We turn the Self-organizing Map (SOM) into an Oriented and Scalable Map (OS-Map) by generalizing the neighborhood function and the winner selection. The homogeneous Gaussian neighborhood function is replaced with the matrix exponential. Thus we can specify the orientation either in the map space or in the data space. Moreover, we associate the map's global scale with the locality of winner selection. Our model is suited for a number of graphical applications such as texture/image synthesis, surface parameterization, and solid texture synthesis. OS-Map is more generic and versatile than the task-specific algorithms for these applications. Our work reveals the overlooked strength of SOMs in processing images and geometries. (C) 2016 Elsevier Ltd. All rights reserved.