1. A computer-implemented method for creating a character for animation, the method comprising: associating spatial variables with a first three-dimensional mesh, wherein the first three-dimensional mesh specifies a shape of a first character and wherein the spatial variables have initial values that correspond to a position in three-dimensional space relative to one or more vertices on the first three-dimensional mesh; providing the first three-dimensional mesh with a modular rig structure comprising character components from a particular collection of character components, wherein the particular collection of character components is defined for use with the first three-dimensional mesh, and wherein each character component is associated with one or more of the spatial variables and a geomset, wherein the geomset represents at least one of a portion of skeletal geometry and animation information for the first three-dimensional mesh and associating each character component with a geomset specifies a configuration of the geomset with respect to the first three-dimensional mesh; modifying, using a computer system, the first three-dimensional mesh to generate a second three-dimensional mesh, wherein the second three-dimensional mesh specifies a shape of a second character; setting new values for the spatial variables for the second three-dimensional mesh that define a configuration of each of the character components in the modular rig structure for the second three-dimensional mesh, where the new values for the spatial variables are based on a difference in shape between the first three-dimensional mesh and the second-three dimensional mesh, wherein the new values for the spatial variables also define a configuration for the geomsets associated with the character components for the second three-dimensional mesh; automatically transforming the geomsets, in multiple progressive refinements, based at least in part on the new values for the spatial variables, wherein the transformed geomsets are adapted to the second three-dimensional mesh; and storing the character components and the transformed geomsets in a new collection of character components that is defined for use with the second three-dimensional mesh, including storing an association of the character components in the new collection of character components to one or more of the new values for the spatial variables.