Although the Marching Cube (MC) algorithm is very popular for displaying images of voxel-based objects, its slow surface extraction process is usually considered to be one of its major disadvantages. It was pointed out that for the original MC algorithm, we can limit vertex calculations to once per vertex to speed up the surface extraction process, however, it did not mention how this process could be done efficiently. Neither was the reuse of these MC vertices looked into seriously in the literature. In this paper, we propose a “Group Marching Cube” (GMC) algorithm, to reduce the time needed for the vertex identification process, which is part of the surface extraction process. Since most of the triangle-vertices of an iso-surface are shared by many MC triangles, the vertex identification process can avoid the duplication of the vertices in the vertex array of the resultant triangle data. The MC algorithm is usually done through a hash table mechanism proposed in the literature and used by many software systems. Our proposed GMC algorithm considers a group of voxels simultaneously for the application of the MC algorithm to explore interesting features of the original MC algorithm that have not been discussed in the literature. Based on our experiments, for an object with more than 1 million vertices, the GMC algorithm is 3 to more than 10 times faster than the algorithm using a hash table. Another significant advantage of GMC is its compatibility with other algorithms that accelerate the MC algorithm. Together, the overall performance of the original MC algorithm is promoted even further.

In medical education, many of computerized Problem-Based Learning (PBL) systems are used into their training curricula. But these systems do not truly reflect the situations which practitioners may actually encounter in a real medical environment, and hence their effectiveness as learning tools is somewhat limited. Therefore, the present study analyzes the computerized PBL teaching case, and considers how a clinical teaching case can best be presented to the student. Specifically, this paper attempts to develop a web-based PBL system which emulates the real clinical situation by introducing the concept of a "time sequence" within each teaching case. The proposed system has been installed in the medical center of National Cheng Kung University in Taiwan for testing purposes. The participants in this study were 50 of 5th grade (equivalent to 1st grade students in a medical school of the American medical education system) students for the evaluation process. Some experiments are conducted to verify the advantages of designing teaching cases with the concept of the "time sequence."