Abstract: We present a new parameterized representation called surface distance maps for distance computations on piecewise 2-manifold primitives. Given a set of orientable 2-manifold primitives, the surface distance map represents the (non-zero) signed distance-to-closest-primitive mapping at each point on a 2-manifold. The distance mapping is computed from each primitive to the set of remaining primitives. We present an interactive algorithm for computing the surface distance map of triangulated meshes using graphics hardware. We precompute a surface parameterization and use the it to define an affine transformation for each mesh primitive. Our algorithm efficiently computes the distance field by applying this affine transformation to the distance functions of the primitives and evaluating these functions using texture mapping hardware. In practice, our algorithm can compute very high resolution surface distance maps at interactive rates and provides tight error bounds on their accuracy. We use surface distance maps for path planning and proximity query computation among complex models in dynamic environments. Our approach can perform planning and proximity queries in a dynamic environment with hundreds of objects at interactive rates and offer significant speedups over prior algorithms.