Math: Wedge problem

programming
1

Hello everybody,

Could somebody help me? I am using Ric Ewing’s drawWedge() method that can be found here (or see below the code).
Pretty easy to use, but I have problems to understand it. I can’t figure out how I could count from this the coordinates of the “middle-point” of the wedge lying on the outer border of the wedge. See the attached image, I would like to get the coordinates of the red dot. Anybody has an idea?
Thanks a lot, all comments greatly appreciated!

Cheers,
P.


MovieClip.prototype.drawWedge = function(x, y, startAngle, arc, radius, yRadius) {
    // ==============
    // mc.drawWedge() - by Ric Ewing (ric@formequalsfunction.com) - version 1.3 - 6.12.2002
    //
    // x, y = center point of the wedge.
    // startAngle = starting angle in degrees.
    // arc = sweep of the wedge. Negative values draw clockwise.
    // radius = radius of wedge. If [optional] yRadius is defined, then radius is the x radius.
    // yRadius = [optional] y radius for wedge.
    // ==============
    // Thanks to: Robert Penner, Eric Mueller and Michael Hurwicz for their contributions.
    // ==============
    if (arguments.length<5) {
        return;
    }
    // move to x,y position
    this.moveTo(x, y);
    // if yRadius is undefined, yRadius = radius
    if (yRadius == undefined) {
        yRadius = radius;
    }
    // Init vars
    var segAngle, theta, angle, angleMid, segs, ax, ay, bx, by, cx, cy;
    // limit sweep to reasonable numbers
    if (Math.abs(arc)>360) {
        arc = 360;
    }
    // Flash uses 8 segments per circle, to match that, we draw in a maximum
    // of 45 degree segments. First we calculate how many segments are needed
    // for our arc.
    segs = Math.ceil(Math.abs(arc)/45);
    // Now calculate the sweep of each segment.
    segAngle = arc/segs;
    // The math requires radians rather than degrees. To convert from degrees
    // use the formula (degrees/180)*Math.PI to get radians.
        theta = -(segAngle/180)*Math.PI;
    // convert angle startAngle to radians
    angle = -(startAngle/180)*Math.PI;
    // draw the curve in segments no larger than 45 degrees.
    if (segs>0) {
        // draw a line from the center to the start of the curve
        ax = x+Math.cos(startAngle/180*Math.PI)*radius;
        ay = y+Math.sin(-startAngle/180*Math.PI)*yRadius;
        this.lineTo(ax, ay);
        // Loop for drawing curve segments
        for (var i = 0; i<segs; i++) {
            angle += theta;
            angleMid = angle-(theta/2);
            bx = x+Math.cos(angle)*radius;
            by = y+Math.sin(angle)*yRadius;
            cx = x+Math.cos(angleMid)*(radius/Math.cos(theta/2));
            cy = y+Math.sin(angleMid)*(yRadius/Math.cos(theta/2));
            this.curveTo(cx, cy, bx, by);
        }
        // close the wedge by drawing a line to the center
        this.lineTo(x, y);
    }
};