse_ctl;
}

// ?setup?event?listeners
this .addEventListener(Event.ENTER_FRAME,?run);
this .addEventListener(Event.ENTER_FRAME,?key_response);
stage.addEventListener(KeyboardEvent.KEY_DOWN,?key_down);
stage.addEventListener(KeyboardEvent.KEY_UP,?key_up);
stage.addEventListener(MouseEvent.CLICK,?clicked);

?

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总结一下,这篇文章中的三角函数部分可能有些抽象,因为是在3D空间中完成的,如果你把所有的例子首先映射到2D平面上会想对好理解一些。不过还是那句话,不要担心,你只要知道如何使用这些方程就可以了。

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注意:物体自身围绕中心的3D旋转

有一点不知道你有没有注意,那就是在本文的开头,我做了几个摄像机的旋转演示。在演示里,摄像机(物体)都是本身在旋转,而并不是我们的眼睛(摄像机)在旋转。虽然到目前为止的文章里,还没有讨论到如何让物体自身旋转,不过很快就会看到一些例子。注:我做这些演示唯一想说明的就是三种旋转的机制,所以请不要着急那些演示是怎么做出来的。

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其实,关于Flash和3D空间的基本知识的介绍到这里我想应该结束了,从下篇文章开始就要关注3D物体,因此,如果对前面文章中的基础知识还是模模糊糊的话,完全可以不必担心。不过我还是建议你自己多实验一些小例子,增加自己的空间感。相信你在不久的将来就可以开发自己的3D Engine了,加油,ALL THINGS ARE POSSIBLE!


上一篇????????? 目录????????? 下一篇

非常抱歉,文中暂时不提供源文件下载,如果你需要源文件,请来信或者留言给我。笔者利用工作之余写这些文章,付出了很多汗水,希望读者和转载者能够尊重作者的劳动。

作者:Yang?Zhou
出处:http://yangzhou1030.cnblogs.com 本文版权归作者和博客园共有,转载未经作者同意必须保留此段声明。请在文章页面明显位置给出原文连接,作者保留追究法律责任的权利。

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