I have received a couple requests for x-at-y methods in the advanced quadratic and cubic Bezier classes to complement the existing y-at-x methods. Fortunately, the algorithm is the same, just a different set of coefficients, so it was an easy addition.

The x-at-y problem is typically used to distribute sprites left-to-right and top-to-bottom along the contour of a Bezier curve. The y-coordinate of the first sprite is fixed. The horizontal location is determined by the x-coordinate of the Bezier curve corresponding to the specified y-coordinate (plus some offset). Sprites are ‘stacked’ along the contour of the curve by incrementing the y-coordinate based on the height of the previous sprite plus some offset, then repeating the algorithm.

The following diagrams illustrate the quadratic and cubic cases.

These methods are in the AdvancedQuadraticBezier and AdvancedCubicBezier classes. Update SVN and enjoy.