1. A computer-implemented method for depicting freeform curves comprising the acts of: receiving a plurality of data structures associated with a first curve, wherein the first curve is a freeform curve; computing, using a processor, a first plurality of line segments to approximate the first curve by evaluating an affine combination, wherein a plurality of the computed first line segments are approximately equal in length to their respective portions of the first curve; providing the computed first line segments to an animation process, wherein the computed first line segments are to be animated by the animation process; receiving a second plurality of line segments from the animation process, wherein the second plurality of line segments is based on the computed first line segment and the animation process; computing, using the processor, a second curve to approximate the second plurality of line segments by solving a linear system of equations, wherein the second curve is a freeform curve, wherein a plurality of segments of the computed second curve are approximately equal in length to their respective line segments, and wherein the linear system of equations comprises a tridiagonal matrix defined by the affine combination; and causing a display of the computed second curve.