This paper presents a technique for decomposing a triangulated model into a set of triangle fans. We show that the triangle fan representation improves the performance of several fundamental geometric algorithms operating over triangle meshes. We present two accelerated algorithms, one for computing the nearest intersection between a ray and a fan of triangles, and one for computing the Euclidean distance from a point to a fan of triangles. We demonstrate the effectiveness of the triangle fan representation in several applications, including collision detection, implicit surface modeling and fast ray-tracing.