A review of wildland fire spread modelling, 1990-present 3: Mathematical analogues and simulation models

In recent years, advances in computational power and spatial data analysis (GIS, remote sensing, etc) have led to an increase in attempts to model the spread and behvaiour of wildland fires across the landscape. This series of review papers endeavours to critically and comprehensively review all types of surface fire spread models developed since 1990. This paper reviews models of a simulation or mathematical analogue nature. Most simulation models are implementations of existing empirical or quasi-empirical models and their primary function is to convert these generally one dimensional models to two dimensions and then propagate a fire perimeter across a modelled landscape. Mathematical analogue models are those that are based on some mathematical conceit (rather than a physical representation of fire spread) that coincidentally simulates the spread of fire. Other papers in the series review models of an physical or quasi-physical nature and empirical or quasi-empirical nature. Many models are extensions or refinements of models developed before 1990. Where this is the case, these models are also discussed but much less comprehensively.Comment: 20 pages + 9 pages references + 1 page figures. Submitted to the International Journal of Wildland Fir

Defining urban and rural regions by multifractal spectrums of urbanization

The spatial pattern of urban-rural regional system is associated with the dynamic process of urbanization. How to characterize the urban-rural terrain using quantitative measurement is a difficult problem remaining to be solved. This paper is devoted to defining urban and rural regions using ideas from fractals. A basic postulate is that human geographical systems are of self-similar patterns associated with recursive processes. Then multifractal geometry can be employed to describe or define the urban and rural terrain with the level of urbanization. A space-filling index of urban-rural region based on the generalized correlation dimension is presented to reflect the degree of geo-spatial utilization in terms of urbanization. The census data of America and China are adopted to show how to make empirical analyses of urban-rural multifractals. This work is not so much a positive analysis as a normative study, but it proposes a new way of investigating urban and rural regional systems using fractal theory.Comment: 21 pages, 4 figures, 6 table

Fractal descriptors based on the probability dimension: a texture analysis and classification approach

In this work, we propose a novel technique for obtaining descriptors of gray-level texture images. The descriptors are provided by applying a multiscale transform to the fractal dimension of the image estimated through the probability (Voss) method. The effectiveness of the descriptors is verified in a classification task using benchmark over texture datasets. The results obtained demonstrate the efficiency of the proposed method as a tool for the description and discrimination of texture images.Comment: 7 pages, 6 figures. arXiv admin note: text overlap with arXiv:1205.282

Combining Procedural and Hand Modeling Techniques for Creating Animated Digital 3D Natural Environments

This thesis focuses on a systematic solution for rendering 3D photorealistic natural environments using Maya\u27s procedural methods and ZBrush. The methods used in this thesis started with comparing two industry specific procedural applications, Vue and Maya\u27s Paint Effects, to determine which is better suited for applying animated procedural effects with the highest level of fidelity and expandability. Generated objects from Paint Effects contained the highest potential through object attributes, texturing and lighting. To optimize results further, compatibility with sculpting programs such as ZBrush are required to sculpt higher levels of detail. The final combination workflow produces results used in the short film Fall. The need for producing these effects is attributed to the growth of the visual effect industry\u27s ability to deliver realistic simulated complexities of nature and as such, the public\u27s insatiable need to see them on screen. Usually, however, the requirements for delivering a photorealistic digital environment fall under tight deadlines due to various phases of the visual effects project being interconnected across multiple production houses, thereby requiring the need for effective methods to deliver a high-end visual presentation. The use of a procedural system, such as an L-system, is often an initial step within a workflow leading toward creating photorealistic vegetation for visual effects environments. Procedure-based systems, such as Maya\u27s Paint Effects, feature robust controls that can generate many natural objects. A balance is thus created between being able to model objects quickly, but with limited detail, and control. Other methods outside this system must be used to achieve higher levels of fidelity through the use of attributes, expressions, lighting and texturing. Utilizing the procedural engine within Maya\u27s Paint Effects allows the beginning stages of modeling a 3D natural environment. ZBrush\u27s manual system approach can further bring the aesthetics to a much finer degree of fidelity. The benefit in leveraging both types of systems results in photorealistic objects that preserve all of the procedural and dynamic forces specified within the Paint Effects procedural engine

New Method for Estimating Fractal Dimension in 3D Space and Its Application to Complex Surfaces

The concept of “surface modeling” generally describes the process of representing a physical or artificial surface by a geometric model, namely a mathematical expression. Among the existing techniques applied for the characterization of a surface, terrain modeling relates to the representation of the natural surface of the Earth. Cartographic terrain or relief models as three-dimensional representations of a part of the Earth's surface convey an immediate and direct impression of a landscape and are much easier to understand than two-dimensional models. This paper addresses a major problem in complex surface modeling and evaluation consisting in the characterization of their topography and comparison among different textures, which can be relevant in different areas of research. A new algorithm is presented that allows calculating the fractal dimension of images of complex surfaces. The method is used to characterize different surfaces and compare their characteristics. The proposed new mathematical method computes the fractal dimension of the 3D space with the average space component of Hurst exponent H, while the estimated fractal dimension is used to evaluate, compare and characterize complex surfaces that are relevant in different areas of research. Various surfaces with both methods were analyzed and the results were compared. The study confirms that with known coordinates of a surface, it is possible to describe its complex structure. The estimated fractal dimension is proved to be an ideal tool for measuring the complexity of the various surfaces considered

New method for estimating fractal dimension in 3d space and its application to complex surfaces

The concept of “surface modeling” generally describes the process of representing a physical or artificial surface by a geometric model, namely a mathematical expression. Among the existing techniques applied for the characterization of a surface, terrain modeling relates to the representation of the natural surface of the Earth. Cartographic terrain or relief models as threedimensional representations of a part of the Earth's surface convey an immediate and direct impression of a landscape and are much easier to understand than two-dimensional models. This paper addresses a major problem in complex surface modeling and evaluation consisting in the characterization of their topography and comparison among different textures, which can be relevant in different areas of research. A new algorithm is presented that allows calculating the fractal dimension of images of complex surfaces. The method is used to characterize different surfaces and compare their characteristics. The proposed new mathematical method computes the fractal dimension of the 3D space with the average space component of Hurst exponent H, while the estimated fractal dimension is used to evaluate, compare and characterize complex surfaces that are relevant in different areas of research. Various surfaces with both methods were analyzed and the results were compared. The study confirms that with known coordinates of a surface, it is possible to describe its complex structure. The estimated fractal dimension is proved to be an ideal tool for measuring the complexity of the various surfaces considered