A simplified version of my projects with bezier curves. Now 100% more intuitive! Please see the expanded version here: https://scratch.mit.edu/projects/44535532/ Drag the points around to draw bezier curves. Curves will start at a green point, pass through the blue ones, and end at a red one. The Resolution slider will change the smoothness of the curve at the cost of time. Smoother curves will take longer to draw. There is also a block to move sprites along a curve over a period of time. Use the Butterfly Speed slider to change the speed. Due to a mathematical oversight, the butterfly speed may not be constant.
I pretty much just took the algorithms from Wikipedia, though I did do the math so that the curve can pass through a specified point. Please DO use the custom blocks for whatever you want. Wikipedia article on Bezier Curves: http://en.wikipedia.org/wiki/B%C3%A9zier_curve