Here, we investigated the CAT02 and HPE triangles in both x,y and u,v spaces. It was found that in u,v space, the HPE triangle is separated into two regions by the line 3u-8v+6=0, which is the u,v image of X+Y+Z=0 under the mapping from (X,Y,Z) to (u,v). 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+Y+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. (c) 2013 Wiley Periodicals, Inc. Col Res Appl, 40, 30-39, 2015