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 Tutorials » 3D
In-depth: The MathWe'll have to calculate a number of things:
What was the deal with these trigonometric functions again?
And this pythagoras thingy?
Important! - Flash works in radians! The formula for calculating degrees from radians is:
Calculating the facet anglesTo save me some serious paper filling calculations I've built in an angle detector (it's the lower left button). Just drag point1 and point2 parallel with the desired angle ;-)
onClipEvent (enterFrame) {
//place the line between mcs point1 and point2
//notice the width and height of this line are 100
this._x = _root.angledetect.point1._x;
this._y = _root.angledetect.point1._y;
this._xscale = (_root.angledetect.point2._x-_root.angledetect.point1._x);
this._yscale = (_root.angledetect.point2._y-_root.angledetect.point1._y);
// Math.atan for angles
xa= this._width;
ya= this._height;
_parent.angle=(Math.atan(ya/xa))/(Math.PI/180);
// -------------------------------
// make less decimals and calculate angle2
_parent.angle=(int(_parent.angle*100))/100
_parent.point1.angle= _parent.angle
_parent.point2.angle= 90 - _parent.angle
// -------------------------------
}
The light source angle on the xy-axisWe'll use Math.atan to calculate this angle: we know A and B (distance base to light source on x and on y): xt= xm - xb; yt= ym - yb; xb and yb are the base coordinates, xm and ym the coordinates of the light source. _root.DgrMouseX=int(Math.atan(yt/xt) / _root.convrad); This function gives a flash angle, further on we'll recalculate this angle to an angle between 0 and 360 degrees. The light source angle on the z axisThe fixed distance of the light source lets us calculate the angle it has. We know that side (C) will be the radius of the sphere, in this case 180. We calculate A (DeltaX) by using pythagoras on xt and yt. _root.DeltaX=Math.sqrt(xt*xt+yt*yt); Then we use the Math.acos on A and C to calculate the z-angle: _root.DgrMouseZ=(Math.acos(_root.DeltaX/180))/_root.convrad); Flash and anglesFlash treats degrees a little different than we're used to, so we'll re-calculate them to something more handable: if(xt <0 && yt> 0){
_root.DgrMouseX += 270;
} else if(xt <0 && yt <= 0){
_root.DgrMouseX += 270;
} else if(xt>= 0 && yt <= 0){
_root.DgrMouseX += 90;
} else if(xt>= 0 && yt>= 0){
_root.DgrMouseX += 90;
}
This'll return any angle to one between 0 and 360 degrees counting from 0 at the top clockwise to 360. On to the whiteness!Each facet calculates it's own whiteness. The whiteness is done by setting the _alpha of a white facet MC over the background of the object. function SinMouseX(AngleX) {
return Math.cos(Math.PI/180 * (_root.DgrMouseX - AngleX));
}
This function sets the most fierce point at FacetX and the less fierce point at (FacetX - 180) degrees. Then we set the _alpha. The ratio is 50% so z-angle and xy-angle have an equally strong influence: function AlphaMouseX(Z,X) {
return ((_root.DgrMouseZ/Z) * _root.ratio + X * (100 - _root.ratio));
}
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Lighting on 3D Objects
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