DEGREE PROJECT IN COMPUTER SCIENCE AND ENGINEERING, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2019 Procedural Generation of Volumetric Data for Terrain HENRIQUE FURTADO MACHADO KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE Sammanfattning En proceduell metod har framställts för att generera volymdata för terräng- er med hjälp av en höjdkarta samt information om terrängens material. Till skillnad från tidigare metoder har följande nyttjat den omfattande forskningen kring genererad terräng. Det här genom att anpassa materialens lager till ter- rängens topologi. Metoden tillåter användaren att specifiera materialen som stratifierade eller eroderade, vilket genereras olika: stratifierat material stap- las och generar på så vis materialen i lager, medan eroderat material samlas på jämn terräng. Vi jämför en termisk erosionsmetod med originellt tillväga- gångssätt som nyttjar användarinformation om terrängens lutning som en gen- väg till att generera eroderade lager samt presterar signifikant bättre. Fördelar samt nackdelar med båda teknikerna utforskas och diskuteras. Procedural Generation of Volumetric Data for Terrain Henrique Furtado Machado School of Electrical Engineering and Computer Science KTH Royal Institute of Technology [email protected] Figure 1: Procedually generated volumetric material layers . ABSTRACT 1 INTRODUCTION A procedural method is proposed to generate volumetric data for Terrain is often an integral part of virtual applications such as terrain using a surface height map and information about materials games, feature film special effects and simulations. Creating land- as input. In contrast to previous explored methods this approach scapes with a high level of detail can be a time consuming task takes advantage of the extensive research on surface terrain gener- for artists and developers, thus several techniques have been pro- ation by adapting the material layers to the topology of the input posed to procedurally generate them. Using these techniques it is terrain. The method allows the user to specify materials as stratified possible to randomly create expansive environments in a matter or eroded, which are generated differently: stratified materials are of seconds. These methods have been explored both in the field stacked to generate material layers while eroded materials accumu- of computer graphics and procedural content generation, and can late on even terrain. We compare a thermal erosion method and broadly be categorized as procedural-based, simulation-based or an original approach that uses information about the slope of the example-based methods [Galin et al. 2019]. terrain as a shortcut to generate eroded layers and performs signifi- The use of procedural generation is even more relevant for ap- cantly better. The advantages and drawbacks of each technique are plications that require volumetric terrain - terrain in which there explored and discussed. is also information about subsurface materials - since the amount of data that has to be created is exponentially larger. The success of Minecraft 1, a game in which players explore a procedurally generated virtual world that they can dig through to find caves KEYWORDS and secrets underground shows the demand for techniques that generate volumetric terrain. procedural terrain generation, volumetric terrain, thermal erosion, procedural modelling 1https://www.minecraft.net/ 1 User generated material information Input height map Output terrain Stratified layers Erosion Simulation generation Figure 2: Step by step of the proposed method. In the literature, volumetric models for storing data are often that can be observed in large-scale terrain. This is often achieved used to improve surface terrain using erosion techniques [Mus- through the use of fractional Brownian motion (fBm), where the grave et al. 1989] or by adding interesting features such as arches same base function is sampled with increasing frequencies and and overhangs [Gamito and Musgrave 2001; Peytavie et al. 2009]. decreasing amplitudes generating the so called octaves which are However, very little has been explored regarding techniques that then added together [Fournier et al. 1982]. generate volumetric material data for terrain, and the only method The midpoint displacement and diamond-square algorithms are present in the literature produces uninteresting surface terrain popular examples of base functions that are used to generate octaves [Santamaría-Ibirika et al. 2014]. for the fBm. These subdivision algorithms iteratively divide the In this paper a method is introduced to generate appropriate terrain while adding random displacements on the grid that is volumetric data that adapts to the topology of the surface terrain created [Mandelbrot 1983]. provided as input. In order to achieve these results, two different Another popular option of base function for the fBm are noise methods are proposed to generate what are referred to as eroded functions [Lagae et al. 2010]. Since the introduction of Perlin noise materials. While the stratified materials form the layers that are [Perlin 1985], many different variations, improvements and ex- stacked on top of each other to create the static part of the volu- tensions have been proposed and used for terrain generation. The metric terrain, the eroded materials accumulate on areas with even original Perlin noise and most of its extensions are a type of gradient terrain. To generate them, one of the proposed methods is a tra- noise, where the a grid of pseudo random gradients are generated ditional approach based on thermal erosion techniques, while the and the values between them are interpolated based on the dot other is a novel technique that takes advantage of the derivatives products of the gradients on the nearest vertices. of the terrain height to produce similar looking results with much Procedural techniques, although powerful and easily implemented, higher efficiency. have several drawbacks. They fail to capture some characteristics of real-world terrain, such as the structure of mountain ridges and 2 RELATED WORK other specific land forms. The generated terrain tends to be very repetitive and the lack of control means that the user must have The research field of procedural content generation (PCG) investi- technical understanding of the parameters to be able to modify the gates the algorithmic creation of content. It aims to allow content to generation process in a meaningful way. be generated automatically, and can therefore reduce the workload of artists and designers [Hendrikx et al. 2013]. One of the most 2.1.2 Physical simulations tend to focus more on modelling the important parts of any game is the terrain the user will traverse systems that generate and modify the terrain then on how it will through and sometimes interact with while playing. PCG of ter- ultimately look like. The majority of simulation techniques focuses rain, also known as procedural modelling of terrain, is a widely on erosion, that is, a processes that removes material from one area researched area [Smelik et al. 2014], and has been used in several of the terrain and moves it to another location. These are often commercially successful applications, such as games and movies. used to simulate the effects of rainfall, wind, water streams and time, and may be used in combination with procedural techniques 2.1 Terrain Generation in order to improve the terrain generated by them. Several methods have been proposed to generate and modify terrain. Hydraulic erosion aims to simulate the effects of water, usually These methods generally fall into three categories: procedural tech- rain, on the landscape. The most common implementation works niques, physical simulations and example-based methods [Galin by depositing droplets of water at random points of the terrain and et al. 2019]. allowing them to move through it while removing or depositing material in the process [Olsen 2004]. The amount eroded by droplet 2.1.1 Procedural techniques rely on algorithms which are not of water during a time step depends on its volume and the amount trying to emulate geological processes. Commonly, these methods of sediment it is already carrying. This type of erosion tends to rely on fractal models, attempting to mimic the fractal properties form steeper slopes and larger valleys. 2 Thermal erosion is another commonly used erosion technique. larger, and a naive implementation will require O¹n3º instead. This The goal here is to simulate the weathering that naturally occurs can be improved by using Sparse Voxel Octrees [Laine and Karras on real-world terrain where material is set loose and accumulates 2010] and other compression techniques [Kämpe et al. 2013], but at the bottom of steep slopes [Musgrave et al. 1989]. At each time still performs worse than height maps memory-wise. The voxel step loose material is moved from one point to another if the height model is widely used for physical simulation techniques such as difference between them is larger than a predetermined settlement erosion, providing much better results than height maps. angle. 2.2.3 Layer representations arose from the observation that real- Although the most prevalent topic in research, erosion tech- world terrain is structured in stratified layers. That is, usually, there niques are not the only simulation methods that have been explored. are few changes of material layers vertically. That means that it is Work has been done with the simulation of tectonic activity, by not