The Visualization Toolkit (vtk) is a freely available C++ class library for 3D graphics and visualization. We describe core characteristics of the toolkit. This includes a description of object oriented models for graphics and visualization; methods for synchronizing system execution; a summary of data representation schemes; the role of C++; issues in portability across PC and Unix systems; and how we automatically wrap the C++ class library with interpreted languages such as Java and Tcl. We also demonstrate the capabilities of the system for scalar, vector, tensor, and other visualization techniques.

The National Library of Medicine is creating a digital atlas of the human body. This project, called the Visible Human, has already produced computed tomography, magnetic resonance imaging and physical cross-sections of a human male cadaver. This paper describes a methodology and results for extracting surfaces from the Visible Male's CT data. We use surface connectivity and isosurface extraction techniques to create polygonal models of the skin, bone, muscle and bowels. We also report early experiments with the physical cross-sections.

Swept surfaces and volumes are generated by moving a geometric model through space. Swept surfaces and volumes are important in many computer-aided design applications including geometric modeling, numerical cutter path generation, and spatial path planning. In this paper we describe a numerical algorithm to generate swept surfaces and volumes using implicit modeling techniques. The algorithm is applicable to any geometric representation for which a distance function can be computed. The algorithm also treats degenerate trajectories such as self-intersection and surface singularity. We show applications of this algorithm to maintainability design and robot path planning.>

Three dimensional computer models of the anatomy generated from volume acquisitions of computed tomography and magnetic resonance imaging are useful adjuncts to 2D images. This paper describes a system that merges the computer generated 3D models with live video to enhance the surgeon's understanding of the anatomy beneath the surface. The system can be used as a planning aid before the operation and provide additional information during an operation. The application of the system to a brain operation is described.>

The polygon remains a popular graphics primitive for computer graphics application. Besides having a simple representation, computer rendering of polygons is widely supported by commercial graphics hardware and software.

VISAGE, a scientific visualization system implemented in an object-oriented, message passing environment, is described. The system includes over 500 classes ranging from visualization and graphics to Xlib and Motif user interface. Objects are created using compiled C and interact through an interpreted scripting language. The result is a flexible yet efficient system that has found wide application. The object architecture, the major issues faced when designing the visualization classes, and sample applications are also described.>

We propose a new approach to the problem of generating a simple topologically-closed geometric model from a point-sampled volume data set. We call such a model a Geometrically Deformed Model or GDM. A GDM is created by placing a 'seed' model in the volume data set. The model is then deformed by a relaxation process that minimizes a set of constraints that provides a measure of how well the model fits the features in the data. Constraints are associated with each vertex in the model that control local deformation, interaction between the model and the data set, and the shape and topology of the model. Once generated, a GDM can be used for visualization, shape recognition, geometric measurements, or subjected to a series of geometric operations. This technique is of special importance because of the advent of nondestructive sensing equipment (CT, MRI) that generates point samples of true three-dimensional objects.

Television coverage of golf fails to bring the viewer an appreciation of the complex topography of a golf green and how that topography affects the putting of golf balls. A computer graphics simulation that enhances the viewer's perception of these features using shaded polygonal models of the actual golf green used in tournaments is presented. Mathematical modeling of the golf ball's trajectory on its way toward the hole further enhances viewer understanding. A putting difficulty map assesses the relative difficulty of putting from each location on the green to a given pin position. The object-oriented system is written in C and runs on a variety of 3D graphics workstations. As an experiment, the system was used at a professional golf tournament and correctly simulated all putts during the final round.>

A method is presented for the visualization of 3D vector fields. The stream polygon, which is a regular, n-sided polygon, oriented normal to the local vector, can present local deformations due to rigid body rotation and both normal and shear strain. The effect of translation and scalar functions can be represented by sweeping the stream polygon along the streamline, and by appropriately varying the radius and shading the surface of the resulting streamtube. A mathematical foundation for the stream is developed, and examples with application to velocity field visualization are provided.>

We present a new algorithm, called marching cubes, that creates triangle models of constant density surfaces from 3D medical data. Using a divide-and-conquer approach to generate inter-slice connectivity, we create a case table that defines triangle topology. The algorithm processes the 3D medical data in scan-line order and calculates triangle vertices using linear interpolation. We find the gradient of the original data, normalize it, and use it as a basis for shading the models. The detail in images produced from the generated surface models is the result of maintaining the inter-slice connectivity, surface data, and gradient information present in the original 3D data. Results from computed tomography (CT), magnetic resonance (MR), and single-photon emission computed tomography (SPECT) illustrate the quality and functionality of marching cubes. We also discuss improvements that decrease processing time and add solid modeling capabilities.