Abstract Digital terrains are central to realistic landscape depiction, yet authoring tools must balance perceptual realism with intuitive artistic control. We propose a compact vector‐based representation that models terrain as nested iso‐contours, inspired by geomorphology and cartography. Our method departs from traditional grid‐based elevation models by generating contours through an inward Open Eden Growth simulation, followed by marching‐triangles reconstruction into a Triangulated Irregular Network. This contour framework supports direct editing such as warping, slope modulation, and smoothing, while allowing reconstruction of a standard elevation map for downstream processing, including erosion and amplification. The approach enables the creation of diverse, realistic terrains from minimal user input and offers simple yet powerful control for designers.

We introduce the PhaseTree, a novel hierarchical construction-tree representation for compactly modeling volumetric objects composed of multiple phases or materials across scales. An object is defined as a single construction tree that combines phase-aware primitives through composition and warping operators, yielding a unified multiphase signed distance representation that naturally supports complex topologies and interfaces between phases. The PhaseTree is compatible with standard signed distance field workflows: single-phase algorithms can be directly promoted to a PhaseTree, and conversely reduced without loss of information. As a result, our model integrates seamlessly with existing algorithms and rendering pipelines. We extend classical Sphere Tracing to robustly handle multiphase configurations and show that, despite the additional expressiveness, our implementation preserves the compactness and resolution independence of signed distance fields and incurs less than a 25% runtime overhead compared to single-phase Sphere Tracing.

Abstract Synthetic landscape generation is an active research area within Computer Graphics. Algorithms for terrain synthesis and ecosystem simulations often rely on simple descriptors such as slope, light accessibility, and drainage area. Typically, the results are assessed from a perceptual standpoint, focusing primarily on visual plausibility. Other fields, such as Geomorphology and Earth Sciences, have already proposed several analytical descriptors to measure various terrain properties. This work aims to bridge the gap between these disciplines and Computer Graphics. We provide a comprehensive review of commonly used terrain metrics that may be relevant for landscape synthesis, analysis, or simulations. Additionally, we compare the approaches used in Computer Graphics to see if these metrics, or similar ones, have already been introduced. Moreover, we report feedback from a preliminary study conducted with a group of artists to evaluate the potential applications of previously unused metrics. By implementing all these metrics, we enable performance comparisons. Together with the provided correlation matrix, this helps identify instances where a simpler and faster metric can serve as a proxy for a more computationally intensive one.

We introduce Sphere Carving , a novel method for automatically computing bounding volumes that closely bound a procedurally defined implicit surface. Starting from an initial bounding volume located far from the object, we iteratively approach the surface by leveraging the signed distance function information. Field function queries define a set of empty spheres, from which we extract intersection points that are used to compute a bounding volume. Our method is agnostic of the function representation and only requires a conservative signed distance field as input. This encompasses a large set of procedurally defined implicit surface models such as exact or Lipschitz functions, BlobTrees, or even neural representations. Sphere Carving is conceptually simple, independent of the function representation, requires a small number of function queries to create bounding volumes, and accelerates queries in Sphere Tracing and polygonization.

Modeling high-resolution terrains is a perennial challenge in the creation of virtual worlds. In this paper, we focus on the amplification of a low-resolution input terrain into a high-resolution, hydrologically consistent terrain featuring complex patterns by a multi-scale approach. Our framework combines the best of both worlds, relying on physics-inspired erosion models producing consistent erosion landmarks and introducing control at different scales, thus bridging the gap between physics-based erosion simulations and multi-scale procedural modeling. The method uses a fast and accurate approximation of different simulations, including thermal, stream power erosion and deposition performed at different scales to obtain a range of effects. Our approach provides landscape designers with tools for amplifying mountain ranges and valleys with consistent details.

Large-scale terrains are essential in the definition of virtual worlds. Given the diversity of landforms and the geomorphological complexity, there is a need for authoring techniques offering hydrological consistency without sacrificing user control. In this article, we bridge the gap between large-scale erosion simulation and authoring into an efficient framework. We set aside modeling in the elevation domain in favour of the uplift domain and compute emerging reliefs by simulating the stream power erosion. Our simulation relies on a fast yet accurate approximation of drainage area and flow routing to compute the erosion interactively, which allows for incremental authoring. Our model provides landscape artists with tools for shaping mountain ranges and valleys, such as copy-and-paste operations; warping for imitating folds and faults; and point and curve elevation constraints to precisely sculpt ridges or carve river networks. It also lends itself to inverse procedural modeling by reconstructing the uplift from an input digital elevation model and allows hydrologically consistent blending between terrain patches.