Here, we investigated the CAT02 and HPE triangles in both x,y and u 0 ,v 0 spaces. It was found that in u 0 ,v 0 space, the HPE triangle is separated into two regions by the line 3u 0 2 8v 0 1 6 5 0, which is the u 0 ,v 0 image of X 1 Y 1 Z 5 0 under the mapping from (X,Y,Z) to (u 0 ,v 0 ). One of these two regions admits all-positive R,G,B triplets and the other all-negative R,G,B triplets, under the case of (X 1 Y 1 Z) > 0. The findings of this study explained the computation problems of CAT02 and provided methods for solving the Yellow-Blue and Purple problems simultaneously. V