A color mapping technique that provides an intuitive visualization of surface normals is described. The surface normals can be associated with a mesh for a virtual object to be displayed in augmented reality. The color mapping technique can map a unit sphere in a color space to an octahedron. The vertices of the octahedron can be aligned with prime colors of the color space. To perform the alignment, a rotation and shear matrix can be determined from coordinates for octahedron positions and coordinates of colors in the color space. The rotation and shear can provide that each region of the unit color sphere is dominated by a single prime color, with gradients between prime colors being visually balanced. Surface normals of a mesh for a virtual object can be visualized using the color mapping, and a viewer can readily determine how distant in terms of rotation two surface normals are from each other.