Abstract To support the design and subsequent generation of terrestrial planets for use in the creative media, we propose a solution that employs a generative model trained on satellite data from planetary bodies with a defined solid surface, such as the Earth and Mars. A user sketches coarse elevation, landcover, temperature, and precipitation directly onto a globe. Our model then infers high‐resolution heightmap and surface appearance layers at planetary scales, with sufficient detail to enable animated flyovers within the exosphere at a distance of a few thousand kilometers from the planet surface. We address the issue of distortion in the mapping from atlas to globe using a quadsphere representation, and the consistency of large‐scale geomorphological features by extracting a global river network from the sketch inputs and providing this as conditioning to the diffusion. As our results demonstrate, our generative model provides a balance between: authoring control through a multi‐layer painting interface with a satellite image pre‐visualization; computation times proportional to the surface area being generated; landscape diversity, displaying, without repetition artefacts, the full range of elevation and landcover features drawn from multiple source planets, and geomorphological plausibility through the provision of a consistent uninterrupted exorheic global river network, where the input sketches allow.

A common process in authoring digital scenes for games, films, and virtual environments is for artists to construct 3D geometry that matches a 2D perspective reference image. In the case of the bare-earth terrain, this is typically a manual process since, unlike for trees and buildings, few inverse reconstruction methods currently exist. To address this, we introduce a method for automatically inferring a detailed, consistent, and complete terrain heightmap from a single photographic image. Our initial phase involves extracting camera parameters and a 3D pointmap from the input image, which is then transformed into a heightmap. However, this only recovers the unoccluded portions of the terrain visible from the perspective of the image. The next phase thus entails the generation of plausible occluded regions using a diffusion model trained on terrain elevation data. The entire process is guided by three consistency principles: geomorphological consistency (the features of the occluded terrain resemble the visible portions), hydrological consistency (the river network is uninterrupted and flows reliably), and view consistency (the shape of the rendered terrain accurately matches the input image). We demonstrate that our method obeys these principles, reliably generates terrains across various scales, and integrates with scene authoring workflows.

Abstract We present a method for animating herds that automatically tunes a microscopic herd model based on a short video clip of real animals. Our method handles videos with dense herds, where individual animal motion cannot be separated out. Our contribution is a novel framework for extracting macroscopic herd behaviour from such video clips, and then deriving the microscopic agent parameters that best match this behaviour. To support this learning process, we extend standard agent models to provide a separation between leaders and followers, better match the occlusion and field‐of‐view limitations of real animals, support differentiable parameter optimization and improve authoring control. We validate the method by showing that once optimized, the social force and perception parameters of the resulting herd model are accurate enough to predict subsequent frames in the video, even for macroscopic properties not directly incorporated in the optimization process. Furthermore, the extracted herding characteristics can be applied to any terrain with a palette and region‐painting approach that generalizes to different herd sizes and leader trajectories. This enables the authoring of herd animations in new environments while preserving learned behaviour.

We propose a simple method for the intuitive authoring and efficient animation of virtual tornadoes. Users control the tornado kinematics by sketching two types of curves to specify the initial geometry of the tornado’s core and the profile of the surrounding swirling air, known as the funnel. The first input, a 3D curve, initializes the core as a vortex filament. This filament induces a swirl flow and advects according to its initial curvature, resulting in progressive bending and twisting. The second input consists of one or multiple 2D profile curves that parameterize the Stokes stream function, governing the radial and axial motion of the air around the core and thereby dictate the funnel shape over time. The core and funnel profile are coupled in local frames through closed-form velocities, which together describe the rotation, sliding and uplift within the tornado’s air volume. As shown in our case studies, our method provides a controllable and efficient way to animate visually plausible tornadoes capable of tearing off infrastructure and transporting debris, as well as interacting with uneven terrain.

Abstract Terrain analysis plays an important role in computer graphics, hydrology and geomorphology. In particular, analyzing the path of material flow over a terrain with consideration of local depressions is a precursor to many further tasks in erosion, river formation, and plant ecosystem simulation. For example, fluvial erosion simulation used in terrain modeling computes water discharge to repeatedly locate erosion channels for soil removal and transport. Despite its significance, traditional methods face performance constraints, limiting their broader applicability. In this paper, we propose a novel GPU flow routing algorithm that computes the water discharge in 𝒪(log n) iterations for a terrain with n vertices (assuming n processors). We also provide a depression routing algorithm to route the water out of local minima formed by depressions in the terrain, which converges in 𝒪(log2 n) iterations. Our implementation of these algorithms leads to a 5× speedup for flow routing and 34 × to 52 × speedup for depression routing compared to previous work on a 10242 terrain, enabling interactive control of terrain simulation.

Abstract Explosive volcanic eruptions rank among the most terrifying natural phenomena, and are thus frequently depicted in films, games, and other media, usually with a bespoke once‐off solution. In this paper, we introduce the first general‐purpose model for bi‐directional interaction between the atmosphere and a volcano plume. In line with recent interactive volcano models, we approximate the plume dynamics with Lagrangian disks and spheres and the atmosphere with sparse layers of 2D Eulerian grids, enabling us to focus on the transfer of physical quantities such as temperature, ash, moisture, and wind velocity between these sub‐models. We subsequently generate volumetric animations by noise‐based procedural upsampling keyed to aspects of advection, convection, moisture, and ash content to generate a fully‐realized volcanic skyscape. Our model captures most of the visually salient features emerging from volcano‐sky interaction, such as windswept plumes, enmeshed cap, bell and skirt clouds, shockwave effects, ash rain, and sheathes of lightning visible in the dark.

The creation of truly believable simulated natural environments remains an unsolved problem in Computer Graphics. This is, in part, due to a lack of visual variety. In nature, apart from variation due to abiotic and biotic growth factors, a significant role is played by disturbance events, such as fires, windstorms, disease, and death and decay processes, which give rise to both standing dead trees (snags) and downed woody debris (logs). For instance, snags constitute on average 10% of unmanaged forests by basal area, and logs account for 2 \(\frac{1}{2}\) times this quantity. While previous systems have incorporated individual elements of disturbance (e.g., forest fires) and decay (e.g., the formation of humus), there has been no unifying treatment, perhaps because of the challenge of matching simulation results with generated geometric models. In this paper, we present a framework that combines an ecosystem simulation, which explicitly incorporates disturbance events and decay processes, with a model realization process, which balances the uniqueness arising from life history with the need for instancing due to memory constraints. We tested our hypothesis concerning the visual impact of disturbance and decay with a two-alternative forced-choice experiment ( n = 116). Our findings are that the presence of dead wood in various forms, as snags or logs, significantly improves the believability of natural scenes, while, surprisingly, general variation in the number of model instances, with up to 8 models per species, and a focus on disturbance events, does not.

Abstract Generating heightfield terrains is a necessary precursor to the depiction of computer‐generated natural scenes in a variety of applications. Authoring such terrains is made challenging by the need for interactive feedback, effective user control, and perceptually realistic output encompassing a range of landforms. We address these challenges by developing a terrain‐authoring framework underpinned by an adaptation of diffusion models for conditional image synthesis, trained on real‐world elevation data. This framework supports automated cleaning of the training set; authoring control through style selection and feature sketches; the ability to import and freely edit pre‐existing terrains, and resolution amplification up to the limits of the source data. Our framework improves on previous machine‐learning approaches by: expanding landform variety beyond mountainous terrain to encompass cliffs, canyons, and plains; providing a better balance between terseness and specificity in user control, and improving the fidelity of global terrain structure and perceptual realism. This is demonstrated through drainage simulations and a user study testing the perceived realism for different classes of terrain. The full source code, blender add‐on, and pre‐trained models are available.

We introduce the first solution for simulating the formation and evolution of glaciers, together with their attendant erosive effects, for periods covering the combination of glacial and inter-glacial cycles. Our efficient solution includes both a fast yet accurate deep learning-based estimation of highorder ice flows and a new, multi-scale advection scheme enabling us to account for the distinct time scales at which glaciers reach equilibrium compared to eroding the terrain. We combine the resulting glacial erosion model with finer-scale erosive phenomena to account for the transport of debris flowing from cliffs. This enables us to model the formation of terrain shapes not previously adequately modeled in Computer Graphics, ranging from U-shaped and hanging valleys to fjords and glacial lakes.

Abstract 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.

Abstract Although an important component of natural scenes, the representation of skyscapes is often relatively simplistic. This can be largely attributed to the complexity of the thermodynamics underpinning cloud evolution and wind dynamics, which make interactive simulation challenging. We address this problem by introducing a novel layered model that encompasses both terrain and atmosphere, and supports efficient meteorological simulations. The vertical and horizontal layer resolutions can be tuned independently, while maintaining crucial inter‐layer thermodynamics, such as convective circulation and land‐air transfers of heat and moisture. In addition, we introduce a cloud‐form taxonomy for clustering, classifying and upsampling simulation cells to enable visually plausible, finely‐sampled volumetric rendering. As our results demonstrate, this pipeline allows interactive simulation followed by up‐sampled rendering of extensive skyscapes with dynamic clouds driven by consistent wind patterns. We validate our method by reproducing characteristic phenomena such as diurnal shore breezes, convective cells that contribute to cumulus cloud formation, and orographic effects from moist air driven upslope.

In computer graphics populating a large-scale natural scene with plants in a fashion that both reflects the complex interrelationships and diversity present in real ecosystems and is computationally efficient enough to support iterative authoring remains an open problem. Ecosystem simulations embody many of the botanical influences, such as sunlight, temperature, and moisture, but require hours to complete, while synthesis from statistical distributions tends not to capture fine-scale variety and complexity. Instead, we leverage real-world data and machine learning to derive a canopy height model (CHM) for unseen terrain provided by the user. Trees in the canopy layer are then fitted to the resulting CHM through a constrained iterative process that optimizes for a given distribution of species, and, finally, an understorey layer is synthesised using distributions derived from biome-specific undergrowth simulations. Such a hybrid data-driven approach has the advantage that it incorporates subtle biotic, abiotic, and disturbance factors implicitly encoded in the source data and evidences accepted biological behaviour, such as self-thinning, climatic adaptation, and gap dynamics.

The use of haptic props in a virtual environment setting is purported to improve both user immersion and task performance. While the efficacy of various forms of haptics has been tested through user experiments, this is not the case for hand-held tool props, an important class of input device with both gaming and non-gaming applications. From a cost and complexity of implementation perspective it is also worth investigating the relative benefits of the different types of passive and active haptics that can be incorporated into such props.

Abstract While analysing and synthesising 2D distributions of points has been applied both to the generation of textures with discrete elements and for populating virtual worlds with 3D objects, the results are often inaccurate since the spatial extent of objects cannot be expressed. We introduce three improvements enabling the synthesis of more general distributions of elements. First, we extend continuous pair correlation function (PCF) algorithms to multi‐class distributions using a dependency graph, thereby capturing interrelationships between distinct categories of objects. Second, we introduce a new normalised metric for disks, which makes the method applicable to both point and possibly overlapping disk distributions. The metric is specifically designed to distinguish perceptually salient features, such as disjoint, tangent, overlapping, or nested disks. Finally, we pay particular attention to convergence of the mean PCF as well as the validity of individual PCFs, by taking into consideration the variance of the input. Our results demonstrate that this framework can capture and reproduce real‐life distributions of elements representing a variety of complex semi‐structured patterns, from the interaction between trees and the understorey in a forest to droplets of water. More generally, it applies to any category of 2D object whose shape is better represented by bounding circles than points.

Abstract Terrains are a crucial component of three‐dimensional scenes and are present in many Computer Graphics applications. Terrain modeling methods focus on capturing landforms in all their intricate detail, including eroded valleys arising from the interplay of varied phenomena, dendritic mountain ranges, and complex river networks. Set against this visual complexity is the need for user control over terrain features, without which designers are unable to adequately express their artistic intent. This article provides an overview of current terrain modeling and authoring techniques, organized according to three categories: procedural modeling, physically‐based simulation of erosion and land formation processes, and example‐based methods driven by scanned terrain data. We compare and contrast these techniques according to several criteria, specifically: the variety of achievable landforms; realism from both a perceptual and geomorphological perspective; issues of scale in terms of terrain extent and sampling precision; the different interaction metaphors and attendant forms of user‐control, and computation and memory performance. We conclude with an in‐depth discussion of possible research directions and outstanding technical and scientific challenges.

Abstract This paper addresses the problem of creating animated riverscapes through a novel procedural framework that generates the inscribing geometry of a river network and then synthesizes matching real‐time water movement animation. Our approach takes bare‐earth heightfields as input, derives hydrologically‐inspired river network trajectories, carves riverbeds into the terrain, and then automatically generates a corresponding blend‐flow tree for the water surface. Characteristics, such as the riverbed width, depth and shape, as well as elevation and flow of the fluid surface, are procedurally derived from the terrain and river type. The riverbed is inscribed by combining compactly supported elevation modifiers over the river course. Subsequently, the water surface is defined as a time‐varying continuous function encoded as a blend‐flow tree with leaves that are parameterized procedural flow primitives and internal nodes that are blend operators. While river generation is fully automated, we also incorporate intuitive interactive editing of both river trajectories and individual riverbed and flow primitives. The resulting framework enables the generation of a wide range of river forms, ranging from slow meandering rivers to rapids with churning water, including surface effects, such as foam and leaves carried downstream.

Mountainous digital terrains are an important element of many virtual environments and find application in games, film, simulation and training. Unfortunately, while existing synthesis methods produce locally plausible results they often fail to respect global structure. This is exacerbated by a dearth of automated metrics for assessing terrain properties at a macro level. We address these issues by building on techniques from orometry, a field that involves the measurement of mountains and other relief features. First, we construct a sparse metric computed on the peaks and saddles of a mountain range and show that, when used for classification, this is capable of robustly distinguishing between different mountain ranges. Second, we present a synthesis method that takes a coarse elevation map as input and builds a graph of peaks and saddles respecting a given orometric distribution. This is then expanded into a fully continuous elevation function by deriving a consistent river network and shaping the valley slopes. In terms of authoring, users provide various control maps and are also able to edit, reposition, insert and remove terrain features all while retaining the characteristics of a selected mountain range. The result is a terrain analysis and synthesis method that considers and incorporates orometric properties, and is, on the basis of our perceptual study, more visually plausible than existing terrain generation methods.

While three-dimensional landforms, such as arches and overhangs, occupy a relatively small proportion of most computer-generated landscapes, they are distinctive and dramatic and have an outsize visual impact. Unfortunately, the dominant heightfield representation of terrain precludes such features, and existing in-memory volumetric structures are too memory intensive to handle larger scenes. In this article, we present a novel memory-optimized paradigm for representing and generating volumetric terrain based on implicit surfaces. We encode feature shapes and terrain geology using construction trees that arrange and combine implicit primitives. The landform primitives themselves are positioned using Poisson sampling, built using open shape grammars guided by stratified erosion and invasion percolation processes, and, finally, queried during polygonization. Users can also interactively author landforms using high-level modeling tools to create or edit the underlying construction trees, with support for iterative cycles of editing and simulation. We demonstrate that our framework is capable of importing existing large-scale heightfield terrains and amplifying them with such diverse structures as slot canyons, sea arches, stratified cliffs, fields of hoodoos, and complex karst cave networks.

Abstract We introduce a novel method for interactive generation of visually consistent, snow‐covered landscapes and provide control of their dynamic evolution over time. Our main contribution is the real‐time phenomenological simulation of avalanches and other user‐guided events, such as tracks left by Nordic skiing, which can be applied to interactively sculpt the landscape. The terrain is modeled as a height field with additional layers for stable, compacted, unstable, and powdery snow, which behave in combination as a semi‐viscous fluid. We incorporate the impact of several phenomena, including sunlight, temperature, prevailing wind direction, and skiing activities. The snow evolution includes snow‐melt and snow‐drift, which affect stability of the snow mass and the probability of avalanches. A user can shape landscapes and their evolution either with a variety of interactive brushes, or by prescribing events along a winter season time‐line. Our optimized GPU‐implementation allows interactive updates of snow type and depth across a large (10 × 10km) terrain, including real‐time avalanches, making this suitable for visual assets in computer games. We evaluate our method through perceptual comparison against exiting methods and real snow‐depth data.

One challenge in portraying large-scale natural scenes in virtual environments is specifying the attributes of plants, such as species, size and placement, in a way that respects the features of natural ecosystems, while remaining computationally tractable and allowing user design. To address this, we combine ecosystem simulation with a distribution analysis of the resulting plant attributes to create biome-specific databases, indexed by terrain conditions, such as temperature, rainfall, sunlight and slope. For a specific terrain, interpolated entries are drawn from this database and used to interactively synthesize a full ecosystem, while retaining the fidelity of the original simulations. A painting interface supplies users with semantic brushes for locally adjusting ecosystem age, plant density and variability, as well as optionally picking from a palette of precomputed distributions. Since these brushes are keyed to the underlying terrain properties a balance between user control and real-world consistency is maintained. Our system can be be used to interactively design ecosystems up to 5 × 5 km2 in extent, or to automatically generate even larger ecosystems in a fraction of the time of a full simulation, while demonstrating known properties from plant ecology such as succession, self-thinning, and underbrush, across a variety of biomes.

We introduce a novel framework for interactive landscape authoring that supports bi-directional feedback between erosion and vegetation simulation. Vegetation and terrain erosion have strong mutual impact and their interplay influences the overall realism of virtual scenes. Despite their importance, these complex interactions have been neglected in computer graphics. Our framework overcomes this by simulating the effect of a variety of geomorphological agents and the mutual interaction between different material and vegetation layers, including rock, sand, humus, grass, shrubs, and trees. Users are able to exploit these interactions with an authoring interface that consistently shapes the terrain and populates it with details. Our method, validated through side-by-side comparison with real terrains, can be used not only to generate realistic static landscapes, but also to follow the temporal evolution of a landscape over a few centuries.