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.

The problem of digital painting is considered from a signal processing viewpoint, and is reconsidered as a problem of directed texture synthesis. It is an important characteristic of natural texture that detail may be evident at many scales, and the detail at each scale may have distinct characteristics. A "sparse convolution " procedure for generating random textures with arbitrary spectral content is described. The capability of specifying the texture spectrum (and thus the amount of detail at each scale) is an improvement over stochastic texture synthesis processes which are scalebound or which have a prescribed 1/f spectrum. This spectral texture synthesis procedure provides the basis for a digital paint system which rivals the textural sophistication of traditional artistic media. Applications in terrain synthesis and texturing computerrendered objects are also shown.

Recent research in haptic systems has begun to focus on the generation of textures to enhance haptic simulations. Synthetic texture generation can be achieved through the use of stochastic modeling techniques to produce random and pseudo-random texture patterns. These models are based on techniques used in computer graphics texture generation and textured image analysis and modeling. The goal for this project is to synthesize haptic textures that are perceptually distinct. Two new rendering methods for haptic texturing are presented for implementation of stochastic based texture models using a 3 DOF point interaction haptic interface. The synthesized textures can be used in a myriad of applications, including haptic data visualization for blind individuals and overall enhancement of haptic simulations. Keywords: haptic, synthetic texture, stochastic models, visualization 1. INTRODUCTION Haptic rendering involves the computation of forces to be generated by a force-reflecting interface...

This paper deals with modelling point sets with attributes. A point set in a geometric space of an arbitrary dimension is a geometric model of a real object or process under consideration. An attribute is a mathematical model of a real object or process property of an arbitrary nature (material, photometric, physical, statistical, etc.) defined for any point of the point set. We provide a survey of different modelling techniques related to point sets with attributes. This survey spans such different areas as solid modelling, heterogeneous objects modelling, scalar fields or "implicit surface" modelling, and volume graphics. Then, on the basis of this survey we formulate requirements to a general model of hypervolumes (multidimensional point sets with multiple attributes). A general hypervolume model and its components such as objects, operations, and relations are introduced and discussed. A function representation (FRep) is used as the basic model for the point set geometry and attributes represented independently using real-valued scalar functions of several variables. Each function defining the geometry or an attribute is evaluated at the given point by a procedure traversing a constructive tree structure with primitives in the leaves and operations in the nodes of the tree. This reflects the constructive nature of the symmetric approach to modelling geometry and associated attributes in multidimensional space. To demonstrate a particular application of the proposed general model, we consider in detail the problem of texturing, introduce a model of constructive hypervolume texture, and discuss its implementation. The well-known concept of solid texturing is extended in two directions: constructive modelling of space partitions for texturing and modelling of mul...

A key topic in computer graphics is the realistic representation of natural phenomena. Among the natural objects, one of the most interesting (and most difficult to deal with) is water. Its inherent complexity, far beyond that of most artificial objects, represents an irresistible challenge for the computer graphics world. Thus, during the last two decades we have witnessed an increasing number of papers addressing this problem from several points of view. However, the computer graphics community still lacks a survey classifying the vast literature on this topic, which is certainly unorganized and dispersed and hence, difficult to follow. This paper aims to fill this gap by offering a historical survey on the most relevant computer graphics techniques developed during the 1980s and 1990s for realistic modeling, rendering and animation of water.

The concept of solid texturing is extended in two directions: constructive modeling of space partitions for texturing and modeling of multidimensional textured objects called hypervolumes. A hypervolume is considered as a point set with attributes of both physical (density, temperature, etc.) and photometric (color, transparency, diffuse and specular reflections, etc.) nature. The point set geometry and attributes are modeled independently using realvalued scalar functions of several variables. Each realvalued function defining geometry or an attribute is evaluated at the given point by a procedure traversing a constructive tree structure with primitives in the leaves and operations in the nodes of the tree. This approach provides a framework for modeling, texturing and visualization of 3D solids, time- dependent and multidimensional objects in a completely uniform manner. We introduced a special modeling language and implemented software tools supporting the proposed approach. The concept of constructive hypervolume textures is independent of the geometry representation. We provide examples of textured Frep and BRep objects as illustrations.