iPhone iOS Generate star, sunburst or polygon UIBezierPath programmatically

I know this old, but I was curious about the first part of this question myself, and going off jrturton's post, I created a custom UIView that generates a UIBezierPath from center of the view. Even animated it spinning for bonus points. Here is the result:

The code I used is here:

- (void)drawRect:(CGRect)rect {
CGFloat radius = rect.size.width/2.0f;

[self.fillColor setFill];
[self.strokeColor setStroke];

UIBezierPath *bezierPath = [UIBezierPath bezierPath];
CGPoint centerPoint = CGPointMake(rect.origin.x + radius, rect.origin.y + radius);

CGPoint thisPoint = CGPointMake(centerPoint.x + radius, centerPoint.y);
[bezierPath moveToPoint:centerPoint];

CGFloat thisAngle = 0.0f;
CGFloat sliceDegrees = 360.0f / self.beams / 2.0f;

for (int i = 0; i < self.beams; i++) {

    CGFloat x = radius * cosf(DEGREES_TO_RADIANS(thisAngle + sliceDegrees)) + centerPoint.x;
    CGFloat y = radius * sinf(DEGREES_TO_RADIANS(thisAngle + sliceDegrees)) + centerPoint.y;
    thisPoint = CGPointMake(x, y);
    [bezierPath addLineToPoint:thisPoint];
    thisAngle += sliceDegrees;

    CGFloat x2 = radius * cosf(DEGREES_TO_RADIANS(thisAngle + sliceDegrees)) + centerPoint.x;
    CGFloat y2 = radius * sinf(DEGREES_TO_RADIANS(thisAngle + sliceDegrees)) + centerPoint.y;
    thisPoint = CGPointMake(x2, y2);
    [bezierPath addLineToPoint:thisPoint];
    [bezierPath addLineToPoint:centerPoint];
    thisAngle += sliceDegrees;

}

[bezierPath closePath];

bezierPath.lineWidth = 1;
[bezierPath fill];
[bezierPath stroke];

}

And you can download a sample project here:

https://github.com/meekapps/Sunburst

I'm not aware of an algorithm to create these but I do have some advice - create your bezier path such that (0,0) is the centre of the sunburst, then define however many points you need to draw one "beam" of your sunburst going upwards, returning to (0,0)

Then, for as many beams as you want, perform a loop: apply a rotation transform (2 pi / number of beams) to your sunbeam points (CGPointApplyTransform), and add them to the path.

Once you are finished, you can translate and scale the path for drawing.

I used a similar process to draw star polygons recently and it was very simple. Credit to Rob Napier's book for the idea.