Abstract: A number of methods for constructing bounding volume hierarchies and point-based octrees on the GPU are based on the idea of ordering primitives along a space-filling curve. A major shortcoming with these methods is that they construct levels of the tree sequentially, which limits the amount of parallelism that they can achieve. We present a novel approach that improves scalability by constructing the entire tree in parallel. Our main contribution is an in-place algorithm for constructing binary radix trees, which we use as a building block for other types of trees.