Abstract: A computationally time and space efficient data structure and method and system for using the same for surface rendering. The basis for the new data structure lies in organizing a volume data set for surface rendering into a new format where the cells needed for the surface rendering can be searched and displayed more efficiently. Given a threshold t specified by the user, the present data structure is able to efficiently identify all surface cells saving valuable processing time by providing three unique beneficial characteristics. First, given a threshold t, it can directly provide all S-cells without having to check most of the 1-cells and 0-cells such that no time is wasted on visiting the intermediate nodes. Second, it facilitates significant savings in memory space where the data structure only requires N.sup.3 pointers for data storage saving memory space for all intermediate nodes, i.e. O(N.sup.3) pairs of (Min, Max).

Abstract: A hypercube system which has been modified by adding additional communication links between the most distant nodes of a classic hypercube topology is described herein. This improvement in a hypercube topology is termed as a Modified Hypercube topology. Such a topology contains extra links which connects a node to another node in the topology which requires the greatest number of nodal hops over the shortest path. Also stated another way, that node having the greatest number of singly traversed or hopped nodes along the shortest path from an originating node to that node makes that node the most distant processor node. If hamming were to be implemented in the system, there is added an extra link between two nodes having the greatest hamming distance. Such a system makes a technological trade off to reduce the diameter of a classic hypercube at the cost of incrementally increasing the number of I/O ports at each node.