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    <p>The key to getting two bezier curves to join smoothly is that the relevant control points and the start/end points on the curves must be collinear. Think of the control point and the endpoint as forming a line that's tangent to the curve at the endpoint. If one curve starts at the same point where another ends, and if they both have the same tangent line at that point, the curve will be smooth. Here's a bit of code to illustrate:</p> <pre><code>- (void)drawRect:(CGRect)rect { #define commonY 117 CGPoint point1 = CGPointMake(20, 20); CGPoint point2 = CGPointMake(100, commonY); CGPoint point3 = CGPointMake(200, 50); CGPoint controlPoint1 = CGPointMake(50, 60); CGPoint controlPoint2 = CGPointMake(20, commonY); CGPoint controlPoint3 = CGPointMake(200, commonY); CGPoint controlPoint4 = CGPointMake(250, 75); UIBezierPath *path1 = [UIBezierPath bezierPath]; UIBezierPath *path2 = [UIBezierPath bezierPath]; [path1 setLineWidth:3.0]; [path1 moveToPoint:point1]; [path1 addCurveToPoint:point2 controlPoint1:controlPoint1 controlPoint2:controlPoint2]; [[UIColor blueColor] set]; [path1 stroke]; [path2 setLineWidth:3.0]; [path2 moveToPoint:point2]; [path2 addCurveToPoint:point3 controlPoint1:controlPoint3 controlPoint2:controlPoint4]; [[UIColor orangeColor] set]; [path2 stroke]; } </code></pre> <p>Notice that <code>path1</code> ends at <code>point2</code>, <code>path2</code> starts at <code>point2</code>, and control points 2 and 3 share the same Y-value, <code>commonY</code>, with <code>point2</code>. You can change any of the values in the code as you like; as long as those three points all fall on the same line, the two paths will join smoothly. (In the code above, the line is <code>y = commonY</code>. The line doesn't have to be parallel to the X axis; it's just easier to see that the points are collinear that way.)</p> <p>Here's the image that the code above draws:</p> <p><img src="https://i.stack.imgur.com/PPTbv.png" alt="two paths joined smoothly"></p> <p>After looking at your code, the reason that your curve is jagged is that you're thinking of control points as points on the curve. In a bezier curve, the control points are usually not on the curve. Since you're taking the control points from the curve, the control points and the point of intersection are <em>not</em> collinear, and the paths therefore don't join smoothly.</p>
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    1. PODrawing Smooth Curves - Methods Needed
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    1. COHow would I implement this in the code above with a constantly moving set of points?
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    2. CO@BDGapps Math! (Sorry for the flippant answer, but the comments section doesn't lend itself to discussing your non-trivial question.)
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    3. CO@BDGapps It sounds like your problem boils down to where to place the control points. As explained above they need to fall on the line tangent to the curve at the intersection point, but where on the line? That's up to you to some degree. You can figure out where the tangent line is [by taking the derivative](http://tinyurl.com/28z8wts) at the intersection -- that has a lot of information that'll help you in this respect. At the end of the day, yAak is right -- you'll need to do some math, and also make some decisions about how you want the curve to look.
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