Gradient Terrain Authoring

Digital terrains are a foundational element in the computer-generated depiction of natural scenes. Given the variety and complexity of real-world landforms, there is a need for authoring solutions that achieve perceptually realistic outcomes without sacrificing artistic control. In this paper, we propose setting aside the elevation domain in favour of modelling in the gradient domain. Such a slope-based representation is height independent and allows a seamless blending of disparate landforms from procedural, simulation, and real-world sources. For output, an elevation model can always be recovered using Poisson reconstruction, which can include Dirichlet conditions to constrain the elevation of points and curves. In terms of authoring our approach has numerous benefits. It provides artists with a complete toolbox, including: cut-and-paste operations that support warping as needed to fit the destination terrain, brushes to modify region characteristics, and sketching to provide point and curve constraints on both elevation and gradient. It is also a unifying representation that enables the inclusion of tools from the spectrum of existing procedural and simulation methods, such as painting localised high-frequency noise or hydraulic erosion, without breaking the formalism. Finally, our constrained reconstruction is GPU optimized and executes in real-time, which promotes productive cycles of iterative authoring.