Create a proportional S-shaped bezier curve between any two points. Objective-C, Cocos2d, iOS.

gistfile1.m

-(ccBezierConfig)bezierForStartPoint:(CGPoint)startPoint endPoint:(CGPoint)endPoint curviness:(CGFloat)alpha
{
	CGPoint basis1 = ccpLerp(startPoint, endPoint, 0.3333);
  	CGPoint basis2 = ccpLerp(startPoint, endPoint, 0.6666);
	
	// Get a point on the perpendicular line of each of the control points
	CGPoint vector = ccpSub(endPoint, startPoint);

	// First point is to the right, second is to the left, of the line between the start point and end point
	CGPoint v1 = ccpRPerp(vector);
	CGPoint v2 = ccpPerp(vector);
	
	// Translate our two perpendicular vectors over onto our chosen basis points
	CGPoint s1 = ccpAdd(basis1, v1);
	CGPoint s2 = ccpAdd(basis2, v2);
	
	// Apply the alpha to control curviness
	CGPoint l1 = ccpLerp(basis1, s1, alpha);
	CGPoint l2 = ccpLerp(basis2, s2, alpha);
	
	ccBezierConfig bezier = (ccBezierConfig){
		endPoint,	// end point
		l1,			// control point 1
		l2			// control point 2
	};
	
	return bezier;
}