Recently, based on a set of four coplanar points, a projective-invariant digital watermarking has been developed. A combination of line intersection and the cross-ratio relationship of collinear points is used to calculate watermarking embedding locations. The four coplanar points used to derive embedding locations can be obtained from either the image corners or the feature points extracted from the image content. It is shown in this paper that based on the same principle, an alternative algorithm for calculating the watermark embedding locations improves computational efficiency. The proposed method heavily uses the cross-ratio relationship of collinear points, while minimizing the use of line intersection in obtaining embedding locations. This is in contrast with the original method, where embedding locations are mainly obtained from intersections of line pairs. Both analytical and experimental results are provided to demonstrate the improvement.