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Sponsored Feature: Procedural Terrain Generation With Fractional Brownian Motion
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Sponsored Feature: Procedural Terrain Generation With Fractional Brownian Motion


June 3, 2008 Article Start Page 1 of 2 Next
 

[The computer graphics industry has a long history of trying to model the limitless complexities of our real world terrain. In this article kicking off Intel's Visual Computing microsite, Freeman demonstrates several techniques (including the source code) for creating realistic terrain scenes on systems with integrated graphics solutions.]

Introduction

The computer graphics industry has a long history of attempting to model real world terrain. These efforts try to capture the seemingly limitless complexity of natural terrain through modeling and rendering techniques. As early as the late 1960's Dr. Benoit Mandelbrot linked natural forms that maintain a level of self-similarity such as coastlines to mathematical constructs [1]. Notable achievements in this field since that time have utilized fractals to achieve approximations of terrain patches using stochastic processes such as fractional Brownian motion. In this article, we demonstrate several techniques of generating terrain patches as proposed by Dr. F Kenton Musgrave [2] along with texture blending and Shader Model 3.0 to create a synthetic scene on integrated graphics solutions such as the Intel® 965 Express Chipset and Mobile Intel® 965 Express Chipset family.

First, we describe a list of previous work in this field followed by the approach utilized by our implementation, which leverages both the CPU and GPU to render the scene. Source code is provided with the demonstration to be used in your terrain rendering extensions and implementation.

Previous Work

A number of researchers have investigated terrain generation using fractals to perturb surfaces in 2D and 3D space. B. Mandelbrot provided some of the earliest representations of terrain generation with fractals by comparing the self-similarity of mountainous terrain to Brownian motion, resulting in realistic skylines when charting a 2D random walk. Later work by Mandelbrot and Musgrave later showed increasingly compelling approximations of terrain utilizing fractional Brownian motion in 3D space with Perlin noise and the concept of multifractals both represented in [2].

Noise-based systems for generating fractal terrains as proposed by [2] and [4] are not exclusive to creating good approximations to real landscapes as several other calculations have been used to create aesthetically pleasing approximations to real terrain. Of interest in this group, include mid-point displacement calculations including the diamond-square and triangle-edge subdivision algorithms, Poisson faulting, and Fast Fourier Filtering.

While some of these systems can and do produce realistic looking scenes, the noise synthesis method proposed in [2] is utilized in this work as these calculations provide an interesting set of controls to the resulting terrain from a mathematical model. While these properties do not necessarily provide a mechanism to definitively control the shape of the rendered scene as indicated in [5] to constrain terrain to realistic properties, they do provide many interesting real and imaginative results. We present a CPU based set of algorithms demonstrating these controls balanced with smooth stepped texture blending in the pixel shader on the GPU using Microsoft DirectX 9 and Shader Model 3.0.

Implementation

Our implementation was inspired by Musgrave's work in [2], showcasing three methods from that text: simple fBm, hybrid fBm, and the ridged multifractal algorithm, each based on Perlin's noise algorithm. The output from these methods is used to perturb the Z direction of a fixed size polygon mesh.

Figure 3-1. Fractal Terrain, Simple fBm

In Figure 3-1, we present our implementation. On the right hand side, one can see the controls used to adjust properties of each fBm algorithm as selected from the combo box. Our demo is adapted from the BasicHLSL demo from [7] with default algorithm parameters adjust to demonstrate interesting terrain properties.

Method Parameters:

(H) Hurst index - In mathematical literature, classifies the fBm and dictates fractal dimension.

(Lacunarity) - Dictates the gap between successive frequencies.

(Octaves) - Dictates the number of frequencies and scales Level of Detail in the scene.

(Offset) - Offset from the lowest elevation and determines "multifractality" [2].

(Gain) - Controls the amplitude of the frequency.


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