Traditional Shading of Matte Objects

  In addition to drawing edge lines and highlights, we need to shade the surfaces of objects. Traditional diffuse shading sets luminance proportional to the cosine of the angle between light direction and surface normal:  

$$I = k_d k_a + k_d \,\, \mbox{max}\left( 0, \mbox{${\bf \hat{l}}$} \cdot \mbox{${\bf \hat{n}}$} \right)$$ (1)

where I is the RGB color to be displayed for a given point on the surface, k_d is the RGB diffuse reflectance at the point, k_a is the RGB ambient illumination, is the unit vector in the direction of the light source, and is the unit surface normal vector at the point. This model is shown for k_d = 1 and k_a = 0 in Figure 3. This unsatisfactory image hides shape and material information in the dark regions. Additional information about the object can be provided by both highlights and edge lines. These are shown alone in Figure 4 with no shading. We cannot effectively add edge lines and highlights to Figure 3 because the highlights would be lost in the light regions and the edge lines would be lost in the dark regions.

To add edge lines to the shading in Equation 1, we can use either of two standard heuristics. First we could raise k_a until it is large enough that the dim shading is visually distinct from the black edge lines, but this would result in loss of fine details. Alternatively, we could add a second light source, which would add conflicting highlights and shading. To make the highlights visible on top of the shading, we can lower k_d until it is visually distinct from white. An image with hand-tuned k_a and k_d is shown in Figure 5. This is the best achromatic image using one light source and traditional shading. This image is poor at communicating shape information, such as details in the claw nearest the bottom of the image. This part of the image is colored the constant shade k_d k_a regardless of surface orientation.