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The art of scriptable skew

by ericlin@ms1.hinet.net


How to dynamically skew a movieClip ? The common way is make a 180 or 360 frame tween to render the skew angle. The pitfall is that it is not accurate enough. If we want to construct 3D object by multiple skewing face, we can not get a seamless model without crack. So, Can we use math to skew a movieClip ? Here is the secret.

Skewing can be obtained easily by puting movieclip in a stretched movieClip. MovieClip itself does rotation and _parent does stretching. Below is the swf showing a skew of 100x100 square.

The _parent can also do rotation and the movieClip can also do stretch. With various combination of stretch and rotation we can make the square movieClip skew to a shape that we want. But, how do we know how much _rotation and _xscale and _yscale we should apply to _parent and movieClip itself ? I will explain to you.

OK, we can first stretch our movieClip into 100x100 size and then rotate-45 degrees. That will be what we see below. Now try to control 3 parameters: the _parent._yscale, and the _xscale and _yscale of movieClip itself. You can click the buttons to increase and decrease the value. I suggest you to observe the change of _parent._yscale first. That is the core of the skew math. You will realize that, you can easily make a skew with the angle you want and the shape you want. After you get it, we will discuss the math. 

Here is the diagram about the math to calculate the relation ship of skew angle and _parent._yscale; I dont want to explain them in details. You should try to develop the math equation yourself. Anyway, stretchig of _parent._yscale will increase the skew angle and shrink the _parent.yscale will shapen the skew angle. If you figure out this, you will know it is very simple math.

OK, we go step by step to make a a movieClip of 200*100 to conform to the 3 dragable corners. (You can not change the 4th corners, because Flash allowed only a diamond skew. We can not do distortional skew such as perspective skew).

The steps is that: first, we calculate the skew angle Angle(P2-P0-P1); We make a quadrangle with that angle. Then we stretch the arm of "width" and then stretch the arm of "height". The we put the prepared quadrangle to the place we want it to be with setting of _x,_y and _rotation.

Before the function can be applied, some preparation should be done. First, the movieClip that is going to do skew must have its registration point at left-top corner, not at the center of movieClip. Create an empty holder movieClip, and put this movieClip in it. The registration point should be the (0,0) point. Now give your movieClip an instance name of "mc". If you like to give a name you like, for example: "mySkewableMC", then  in the first frame of this holder movieClip, write this.mc=mySkewableMC. 

The above setting is just for my skew function. You can develop your skew function equation and modify them.

The function:

function skewObj (obj, mcW, mcH, pt0, ptH, ptW) {
    function distance (pt1, pt2) {
        var dy = pt2.y-pt1.y;
        var dx = pt2.x-pt1.x;
        var side = Math.sqrt(dy*dy+dx*dx);
        return side;
    }
    obj._x = pt0.x;
    obj._y = pt0.y;
    obj._yscale = 100;
    var angleP2 = Math.atan2(ptW.y-pt0.y, ptW.x-pt0.x);
    var angleP1 = Math.atan2(ptH.y-pt0.y, ptH.x-pt0.x);
    var dAngle = (angleP1-angleP2)/2;
    var arm = Math.sqrt(2)/2/Math.cos(dAngle);
        // original a 100x100 model , now use 1x1 model
    obj._rotation = (180/Math.PI)*(angleP1-dAngle);
    obj.mc._rotation = -45;
    obj._yscale = 100*Math.tan(dAngle);
    obj.mc._xscale = distance(ptW, pt0)*100/arm/mcW;
    obj.mc._yscale = distance(ptH, pt0)*100/arm/mcH;
}

Here, obj is the instance name of your holder movieClip. mcW and mcH are the original width and height of the  movieClip inside the holder. pt0, ptH and ptW are point object with the format of {x:??,y:??}; They are in the same coordinate system of the holder movieClip. 

OK, below is an example to make a movieClip stretched by 3 draggable corners movieClip p0, pH, pW.


H = obj.mc._height;
W = obj.mc._width;
function updateSkew () {
    pt0 = {x:p0._x, y:p0._y};
    ptH = {x:pH._x, y:pH._y};
    ptW = {x:pW._x, y:pW._y};
    skewObj(obj, W, H, pt0, ptH, ptW);
}
updateSkew();