phong lighting scheme in arcmap?

Question

I have seen a few DEM/hillshades in published journal articles that use a phong lighting scheme which gives surfaces a metallic luster. Does anyone know how/if this can be achieved in arcmap?

Answer 1

Yes, it can.

Phong shading is a sum of ambient, diffuse, and (specularly) reflected light.

1. The ambient portion is represented by the usual map of the DEM.

2. The diffuse portion is computed with a hillshade. A "hillshaded DEM" is a weighted sum of ambient and diffuse reflections.

3. The formula for the reflected part of the image can be computed in terms of (i) the direction to the light source (sun), given in terms of its azimuth s_a (degrees east of north) and "elevation" s_e (degrees up from the horizon), (ii) the direction to the viewer, which in a map is always taken to be straight up, (iii) the slope and aspect at each point.

ArcGIS computes hillshades and allows semi-transparent overlays, which is tantamount to forming a positive linear combination of images. Thus the only novelty is to compute the reflection map (3). Spatial Analyst (part of ArcGIS) computes aspect grids (again in degrees east of north) and slope grids (in degrees). The specular reflection therefore can be computed from these grids using raster calculations ("map algebra") according to the Phong shading formula.

The formula requires the component of the reflected light reaching the observer to be raised to a positive power alpha (which determines the "shininess"; the larger it is, the more point-like the reflections become). To find this component we do a small amount of 3D analytic geometry and conversion between spherical and Cartesian coordinates:

• A unit vector in the sun's direction is S = (sin(s_a)sin(s_e), cos(s_a)sin(s_e), cos(s_e)).

• A unit vector normal to the surface (which varies from cell to cell and therefore is given by three grids of coordinates) is N = (sin(aspect)sin(slope), cos(aspect)sin(slope), cos(slope)).

• A unit vector in the reflected direction therefore is R = 2<N, S> N - S. (<,> is the usual dot product.)

• The component of the reflection in the viewer's direction (V = (0,0,1)); namely, <R, V>, is simply the z-coordinate of R. Thus, in the preceding step, you need only compute the third coordinate of the linear combination, not all three coordinates.

By raising this last grid to the alpha power you will have computed the specular component of the reflection (up to a multiple determined by the sun's intensity). That multiple can be set in terms of the transparency parameter in the grid's display. To show the Phong shaded map you will display the three grids--a good order is hillshade, DEM, reflection--with appropriate transparency settings to balance the diffuse, ambient, and specular portions, respectively.

The terminology here--R, N, V, and alpha--is the same as that used in the Wikipedia article.