A principal components (PC)-based transformation was previously introduced for mapping high-dimensional hyperspectral imagery (HSI) into 3-dimensional colorimetric displays [Tyo, Diersen, and Olsen, SPIE vol. 4132, Descour and Shen, Eds., 2001, pp. 147-156]. In this study, the previous work is extended to examine the conical nature of HSI data in the PC-based space. Picturing the data as conical provides insight as to the location of the origin of the cone (which might not be included in the data) and the point of shade. Once the origin of the cone is located, the PC-based color transformation is more stable with respect to hue constancy. Strategies are introduced to make the method invariant, i.e. to ensure that important scene constituents appear with consistent and intuitive presentations.