The work described here extends the power of 2D animation with a form of texture mapping conveniently controlled by line drawings. By tracing points, line segments, spline curves, or filled regions on an image, the animator defines features which can be used to animate the image. Animations of the control features deform the image smoothly. This development is in the tradition of “skeleton”-based animation, and “feature”-based image metamorphosis. By employing numerics developed in the computer vision community for rapid visual surface estimation, several important advantages are realized. Skeletons are generalized to include curved “bones,” the interpolating surface is better behaved, the expense of computing the animation is decoupled from the number of features in the drawing, and arbitrary holes or cuts in the interpolated surface can be accommodated. The same general scattered data interpolation technique is applied to the problem of mapping animation from one image and set of features to another, generalizing the prescriptive power of animated sequences and encouraging reuse of animated motion.