Curved (Parabolic) Cursor Reflection

[yanathin]

I have a bit of a weird problem. I ALMOST have it working how I want it, but my lack of math skills are making it quite difficult. Anyway, I have a glass surface with a curved perspective image. It's almost impossible to explain, so I made an example of what I want to have happen (attached in MX 2004 format). Here's what I have on the reflected cursor MC:

onClipEvent (mouseMove) {
	updateAfterEvent();
	xcoordinate = Math.abs((_root._xmouse/2)-250);
	_x = _root._xmouse;
	_y = (_root._ymouse*-1)+1050+(xcoordinate);
}

Right now, the reflection of the cursor is acting as if it is a triangular, cornered wall behind it rather than a curved one. Obviously this is because I'm taking the absolute value rather than squaring a value (simple algebra, right?) Referring to the attached example, how do I make the reflected cursor follow the red CIRCULAR (parabolic) path instead of the purple triangular path? I can't find the right equation for that parabola for the life of me... PLEASE help, I'd really appreciate it! Thank you!

[Nialsh]

I think I got something pretty close to right.

code:

---

onClipEvent (mouseMove) {

	updateAfterEvent();

	xcoordinate = Math.abs((_root._xmouse/2)-250);

	_x = _root._xmouse;

	yDivide = Math.pow(_root._xmouse-505,2)/2100+527;

	_y = yDivide-(_root._ymouse-yDivide);

}

---

The problem is that your curve is actually an arc, not a parabola so it can't match up perfectly.

You can see that the yDivide equation would look like this algebraically:
y = (x-505)^2/2100+527
A good rule of thumb for all equations in y-intercept is that a number grouped with the x (-505) will move the parent function (y=x^2) that many units to the left, or negative units in this case. A number on the outside (527) will move the line up that many units (but computers use an inverted y axis so positive numbers actually go down). The division by 2100 just makes the parabola wider and I just guessed at it.

Hope this helps
Neal

[yanathin]

Whoa, not only was that quick, but perfectly correct! Thank you SO much!! Turns out I was just going at it wrong.

[Q__Hybrid]

Yanathin,

Here's the parabolic function you need for that curve. It took me a while, but it should work quite well. Just put it in your "cursorref" instance.

onClipEvent (mouseMove) {
	updateAfterEvent();
	// VARS
	var aNum = (122/250000);
	var bNum = 0;
	var cNum = 540;
	var funcOfX = _root.cursorimage._x - 500;
	
	//	FORMULA	
	var firstTerm = aNum * Math.pow(funcOfX, 2);
	var secondTerm = bNum * funcOfX;
	var thirdTerm = cNum;
	var parabolicFormula = firstTerm + secondTerm + thirdTerm;
	
	_x = _root.cursorimage._x;
	_y = parabolicFormula + (parabolicFormula - (_root.cursorimage._y + _root.cursorimage._height));
}

If you want to modify the curve, PM me about the specifics of the quadtratic formula. Otherwise I'll leave it at this for now.

+Q__