Systems and methods for shape animation are described. In one aspect, a degree of freedom is linearly approximated. The degree of freedom is associated with a new form or motion for rendering based on multiple examples that define respective forms or motions within a multi-dimensional abstract space. Each dimension of the abstract space is defined by at least one of an adjective and an adverb. A radial basis function is defined for each of the examples by scaling the radial basis function for each example. The scaling includes evaluating a matrix system to ascertain a plurality of scaling weights. Individual weights are used to scale the radial basis functions. The linear approximation and the radial basis functions are combined to provide a cardinal basis function. The cardinal basis function is used to render the new form or motion.