Abstract: Techniques for smoothing curves used in computer animation are disclosed. In one embodiment, a smoothing application determines a number of tangents to a curve in response to a modification to a knot or the addition of a new knot, by first determining phantom tangents at knots that are neighbors of each knot that is processed. The smoothing application then (1) determines a length of each side of the tangent at each knot being processed as 1/N times the x-axis distance to a neighboring knot on the same side, (2) determines initial angles of the tangent at each knot being processed by pointing a tip of each side of the tangent at a near tip of a previously determined phantom tangent on the same side, and (3) reconciles the initial angles determined for the tangent at each knot being processed by taking a weighted sum of those initial angles.