Abstract We present a real‐time method to capture and simulate the dynamic behavior of watercolor painting. We develop a physically accurate, grid‐based, real‐time fluid simulation based on a reparameterized Thin Film model. The equations are rewritten so as to create principled parameters that finely control the length, thickness, and frequency of dripping. Our close connection with physics allows both theoretical and experimental validation of our method. The resulting system can reproduce dripping, fluid‐air interface, and pigment advection and diffusion, all controllable by the user in real‐time. Our experiments show that artists can use our system to create interesting and varied digital paintings.

Abstract Rendering tree‐based analytical Signed Distance Fields (SDFs) through sphere tracing often requires to evaluate many primitives per tracing step, for many steps per pixel of the end image. This cost quickly becomes prohibitive as the number of primitives that constitute the SDF grows. In this paper, we alleviate this cost by computing local pruned trees that are equivalent to the full tree within their region of space while being much faster to evaluate. We introduce an efficient hierarchical tree pruning method based on the Lipschitz property of SDFs, which is compatible with hard and smooth CSG operators. We propose a GPU implementation that enables real‐time sphere tracing of complex SDFs composed of thousands of primitives with dynamic animation. Our pruning technique provides significant speedups for SDF evaluation in general, which we demonstrate on sphere tracing tasks but could also lead to significant improvement for SDF discretization or polygonization.

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.

Procedural implicit surfaces are a popular representation for shape modeling. They provide a simple framework for complex geometric operations such as Booleans, blending and deformations. However, their editability remains a challenging task: as the definition of the shape is purely implicit, direct manipulation of the shape cannot be performed. Thus, parameters of the model are often exposed through abstract sliders, which have to be nontrivially created by the user and understood by others for each individual model to modify. Further, each of these sliders needs to be set one by one to achieve the desired appearance. To circumvent this laborious process while preserving editability, we propose to directly manipulate the implicit surface in the viewport. We let the user naturally interact with the output shape, leveraging points on a co-parameterization we design specifically for implicit surfaces, to guide the parameter updates and reach the desired appearance faster. We leverage our automatic differentiation of the procedural implicit surface to propagate interactions made by the user in the viewport to the shape parameters themselves. We further design a solver that uses such information to guide an intuitive and smooth user workflow. We demonstrate different editing processes across multiple implicit shapes and parameters that would be tedious by tuning sliders.

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.

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 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.

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.

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.