1. A computer-implemented deformation system comprising: a hardware processor and a system memory; a contact-based deformation modeling software stored in the system memory; wherein the hardware processor is configured to execute the contact-based deformation modeling software to: receive, via an artist interface of the computer-implemented deformation system, a first object geometric data corresponding to a first virtual object; receive, via the artist interface of the computer-implemented deformation system, a second object geometric data corresponding to at least a second virtual object; transform, using a mapping module, the first object geometric data by an n-dimensional mapping onto an object deformation space determined based on n primitive deformations, where n is an integer larger than one; and model, using an analysis module, a deformation of the first virtual object due to a contact with at least the second virtual object, based on the n-dimensional mapping and a definition of direction for an object-to-object contact force.