Lines  Curves  
In the past, you have probably specified a line by the position of it's end points. The Breshenham or antialiased algorithm simply draws a straight line between the two points.  A bezier curve allows you to specify, not only the end points of the line, but also the direction of the line as it passes through the end points. The algorithm draws a curve that passes through the end points at an angle parallel to the specified direction. 
All sorts of curves can be specified with different direction vectors at the end points.  
Reflex curves appear when you set the vectors in different directions.  
You can even make loops. 
Drawing the Curve:
A look back on drawing a line: Drawing a line is a matter of starting at one end point, and moving directly towards the other end point, drawing as you go. This is also known as linear interpolation.


Drawing the curve: To draw a curve, we shall move from linear interpolation, to cubic interpolation.
We choose two end points, and call them A and D. With these four points defined, we can now use a cubic interpolation to draw a curve:

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