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; display, using the artist interface, at least one of a first plurality of circles and a second plurality of half-circles spaced apart along an axis passing through a radial center of each circle and half-circle; receive, via the artist interface of the computer-implemented deformation system, an input from a user of the computer-implemented deformation system to determine an n-dimensional mapping; transform, using a mapping module, the first object geometric data by the n-dimensional mapping onto an object deformation space determined based on n primitive deformations, where n is an integer larger than one; 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; deform the first virtual object according to the modeled deformation; and display the deformed first virtual object.