We present algorithms that greatly decrease the time it takes to display a large number of 3-D mechanical part assemblies by removing all interior parts that cannot be viewed from any viewing angle. The algorithms are based on the minimum axis-aligned bounding box of each part, which avoids complicated computations often needed to determine the interactions of the geometry of the parts. The major contribution of this work is the use of exterior traces of cross sections of the bounding boxes to determine the parts' visibility. It is shown that the processing time increases almost linearly with the number of parts in an assembly of parts. A test on an assembly composed of 490 parts shows that the algorithms decrease the display time by a factor of two while only incorrectly identifying two of these parts as invisible when they should have been identified as visible.