1. A method of animating a non-rigid object in a computer graphics environment, the method comprising: defining a first three-dimensional (3D) curve rigging element representing the non-rigid object, the 3D curve rigging element comprising a plurality of knot primitives, wherein each of the plurality of knot primitives corresponds to: a respective position within a three-dimensional scene; and a respective plurality of animation control attributes that control the movement of the knot primitive during animation; receiving one or more defined values for a first one or more of the plurality of animation control attributes for a first one or more of the plurality of knot primitives; generating one or more values, for a second one or more of the plurality of animation control attributes for a second one or more of the plurality of knot primitives based on the plurality of animation control attributes of a neighboring knot primitive; rendering an animation using the first 3D curve rigging element, using the received one or more defined values, and the generated one or more values; and outputting the rendered animation for display.