We present a novel shape-aware method for synthesizing 2D and 3D discrete element textures consisting of collections of distinct vector graphics objects. Extending the long-proven point process framework, we propose a shape process, a novel stochastic model based on spatial measurements that fully take into account the geometry of the elements. We demonstrate that our approach is well-suited for discrete texture synthesis by example. Our model enables for both robust statistical parameter estimation and reliable output generation by Monte Carlo sampling. Our numerous experiments show that contrary to current state-of-the-art techniques, our algorithm manages to capture anisotropic element distributions and systematically prevents undesirable collisions between objects.