Magnets in Motion


We introduce magnetic interaction for rigid body simulation. Our approach is based on an equivalent dipole method and as such it is discrete from the ground up. Our approach is symmetric as we base both field and force computations on dipole interactions.

Enriching rigid body simulation with magnetism allows for many new and interesting possibilities in computer animation and special effects. Our method also allows the accurate computation of magnetic fields for arbitrarily shaped objects, which is especially interesting for pedagogy as it allows the user to visually discover properties of magnetism which would otherwise be difficult to grasp.

We demonstrate our method on a variety of problems and our results reflect intuitive as well as surprising effects. Our method is fast and can be coupled with any rigid body solver to simulate dozens of magnetic objects at interactive rates.


    author = {Bernhard Thomaszewski and Andreas Gumann and Simon Pabst and Wolfgang Strasser},

    title = {Magnets in Motion},

    journal = {ACM Trans. Graphics (Proc. SIGGRAPH Asia)},

    year = {2008},

    volume = {27},

    number = {5},

    pages = {162:1--162:9},




Bernhard Thomaszewski, Andreas Gumann, Simon Pabst and Wolfgang Strasser

SIGGRAPH Asia (ACM Transactions on Graphics), 2008


[Video (43MB XviD AVI)]

[pre-print PDF 11MB]

Spheres made of a soft ferromagnetic material lifted by a permanent magnet. Sequence of four images out of a complete simulation.

Inhomogeneous induced magnetization. Top: toy magnets have identically oriented homogeneous magnetization (indicated by the coloring) and hence attract each other. The sphere is magnetized with homogeneous direction according to the external field. Bottom: magnets have opposite magnetization and therefore repel each other. As the left toy magnet is moved rightwards its magnetic field induces a corresponding magnetization in the sphere (middle). Continuing this motion, the repelling forces increase but, at the same time, the attracting field induced in the sphere grows up to the point, where the resulting attraction forces exceed the repelling forces and the toy magnet snaps to the sphere (right).

Our method can be used to compute detailed visualizations of magnetic fields using standard streamline techniques.

Simulation scene consisting of a permanently magnetized simple dragon model and a large number of soft-ferromagnetic spheres, 250 in the complete simulation. After being dropped into the scene from above the dragon, some of the spheres stick to the surface of the dragon, held by magnetic interaction. For details on computational costs see Table 1 in the paper.

A superconducting cube levitating above a ferromagnetic ring. Simulation scene on the left and a snapshot of the magnetic field lines on the right.