A comparison of poit-in-polygon tests using the 4 × 4 determinant method

Abstract

Point-in-Polygon Tests are basic geometric algorithms in solid modeling. The 4 × 4 Determinant Method provides a structured framework for all interference problems in the modeling process. The authors have proposed two different algorithms for Point-in-Polygon Tests based on the 4 × 4 Determinant Method, the PNZ Triangle Method and the Vertex Convexity Method. This paper compares the (1) algorithm simplicity, (2) arithmetic operations per vertex, (3) pre-calculable data, (4) accuracy in floating point arithmetic, (5) applicability in special cases, and (6) applicability in faces with curved edges, of the two algorithms. This shows which algorithm is preferable in each situation, and which algorithm is suitable for implementation in a hardware geometric processor. © 1990, The Japan Society for Precision Engineering. All rights reserved.