Two-dimensional line segment–triangle intersection test: revision and enhancement

Abstract

Two-dimensional line segment–triangle intersection test is a part of some 3D triangle–triangle intersection test algorithms. It is the kind of algorithms dealing with intersection of one triangle and line segment obtained as the intersection of the other triangle with the plane which the first triangle lies on. There appeared a number of algorithms each proclaiming its efficiency against to its predecessors with respect to the number of operations. In the paper, we seek out the minimal set of operations. Applying divide and conquer paradigm, we split the operations needed into (a) fixed part consisting of core arithmetic operations and (b) variable part dealing with logical reasoning. As we come to the set of core arithmetic operations that cannot be further minified we realize previous algorithms come to the same set in spite of their different strategies. Further improvement we sought in the area of modern processor architectures. We exploit modern CPU’s parallel processing capabilities like Single instruction, multiple data vectorization, parallel—out-of-order execution and branch prediction and enlighten their strengths and weaknesses for usage in this type of algorithms.