The realistic depiction of smoke, steam, mist and water reacting to a turbulent field such as wind is an attractive and challenging problem. Its solution requires interlocking models for turbulent fields, gaseous flow, and realistic illumination. We present a model for turbulent wind flow having a deterministic component to specify large-scale behaviour, and a stochastic component to model turbulent small-scale behaviour. The small-scale component is generated using space-time Fourier synthesis. Turbulent wind fields can be superposed interactively to create subtle behaviour. An advection-diffusion model is used to animate particle-based gaseous phenomena embedded in a wind field, and we derive an efficient physically-based illumination model for rendering the system. Because the number of particles can be quite large, we present a clustering algorithm for efficient animation and rendering. CR Categories and Subject Descriptors: I.3.7 [Com- puter Graphics]: Three-Dimensional Graphics...

This paper describes the basis for techniques such as stochastic subdivision in the theory of random processes and estimation theory. The popular stochastic subdivision construction is then generalized to provide control of the autocorrelation and spectral properties of the synthesized random functions. The generalized construction is suitable for generating a variety of perceptually distinct high-quality random functions, including those with non-fractal spectra and directional or oscillatory characteristics. It is argued that a spectral modeling approach provides a more powerful and somewhat more intuitive perceptual characterization of random processes than does the fractal model. Synthetic textures and terrains are presented as a means of visually evaluating the generalized subdivision technique. Categories and Subject Descriptors: I.3.3 [Computer Graphics]: Picture/Image Generation; I.3.7 [Computer Graphics]: Three Dimensional Graphics and Realism -<F11.

Stochastic modelling has been successfully used in computer graphics to model a wide array of natural phenomena. In modelling three-dimensional fuzzy or partially translucent phenomena, however, many approaches are hampered by high memory and computation requirements, and by a general lack of user control. We will present a general stochastic modelling primitive that operates on two or more scales of visual detail, and which offers considerable flexibility and control of the model. At the macroscopic level, the general shape of the model is constrained by an ellipsoidal correlation function that controls the interpolation of user-supplied data values. We use a technique called Kriging to perform this interpolation. The microscopic level permits the addition of noise, which allows a user to add interesting visual textural detail and translucency. A wide variety of noisesynthesis techniques can be employed in our model. We shall describe the mathematical structure of our model, and give ...

Stochastic modelling has been successfully used in computer graphics to model a wide array of natural phenomena. In modelling three-dimensional fuzzy or partially translucent phenomena, however, many approaches are hampered by high memory and computation requirements, and by a general lack of user control. The main contribution of this thesis is the introduction of a general stochastic modelling primitive that operates on two or more scales of visual detail. At the macroscopic level, the general shape of the model is constrained by an ellipsoidal correlation function that controls the interpolation of usersupplied data values. A technique called Kriging is used to perform this interpolation. The microscopic level permits the addition of noise, which allows one to add interesting visual textural detail and translucency. A wide variety of noise-synthesis techniques can be employed in our model. The main advantages of the model over existing ones are low storage requirements and the use o...

If you place a large number of points randomly in the unit square, what is the distribution of the radius of the largest circle containing no points? Of the smallest circle containing 4 points? Why do Brownian sample paths have local maxima but not points of increase, and how nearly do they have points of increase? Given two long strings of letters drawn i.i.d. from a finite alphabet, how long is the longest consecutive (resp. non-consecutive) substring appearing in both strings? If an imaginary particle performs a simple random walk on the vertices of a high-dimensional cube, how long does it take to visit every vertex? If a particle moves under the influence of a potential field and random perturbations of velocity, how long does it take to escape from a deep potential well? If cars on a freeway move with constant speed (random from car to car), what is the longest stretch of empty road you will see during a long journey? If you take a large i.i.d. sample from a 2-dimensional rotationally-invariant distribution, what is the maximum over all half-spaces of the deviation between the empirical and

. The geotechnical engineer is often faced with the problem of how to assess the statistical properties of a soil parameter on the basis of a sample measured in-situ or in the laboratory with the defect that some values have been replaced by interval bounds because the corresponding soil parameter values have turned out to exceed the capacity of the measuring instrument. Given such a censored sample the problem is to estimate the mean value, variance and certain fractiles of the distribution of the soil parameter as it would be measured by an instrument of unrestricted range. In many situations only a small censored sample is given. To estimate the characteristic value defined as a lower fractile value corresponding to a codified probability value, the geotechnical engineer is thus urged to supplement the information from the measurements at the actual location by considering whatever prior knowledge is available about the soil parameter distribution. The present paper shows how a char...

Stochastic modelling has been successfully used in computer graphics to model a wide array of natural phenomena. In modelling three-dimensional fuzzy or partially translucent phenomena, however, many approaches are hampered by high memory and computation requirements, and by a general lack of user control. We will present a general stochastic modelling primitive that operates on two or more scales of visual detail, and which offers considerable flexibility and control of the model. At the macroscopic level, the general shape of the model is constrained by an ellipsoidal correlation function that controls the interpolation of user-supplied data values. We use a technique called Kri#in# to perform this interpolation. The microscopic level permits the addition of noise, which allows a user to add interesting visual textural detail and translucency. A wide variety of noisesynthesis techniques can be employed in our model. We shall describe the mathematical structure of our model, and give an attractive rendering implementation that can be embedded in a traditional ray tracer rather than requiring a volume renderer. As an example, we shall apply our approach to the modelling of clouds.