Abstract: In this paper, we propose an efficient method for partial 3D shape matching based on minimizing the geometric distance between the source and the target geometry. Unlike existing methods, our method does not use a feature-based distance in order to obtain a matching score. Instead, we use a fast, GPU-based method to approximate the true geometric distance between the source and the target by rendering the source object into a distance field which was built around the target. This function behaves smoothly in the space of transformations and allows for an efficient gradient-based local optimization. In order to overcome local minima, we use single point correspondences between surface points on the source and the target respectively employing simple, yet efficient local features based on the distribution of normal vectors around a reference point. The best correspondences define starting positions for a local optimization. The high efficiency of the distance computation allows for robust determination of the global minima in less than a second, which makes our method usable in interactive applications. Our method works for any kind of input data since it only requires point data with normal information at each point. We also demonstrate the capability of our algorithm to perform global alignment of similar 3D objects.