Surface rendering is an important technique for volume visualization. Any surface rendering algorithm has two phases - surface generation and rendering. We present a new surface rendering algorithm, which focuses on constructing the surface in a manner that speeds up the rendering phase. The motivation behind this is to reduce the response time for surface manipulations such as interactive rotations. We utilize a MC-like (Marching Cubes) approach to calculate the intersection points and their normals for each cube. But we dynamically link the intersection points to form triangles within the cube according to the locations of the last and the next visited neighboring cubes so that a good meshed surface can be generated. The difficulty with such an approach is that thousands of special cases need to be considered. But, we have found that the occurrence of 5 specific configurations out of the 14 basic MC cube configurations account for over 95% of all the cubes intersected by the iso-surface in most data sets. We process cubes belonging to these 5 configurations in a mesh mode, and the rest are processed in a non-mesh mode. As a result, the number of special cases are reduced substantially. Then a very careful analysis of the 5 configurations for mesh processing leads to just 136 cases, which makes the algorithm very simple. Test results show that the rendering time is almost halved compared to the time required for the rendering of a nonmeshed surface generated by MC.

We propose a new framework for doing scientific visualization that allows the users to freely explore their data set. This framework uses a metaphorical abstraction of a virtual can of spray paint that can be used to render data sets and make them visible. Different cans of spray paint may be used to color the data differently. Different types of spray paint may also be used to highlight different features in the data set. To achieve this, individual paint particles are endowed with intelligent behavior. This idea offers several advantages over existing methods: (1) it generalizes the current techniques of surface, volume and flow visualization under one coherent framework; (2) it works with regular and irregular grids as well as sparse and dense data sets; (3) it allows selective progressive refinement and can be implemented on parallel architectures in a straight forward manner; (4) it is modular, extensible and provides scientists with the flexibility for exploring relationships in ...

(Communicated by Qing Nie) Abstract. Numerical analysis and computational simulation of partial differential equation models in mathematical biology are now an integral part of the research in this field. Increasingly we are seeing the development of partial differential equation models in more than one space dimension, and it is therefore necessary to generate a clear and effective visualisation platform between the mathematicians and biologists to communicate the results. The mathematical extension of models to three spatial dimensions from one or two is often a trivial task, whereas the visualisation of the results is more complicated. The scope of this paper is to apply the established marching cubes volume rendering technique to the study of solid tumour growth and invasion, and present an adaptation of the algorithm to speed up the surface rendering from numerical simulation data. As a specific example, in this paper we examine the computational solutions arising from numerical simulation results of a mathematical model of malignant solid tumour growth and invasion in an irregular heterogeneous three-dimensional domain, i.e., the female breast. Due to the different variables that interact with each other, more than one data set may have to be displayed simultaneously, which can be realized through transparency blending. The usefulness of the proposed method for visualisation in a more general context will also be discussed. 1. Introduction. Mathematical

A 3D B-spline quasi-interpolant is used to extract smooth iso-value surfaces from volume data. In this technique discretization and partial voluming artifacts are reduced by approximating sampled data at voxel centres. Surface normals, necessary for realistic shading, are analytically defined by the approximating function rather than estimated by in an ad hoc way from the volume data. We consider an application where bone surfaces are revealed from CT data by ray-casting and the surfaces are then used to construct models and prostheses. Accurate determination and rendering of bone surfaces is required. A z-buffer shading technique is also described for improved rendering of surface depth-maps. Keywords: Medical imaging, surface rendering, ray-casting, Computed Tomography (CT), prosthesis design 1 INTRODUCTION Surfaces extracted by ray-casting techniques typically exhibit ripples which arise from interpolation and quantisation artifacts. Fig. 1(a) illustrates a typical surface rendere...

The dramatic increase in the use of 3D image acquisition devices over the past decade has inspired major new developments in the display of volume data sets. In this chapter we present an overview of these diverse display methods and discuss the relative advantages and disadvantages of each of the different approaches. In addition, we touch upon some of the major issues involved in creating high-quality images from volume data, including the problems of surface definition and object segmentation. Due in part to the rapid, almost frantic, pace of recent developments in methods for rendering images from volume data, there has not yet emerged any widely accepted taxonomy for these methods. Because the human visual system is adapted for environments in which images of surfaces predominate, most algorithms emphasize in one way or another the display of surface-like information, either implicitly or explicitly. For clarity, we will avoid using the terms "surface rendering " and "volume rendering " to describe the various methods, since although prevalent in the literature they have no precise, commonly accepted definitions. Instead, we will differentiate the various rendering methods using the following three characteristics, which are somewhat more precise and, we hope, less misleading: 1) whether the explicit creation of an intermediate surface representation is required (if so,