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.

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.

Abstract Processing and particularly visualizing implicit surfaces remains computationally intensive when dealing with complex objects built from construction trees. We introduce optimization nodes to reduce the computational cost of the field function evaluation for hierarchical construction trees, while preserving the Lipschitz or conservative properties of the function. Our goal is to propose acceleration nodes directly embedded in the construction tree, and avoid external, accompanying data‐structures such as octrees. We present proxy and continuous level of detail nodes to reduce the overall evaluation cost, along with a normal warping technique that enhances surface details with negligible computational overhead. Our approach is compatible with existing algorithms that aim at reducing the number of function calls. We validate our methods by computing timings as well as the average cost for traversing the tree and evaluating the signed distance field at a given point in space. Our method speeds‐up signed distance field evaluation by up to three orders or magnitude, and applies both to ray‐surface intersection computation in Sphere Tracing applications, and to polygonization algorithms.

Abstract Vector‐based graphics offer numerous advantages over grid‐based models, including resolution independence and ease of manipulation. Despite these benefits, their use in landscape modelling remains uncommon because of a lack of direct editing and interactive feedback, essential for matching the artist's vision. We introduce a new vector‐based model for creating digital terrains based on computationally efficient primitives. We propose a method to convert grid‐based digital elevation maps to this representation with a user‐defined level of accuracy. Once vectorized, the terrain can be authored using interactive high‐level skeleton‐based tools adapted to the primitive representation, allowing local deformations that automatically adapt to underlying geomorphological structures and landforms of the terrain.

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.

Abstract Assisting the authoring of virtual terrains is a perennial challenge in the creation of convincing synthetic landscapes. Particularly, there is a need for augmenting artist‐controlled low‐resolution models with consistent relief details. We present a structured noise that procedurally enhances terrains in real time by adding spatially varying erosion patterns. The patterns can be cascaded, i.e. narrow ones are nested into large ones. Our model builds upon the Phasor noise, which we adapt to the specific characteristics of terrains (water flow, slope orientation). Relief details correspond to the underlying terrain characteristics and align with the slope to preserve the coherence of generated landforms. Moreover, our model allows for artist control, providing a palette of control maps, and can be efficiently implemented in graphics hardware, thus allowing for real‐time synthesis and rendering, therefore permitting effective and intuitive authoring.

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.

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.

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.

Abstract Various terrain modelling methods have been proposed for the past decades, providing efficient and often interactive authoring tools. However, they seldom include any notion of style, which is critical for designers in the entertainment industry. We introduce a new generative network method that bridges the gap between automatic terrain synthesis and authoring, providing a versatile set of authoring tools allowing spatialised style. We build upon the StyleGAN2 architecture and extend it with authoring tools. Given an input sketch or existing elevation map, our method generates a terrain with features that can be authored, enhanced, and augmented using interactive brushes and style manipulation tools. The strength of our approach lies in the versatility and interoperability of the different tools. We validate our method quantitatively with drainage calculation against other previous techniques and qualitatively by asking users to follow a prompt or freely create a terrain.

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.

We present a method for interactively authoring and simulating meandering river networks. Starting from a terrain with an initial low-resolution network encoded as a directed graph, we simulate the evolution of the path of the different river channels using a physically-based migration equation augmented with control terms. The curvature-based terms in the equation allow us to reproduce phenomena identified in geomorphology, such as downstream migration of bends. Control terms account for the influence of the landscape topography and user-defined river trajectory constraints. Our model implements abrupt events that shape meandering networks, such as cutoffs forming oxbow lakes and avulsions. We visually show the effectiveness of our method and compare the generated networks quantitatively to river data by analyzing sinuosity and wavelength metrics. Our vector-based model runs at interactive rates, allowing for efficient authoring of large-scale meandering networks.

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.

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.

Terrains are visually prominent and commonly needed objects in many computer graphics applications. While there are many algorithms for synthetic terrain generation, it is rather difficult to assess the realism of a generated output. This article presents a first step toward the direction of perceptual evaluation for terrain models. We gathered and categorized several classes of real terrains, and we generated synthetic terrain models using computer graphics methods. The terrain geometries were rendered by using the same texturing, lighting, and camera position. Two studies on these image sets were conducted, ranking the terrains perceptually, and showing that the synthetic terrains are perceived as lacking realism compared to the real ones. We provide insight into the features that affect the perceived realism by a quantitative evaluation based on localized geomorphology-based landform features (geomorphons) that categorize terrain structures such as valleys, ridges, hollows, and so forth. We show that the presence or absence of certain features has a significant perceptual effect. The importance and presence of the terrain features were confirmed by using a generative deep neural network that transferred the features between the geometric models of the real terrains and the synthetic ones. The feature transfer was followed by another perceptual experiment that further showed their importance and effect on perceived realism. We then introduce Perceived Terrain Realism Metrics (PTRM), which estimates human-perceived realism of a terrain represented as a digital elevation map by relating the distribution of terrain features with their perceived realism. This metric can be used on a synthetic terrain, and it will output an estimated level of perceived realism. We validated the proposed metrics on real and synthetic data and compared them to the perceptual studies.

Abstract We present a geologically‐based method to generate complex karstic networks. Karsts are a type of landscape formed by the dissolution of highly soluble rocks (generally limestones). In particular, they are characterized by complex underground networks made of varieties of tunnels and breakout chambers with stalagmites and stalactites. Our method computes skeletons of karstic networks by using a gridless anisotropic shortest path algorithm according to field data of the underground system (such as inlets and outlets), geomorphological features and parameters such as faults, inception horizons, fractures, and permeability contrasts. From this skeleton, we define the geometry of the conduits as a signed distance function construction tree combining primitives with blending and warping operators. Our framework provides multiple levels of control, allowing us to author both the structure of the karstic network and the geometric cross‐section shapes and details of the generated conduits.

Abstract We introduce Segment Tracing, a new algorithm that accelerates the classical Sphere Tracing method for computing the intersection between a ray and an implicit surface. Our approach consists in computing the Lipschitz bound locally over a segment to improve the marching step computation and accelerate the overall process. We describe the computation of the Lipschitz bound for different operators and primitives. We demonstrate that our algorithm significantly reduces the number of field function queries compared to previous methods, without the need for additional accelerating data‐structures. Our method can be applied to a vast variety of implicit models ranging from hierarchical procedural objects built from complex primitives, to simulation‐generated implicit surfaces created from many particles.

Glaciers are some of the most visually arresting and scenic elements of cold regions and high mountain landscapes. Although snow-covered terrains have previously received attention in computer graphics, simulating the temporal evolution of glaciers as well as modeling their wide range of features has never been addressed. In this paper, we combine a Shallow Ice Approximation simulation with a procedural amplification process to author high-resolution realistic glaciers. Our multiresolution method allows the interactive simulation of the formation and the evolution of glaciers over hundreds of years. The user can easily modify the environment variables, such as the average temperature or precipitation rate, to control the glacier growth, or directly use brushes to sculpt the ice or bedrock with interactive feedback. Mesoscale and smallscale landforms that are not captured by the glacier simulation, such as crevasses, moraines, seracs, ogives, or icefalls are synthesized using procedural rules inspired by observations in glaciology and according to the physical parameters derived from the simulation. Our method lends itself to seamless integration into production pipelines to decorate reliefs with glaciers and realistic ice features.

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.

We introduce Dendry, a procedural function that generates dendritic patterns and is locally computable. The function is controlled by parameters such as the level of branching, the degree of local smoothing, random seeding and local disturbance parameters, and the range of the branching angles. It is also controlled by a global control function that defines the overall shape and can be used, for example, to initialize local minima. The algorithm returns the distance to a tree structure which is implicitly constructed on the fly, while requiring a small memory footprint. The evaluation can be performed in parallel for multiple points and scales linearly with the number of cores. We demonstrate an application of our model to the generation of terrain heighfields with consistent river networks. A quad core implementation of our algorithm takes about ten seconds for a 512 × 512 resolution grid on the CPU.

Abstract We present a procedural method for authoring synthetic tectonic planets. Instead of relying on computationally demanding physically‐based simulations, we capture the fundamental phenomena into a procedural method that faithfully reproduces large‐scale planetary features generated by the movement and collision of the tectonic plates. We approximate complex phenomena such as plate subduction or collisions to deform the lithosphere, including the continental and oceanic crusts. The user can control the movement of the plates, which dynamically evolve and generate a variety of landforms such as continents, oceanic ridges, large scale mountain ranges or island arcs. Finally, we amplify the large‐scale planet model with either procedurally‐defined or real‐world elevation data to synthesize coherent detailed reliefs. Our method allows the user to control the evolution of an entire planet interactively, and to trigger specific events such as catastrophic plate rifting.

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 We present an interactive aeolian simulation to author hot desert scenery. Wind is an important erosion agent in deserts which, despite its importance, has been neglected in computer graphics. Our framework overcomes this and allows generating a variety of sand dunes, including barchans, longitudinal and anchored dunes, and simulates abrasion which erodes bedrock and sculpts complex landforms. Given an input time varying high altitude wind field, we compute the wind field at the surface of the terrain according to the relief, and simulate the transport of sand blown by the wind. The user can interactively model complex desert landscapes, and control their evolution throughout time either by using a variety of interactive brushes or by prescribing events along a user‐defined time‐line.

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 present a phenomenological approach for modeling and animating cloudscapes. We propose a compact procedural model for representing the different types of cloud over a range of altitudes. We define primitive‐based field functions that allow the user to control and author the cloud cover over large distances easily. Our approach allows us to animate cloudscapes by morphing: instead of simulating the evolution of clouds using a physically‐based simulation, we compute the movement of clouds using key‐frame interpolation and tackle the morphing problem as an Optimal Transport problem. The trajectories of the cloud cover primitives are generated by solving an Anisotropic Shortest Path problem with a cost function that takes into account the elevation of the terrain and the parameters of the wind field.

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.

Authoring virtual terrains presents a challenge and there is a strong need for authoring tools able to create realistic terrains with simple user-inputs and with high user control. We propose an example-based authoring pipeline that uses a set of terrain synthesizers dedicated to specific tasks. Each terrain synthesizer is a Conditional Generative Adversarial Network trained by using real-world terrains and their sketched counterparts. The training sets are built automatically with a view that the terrain synthesizers learn the generation from features that are easy to sketch. During the authoring process, the artist first creates a rough sketch of the main terrain features, such as rivers, valleys and ridges, and the algorithm automatically synthesizes a terrain corresponding to the sketch using the learned features of the training samples. Moreover, an erosion synthesizer can also generate terrain evolution by erosion at a very low computational cost. Our framework allows for an easy terrain authoring and provides a high level of realism for a minimum sketch cost. We show various examples of terrain synthesis created by experienced as well as inexperienced users who are able to design a vast variety of complex terrains in a very short time.

Abstract At large scale, landscapes result from the combination of two major processes: tectonics which generate the main relief through crust uplift, and weather which accounts for erosion. This paper presents the first method in computer graphics that combines uplift and hydraulic erosion to generate visually plausible terrains. Given a user‐painted uplift map, we generate a stream graph over the entire domain embedding elevation information and stream flow. Our approach relies on the stream power equation introduced in geology for hydraulic erosion. By combining crust uplift and stream power erosion we generate large realistic terrains at a low computational cost. Finally, we convert this graph into a digital elevation model by blending landform feature kernels whose parameters are derived from the information in the graph. Our method gives high‐level control over the large scale dendritic structures of the resulting river networks, watersheds, and mountains ridges.

Abstract We propose a novel approach for authoring large scenes with automatic enhancement of objects to create geometric decoration details such as snow cover, icicles, fallen leaves, grass tufts or even trash. We introduce environmental objects that extend an input object geometry with a set of procedural effects that defines how the object reacts to the environment, and by a set of scalar fields that defines the influence of the object over of the environment. The user controls the scene by modifying environmental variables, such as temperature or humidity fields. The scene definition is hierarchical: objects can be grouped and their behaviours can be set at each level of the hierarchy. Our per object definition allows us to optimize and accelerate the effects computation, which also enables us to generate large scenes with many geometric details at a very high level of detail. In our implementation, a complex urban scene of 10 000 m2, represented with details of less than 1 cm, can be locally modified and entirely regenerated in a few seconds.

Abstract In this paper, we present a simple and efficient method to represent terrains as elevation functions built from linear combinations of landform features (atoms). These features can be extracted either from real world data‐sets or procedural primitives, or from any combination of multiple terrain models. Our approach consists in representing the elevation function as a sparse combination of primitives, a concept which we call Sparse Construction Tree, which blends the different landform features stored in a dictionary. The sparse representation allows us to represent complex terrains using combinations of atoms from a small dictionary, yielding a powerful and compact terrain representation and synthesis tool. Moreover, we present a method for automatically learning the dictionary and generating the Sparse Construction Tree model. We demonstrate the efficiency of our method in several applications: inverse procedural modeling of terrains, terrain amplification and synthesis from a coarse sketch.

Abstract Digital landscape realism often comes from the multitude of details that are hard to model such as fallen leaves, rock piles or entangled fallen branches. In this article, we present a method for augmenting natural scenes with a huge amount of details such as grass tufts, stones, leaves or twigs. Our approach takes advantage of the observation that those details can be approximated by replications of a few similar objects and therefore relies on mass‐instancing. We propose an original structure, the Ghost Tile, that stores a huge number of overlapping candidate objects in a tile, along with a pre‐computed collision graph. Details are created by traversing the scene with the Ghost Tile and generating instances according to user‐defined density fields that allow to sculpt layers and piles of entangled objects while providing control over their density and distribution.

Abstract We introduce a compact hierarchical procedural model that combines feature‐based primitives to describe complex terrains with varying level of detail. Our model is inspired by skeletal implicit surfaces and defines the terrain elevation function by using a construction tree. Leaves represent terrain features and they are generic parametrized skeletal primitives, such as mountains, ridges, valleys, rivers, lakes or roads. Inner nodes combine the leaves and subtrees by carving, blending or warping operators. The elevation of the terrain at a given point is evaluated by traversing the tree and by combining the contributions of the primitives. The definition of the tree leaves and operators guarantees that the resulting elevation function is Lipschitz, which speeds up the sphere tracing used to render the terrain. Our model is compact and allows for the creation of large terrains with a high level o detail using a reduced set of primitives. We show the creation of different kinds of landscapes and demonstrate that our model allows to efficiently control the shape and distribution of landform features.

In this work, we introduce a method for resizing a landscape specification, i.e., a vector model containing a set of objects present in a virtual environment. Our goal is to change the landscape dimensions while keeping its overall appearance. Our method is based on the insertion and removal of objects in the specification, followed by some adjustments of the scene adapting the initial model to these changes. Furthermore, this method can be easily extended to use other techniques for spreading objects in the landscape. The adjustment of the scene components consists in performing translations onto the position of the objects based on removal or insertion of paths in the grid created over the scene space, using dynamic programming. This technique is an adaptation of the Seam Carving for vector landscapes specification. This model is simpler than common images, and thus, we can achieve good results using simpler metrics.

We present a framework that allows quick and intuitive modeling of terrains using concepts inspired by hydrology. The terrain is generated from a simple initial sketch, and its generation is controlled by a few parameters. Our terrain representation is both analytic and continuous and can be rendered by using varying levels of detail. The terrain data are stored in a novel data structure: a construction tree whose internal nodes define a combination of operations, and whose leaves represent terrain features. The framework uses rivers as modeling elements, and it first creates a hierarchical drainage network that is represented as a geometric graph over a given input domain. The network is then analyzed to construct watersheds and to characterize the different types and trajectories of rivers. The terrain is finally generated by combining procedural terrain and river patches with blending and carving operators.

Abstract We present a procedural method for generating hierarchical road networks connecting cities, towns and villages over large terrains. Our approach relies on an original geometric graph generation algorithm based on a non‐Euclidean metric combined with a path merging algorithm that creates junctions between the different types of roads. Unlike previous work, our method allows high level user control by manipulating the density and the pattern of the network. The geometry of the highways, primary and secondary roads as well as the interchanges and intersections are automatically created from the graph structure by instantiating generic parameterized models.

Abstract In this paper, we propose an automatic method for generating roads based on a weighted anisotropic shortest path algorithm. Given an input scene, we automatically create a path connecting an initial and a final point. The trajectory of the road minimizes a cost function that takes into account the different parameters of the scene including the slope of the terrain, natural obstacles such as rivers, lakes, mountains and forests. The road is generated by excavating the terrain along the path and instantiating generic parameterized models.

Abstract This paper presents a diffusion method for generating terrains from a set of parameterized curves that characterize the landform features such as ridge lines, riverbeds or cliffs. Our approach provides the user with an intuitive vector‐based feature‐oriented control over the terrain. Different types of constraints (such as elevation, slope angle and roughness) can be attached to the curves so as to define the shape of the terrain. The terrain is generated from the curve representation by using an efficient multigrid diffusion algorithm. The algorithm can be efficiently implemented on the GPU, which allows the user to interactively create a vast variety of landscapes.

Abstract This paper presents a physically based method for simulating the heat transfers between the different environmental elements to synthesize realistic winter sceneries. We simulate the snow fall over the ground, as well as the conductive, convective and radiative thermal transfers using a finite volume method according to the variations of air and dew point temperatures, the amount of snow, cloud cover and day‐night cycles. Our approach takes into account phase changes such as snow melting into water or water freezing into ice.

A method for the design and reconstruction of rough surfaces is introduced. A fractal model based on projected IFS attractors allows the definition of free form fractal shapes controlled with a set of points. Ibis flexible model has good fitting properties for recovering surfaces. The approximation is formulated as a non-linear fitting problem and resolved using a modified LEVENBERG-MARQUARDT minimisation method. The main applications are shape design, shape reconstruction and geometric data compression.

This paper addresses the problem of approximation of natural complex shapes. Using MPEG-7 terminology, this problem can be considered as the search of a descriptor for a shape feature. This shape can be defined either as a frontier between image regions or a natural curve. For this purpose, an original descriptor which combines iterated function system (IFS) model and the notion of free form curves is proposed. A set of control points allows one to define the IFS model in a barycentric space. This generalization adds a real flexibility to fractal approximation techniques enriching the set of contractive operators which are candidate to model the self-similarity. This new descriptor named projected IFS model allows the reconstruction of a shape using a projection via the control points. It is adapted to the representation of both smooth shapes (man-made objects, body,..) and fractal shapes (mountain, cloud, tree,..). Results on synthetic shapes and a real mountain shape are presented.