Abstract Distributed scene graphs are important in virtual reality, both in collaborative virtual environments and in cluster rendering. Modern scalable visualization systems have high local throughput, but collaborative virtual environments (VEs) over a wide‐area network (WAN) share data at much lower rates. This complicates the use of one scene graph across the whole application. Myriad is an extension of the Syzygy VR toolkit in which individual scene graphs form a peer‐to‐peer network. Myriad connections filter scene graph updates and create flexible relationships between nodes of the scene graph. Myriad's sharing is fine‐grained: the properties of individual scene graph nodes to share are dynamically specified (in C++ or Python). Myriad permits transient inconsistency, relaxing resource requirements in collaborative VEs. A test application, WorldWideCrowd, demonstrates collaborative prototyping of a 300‐avatar crowd animation viewed on two PC‐cluster displays and edited on low‐powered laptops, desktops, and over a WAN. We have further used our framework to facilitate collaborative educational experiences and as a vehicle for undergraduates to experiment with shared virtual worlds. Copyright © 2006 John Wiley & Sons, Ltd.

Distributed scene graphs are important in virtual reality, both in collaborative virtual environments and in cluster rendering. In Myriad, individual scene graphs form a peer-to-peer network whose connections filter scene graph updates and create flexible relationships between scene graph nodes in the various peers. Modern scalable visualization systems often feature high intracluster throughput, but collaborative virtual environments (VEs) over a WAN share data at much lower rates, complicating the use of one scene graph system across the whole application. To avoid these difficulties, Myriad uses fine-grained sharing, whereby sharing properties of individual scene graph nodes can be dynamically changed from C++ and Python, and transient inconsistency, which relaxes resource requirements in collaborative VEs. A test application, WorldWideCrowd, implements these methods to demonstrate collaborative prototyping of a 300-avatar crowd animation viewed on two PC-cluster displays and edited on low-powered laptops, desktops, and even over a WAN.

The mathematical process of everting a sphere (turning it inside-out allowing self-intersections) is a grand challenge for visualization because of the complicated, ever-changing internal structure. We have computed an optimal minimax eversion, requiring the least bending energy. Here, we discuss techniques we used to help visualize this eversion for visitors to virtual environments and viewers of our video The Optiverse.

Quaternions play a vital role in the representation of rotations in computer graphics, primarily for animation and user interfaces. Unfortunately, quaternion rotation is often left as an advanced topic in computer graphics education due to difficulties in portraying the four-dimensional space of the quaternions. One tool for overcoming these obstacles is the quaternion demonstrator, a physical visual aid consisting primarily of a belt. Every quaternion used to specify a rotation can be represented by fixing one end of the belt and rotating the other. Multiplication of quaternions is demonstrated by the composition of rotations, and the resulting twists in the belt depict visually how quaternions interpolate rotation. This article introduces to computer graphics the exponential notation that mathematicians have used to represent unit quaternions. Exponential notation combines the angle and axis of the rotation into concise quaternion expression. This notation allows the article to present more clearly a mechanical quaternion demonstrator consisting of a ribbon and a tag, and develop a computer simulation suitable for interactive educational packages. Local deformations and the belt trick are used to minimize the ribbon's twisting and simulate a natural-appearing interactive quaternion demonstrator.