Skeleton-based implicit surfaces, and convolution surfaces in particular, offer an intuitive and expressive representation for geometric modeling. However, their evaluation and rendering remain computationally demanding, and are often affected by aliasing artifacts. In this paper, we introduce a continuous level of detail framework for the automatic simplification of SCALIS convolution surfaces, achieving up to an order-of-magnitude reduction in rendering time while mitigating aliasing artifacts. Our solution dynamically adapts the blending behavior between shape components to preserve the perceived visual appearance of the surface, while progressively simplifying the underlying skeletal geometry. In contrast to traditional simplification techniques, our method allows controlled changes in topological genus when visually beneficial. Our results demonstrate that the proposed framework effectively reduces visual artifacts and computational cost, while maintaining high fidelity to the overall shape.

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.

Abstract We introduce a novel semi‐procedural approach that avoids drawbacks of procedural textures and leverages advantages of data‐driven texture synthesis. We split synthesis in two parts: 1) structure synthesis, based on a procedural parametric model and 2) color details synthesis, being data‐driven. The procedural model consists of a generic Point Process Texture Basis Function (PPTBF), which extends sparse convolution noises by defining rich convolution kernels. They consist of a window function multiplied with a correlated statistical mixture of Gabor functions, both designed to encapsulate a large span of common spatial stochastic structures, including cells, cracks, grains, scratches, spots, stains, and waves. Parameters can be prescribed automatically by supplying binary structure exemplars. As for noise‐based Gaussian textures, the PPTBF is used as stand‐alone function, avoiding classification tasks that occur when handling multiple procedural assets. Because the PPTBF is based on a single set of parameters it allows for continuous transitions between different visual structures and an easy control over its visual characteristics. Color is consistently synthesized from the exemplar using a multiscale parallel texture synthesis by numbers, constrained by the PPTBF. The generated textures are parametric, infinite and avoid repetition. The data‐driven part is automatic and guarantees strong visual resemblance with inputs.

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 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.

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.

Most mountain ranges are formed by the compression and folding of colliding tectonic plates. Subduction of one plate causes large-scale asymmetry while their layered composition (or stratigraphy) explains the multi-scale folded strata observed on real terrains. We introduce a novel interactive modeling technique to generate visually plausible, large scale terrains that capture these phenomena. Our method draws on both geological knowledge for consistency and on sculpting systems for user interaction. The user is provided hands-on control on the shape and motion of tectonic plates, represented using a new geologically-inspired model for the Earth crust. The model captures their volume preserving and complex folding behaviors under collision, causing mountains to grow. It generates a volumetric uplift map representing the growth rate of subsurface layers. Erosion and uplift movement are jointly simulated to generate the terrain. The stratigraphy allows us to render folded strata on eroded cliffs. We validated the usability of our sculpting interface through a user study, and compare the visual consistency of the earth crust model with geological simulation results and real terrains.

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.

Interaction inside virtual reality applications begins usually with simple selection tasks that can be achieved with moderate degrees of performances. More complex operations like modeling or sculpting inside an immersive environment raises however increased needs for precise 3D selections and visual feedback. In a modeling context any 3D location must be targetable, even ones that are outside of initial reach or not graphically represented. Common interaction techniques in virtual reality do not fullfill these goals without switching between different tools. We present an extensive and precise selection technique called the 3D arrow, used for moving and sculpting inside an immersive terrain modeling application. Composed of a graphic mouse-like pointer constrained inside a workspace defined by the region of space at arm's reach, the 3D arrow allow the users to seamlessly reach and target any position of space within the same interaction paradigm and to rotate the view around the pointer. The graphic appearance of the pointer is carefully designed to help users estimate its global and local position in the terrain scenery.

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.

Abstract In this paper, we present a framework for representing complex terrains with such features as overhangs, arches and caves and including different materials such as sand and rocks. Our hybrid model combines a volumetric discrete data structure that stores the different materials and an implicit representation for sculpting and reconstructing the surface of the terrain. Complex scenes can be edited and sculpted interactively with high level tools. We also propose an original rock generation technique that enables us to automatically generate complex rocky sceneries with piles of rocks without any computationally demanding physically‐based simulation.

Abstract In this paper, we present a tiling method for generating piles of rocks without any computationally demanding physically‐based simulation. Previous techniques rely on a periodic tiling of rocks and generate unrealistic repetitive patterns. In contrast, our approach relies on a modified corner cube algorithm to generate a set of aperiodic tiles. We generalize the construction method so that the geometry of rocks should straddle corner cubes with a view to avoiding unrealistic gaps in the arrangement of rocks. Moreover, we propose an original technique to control the shape of rocks into contact by computing the Voronoï cells using a parameterized anisotropic distance. Our method has been successfully used to generate landscapes and stone huts and walls with thousands of rocks piled together.

In this paper, we present a new and efficient spherical harmonics decomposition for spherical functions defining 3D triangulated objects. Such spherical functions are intrinsically associated to star-shaped objects. However, our results can be extended to any triangular object after segmentation into star-shaped surface patches and recomposition of the results in the implicit framework. There is thus no restriction about the genus number of the object. We demonstrate that the evaluation of the spherical harmonics coefficients can be performed by a Monte Carlo integration over the edges, which makes the computation more accurate and faster than previous techniques, and provides a better control over the precision error in contrast to the voxel-based methods. We present several applications of our research, including fast spectral surface reconstruction from point clouds, local surface smoothing and interactive geometric texture transfer.

In this paper, we present a controllable, fast and efficient particle system framework for skeletal implicit surfaces defined by the BlobTree model. We propose efficient algorithms for generating sets of particles for every type of skeletal element and for combining those sets for warping, blending and Boolean nodes. Given a target level of detail, our system generates particles which are distributed uniformly over the implicit surface. Our incremental approach lends itself to interactive editing of complex models

This paper presents a technique for decomposing a triangulated model into a set of triangle fans. We show that the triangle fan representation improves the performance of several fundamental geometric algorithms operating over triangle meshes. We present two accelerated algorithms, one for computing the nearest intersection between a ray and a fan of triangles, and one for computing the Euclidean distance from a point to a fan of triangles. We demonstrate the effectiveness of the triangle fan representation in several applications, including collision detection, implicit surface modeling and fast ray-tracing.

Complex implicit CSG models can be represented hierarchically as a tree of nodes (the BlobTree) . However, current methods cannot be used to visualize changes made to these models at interactive rates due to the large number of potential field evaluations required. A hierarchical spatial caching technique is presented which accelerates evaluations of the potential function. This method introduces the concept of a caching node inserted into the implicit model tree. Caching nodes store exact potential field values at the vertices of a voxel grid and rely on tri-linear and tri-quadratic reconstruction filters to locally approximate the potential field of a sub-tree. A lazy evaluation scheme is used to avoid expensive pre-computation. Polygonization timings with and without caching are compared for a complex model undergoing manipulation in an interactive modeling tool. An order-of-magnitude improvement in visualization time is achieved for complex implicit models containing thousands of primitives.

We introduce a hybrid modeling framework for creating complex objects. Our system relies on an extended CSG tree that assembles skeletal implicit surfaces and polygonal meshes in a coherent fashion: we call this structure the hybridtree. Editing operations are performed by exploiting the complementary abilities of both implicit and parametric surface representations. Implicit surfaces are powerful for combining shapes with Boolean and blending operations, while polygonal meshes are well-suited for local deformations such as FFD and fast visualization. The evaluation of the hybridtree is performed on the fly either through field function queries when the implicit form is required, or through a mesh creation process which is specific and optimized for every kind of node. Both types of queries are achieved in a complete transparent way for the user.

This work presents a procedural method for modeling cracks and fractures in solid materials such as glass, metal and stone. Existing physically based techniques are computationally demanding and lack control over crack and fracture propagation. Our procedural approach provides the designer with simple tools to control the pattern of the cracks and the size and shape of fragments. Given a few parameters, our method automatically creates a vast range of types of cracks and fragments of different shapes.

Abstract This paper presents a system for modeling lichens and simulating their propagation and growth in a virtual scene. Lichens colonize almost every substrate in nature and play an important role in the visual appearance of a natural object. The propagation of lichens over the substrate is performed by an Open Diffusion Limited Aggregation model constrained by the characteristics of the environment. The designer can control the development of lichens with simple parameters. Rendering the complex geometry and texture of lichens is achieved by instantiating three dimensional lichen models stored in an atlas of shapes created after real world images. The lichens obtained by our approach considerably increase the realism of complex natural scenes. Categories and Subject Descriptors (according to ACMCCS):I.3.3 [Computer Graphics]:Three‐Dimensional Graphics and Realism

Although many animation, deformation and metamorphosis techniques have been proposed, the simultaneous combination of those three transformations has never been addressed for three-dimensional objects so far. This paper presents a framework for controlling metamorphosis between two animated implicit models built from skeletal elements. It relies on the animated BlobTree model that encompasses the animation and metamorphosis in a unified and coherent fashion. Our method is general and supports a wide range of animation systems such as key-frames or physically based systems.

This paper presents simple and efficient deformation methods based on a new class of interpolating N-adic subdivision algorithms. Our N-adic scheme is a natural extension of a standard dyadic scheme-each face of the mesh is more generally divided into N/sup 2/ sub-faces-and geometric properties are similar. This framework enables us to locally deform the surface using different tools by either modifying the direction of normals at the vertices of the control mesh, or twisting them. Experiments show that the N-adic decomposition provides a more accurate control over deformations, and proves to be a good alternative to dyadic decompositions.

This paper presents several improvements to the marching triangles algorithm for general implicit surfaces. The original method generates equilateral triangles of constant size almost everywhere on the surface. We present several modifications to adapt the size of the triangles to the curvature of the surface. As cracks may arise in the resulting polygonization, we propose a specific crack‐closing method invoked at the end of the mesh growing step. Eventually, we show that the marching triangles can be used as an incremental meshing technique in an interactive modeling environment. In contrast to existing incremental techniques based on spatial subdvision, no extra data‐structure is needed to incrementally edit skeletal implicit surfaces, which saves both memory and computation time.

Implicit surfaces have proved to be a particularly well suited and efficient model for animating and morphing shapes of arbitrary topologies. The BlobTree model is characterized as a hierarchical combination of skeletal primitives organized in a tree. The nodes hold blending, boolean and warping operators, which allows the design of complex objects. In this paper, we address the metamorphosis of the BlobTree. This appears a difficult task as the tree data‐structures of the initial and final shapes are completely different in the general case, and consequently cannot be matched easily. We propose an original technique that solves the correspondence process and creates an intermediate generic BlobTree model whose instances interpolate the initial and final shapes. The animator may control the correspondence between features and can specify both the speed of transformation and the trajectory of the nodes and the leaves of the generic BlobTree model. This provides the end user with a tight control over the transformation so as to achieve good visual effects.

Automatic blending has characterized the major advantage of implicit surface modeling systems. Recently, the introduction of deformations based on space warping and Boolean operations between primitives has increased the usefulness of such systems. We propose a further enhancement which will extend the range of models that can be easily and intuitively defined with a skeletal implicit surface system. We describe a hierarchical method which allows arbitrary compositions of models that make use of blending, warping and Boolean operations. We call this structure the BlobTree. Blending and space warping are treated in the same way as union, difference and intersection, i.e. as nodes in the BlobTree. The traversal of the BlobTree is described along with two rendering algorithms; a polygonizer and a ray tracer. We present some examples of interesting models which can be made easily using our approach that would be very difficult to represent with conventional systems.

The paper describes an incremental polygonization technique for implicit surfaces built from skeletal elements. The method lends itself as an interactive modeling system as the mesh is updated locally in regions of space where changes in the potential field occurred. The authors rely on an octree decomposition of space combined with Lipschitz conditions to recursively subdivide cells until a given level of precision is reached. Timings show that the incremental algorithm dramatically speeds up the overall polygonization process for complex objects.

Abstract This paper addresses the metamorphosis of soft objects built from skeletons. We propose a new approach that may be split into three steps. The first step consists in an original splitting of the initial and the final shapes with a view to creating a bijective graph of correspondence. In the second step, we assume that the skeletons are convex polygonal shapes, and thus take advantage of the properties of Minkowski sums to characterize the skeletons of intermediate shapes. Eventually, we characterize the intermediate distance and field functions; we describe a set of interpolation methods and propose to use a restricted class of parametrized distance and field functions so as to preserve coherence and speed‐up computations. We show that we can easily extend those results to achieve a Bézier like metamorphosis where control points are replaced by control soft objects; in this scope, we have adapted existing accelerated techniques that build a Bézier transformation from a set of convex polyhedra to any kind of convex polygonal shapes. Eventually, we point out that matching all components of the initial and the final shapes generates amorphous intermediate shapes based on an overwhelming number of intermediate sub‐components. Thus, we propose heuristics with a view to preserving coherence during the transformation and accelerating computations. We have implemented and tested our techniques in an experimental ray‐tracer.