Two new, contrastive point-in-polygon algorithms based on the 4 × 4 determinant method are proposed. By employing the error-free computations of the 4 × 4 determinant method, the algorithms can be very robust. First, a brief introduction to the 4 × 4 determinant method is presented. Secondly, the ideas of reconstructing, in two contrastive ways, a polygon from a sequence of point data are explained and then two algorithms derived from the ideas are presented. Thirdly, characteristics of both algorithms are discussed and compared. The complete programs of the two algorithms are shown.