Gouraud shading for polygon rendering

Gouraud shading (intensity-interpolation scheme) renders a polygon mesh by computing the intensity at each vertex with an illumination model and then linearly interpolating these intensities over the polygon surface.

Steps

1. Vertex normal: find the normal at each vertex by averaging the normals of all polygons meeting at that vertex.

   N_v = (Σ N_k) / |Σ N_k|

2. Vertex intensity: apply the illumination model at each vertex using N_v.

3. Edge interpolation: for a scan line y_s crossing an edge from vertex 1 (y1) to vertex 2 (y2):

   I_a = ((y_s − y2)/(y1 − y2))·I1 + ((y1 − y_s)/(y1 − y2))·I2

   (Incremental form: moving down one scan line, I' = I + (I2 − I1)/(y1 − y2).)

4. Scan-line interpolation: between the left (a) and right (b) intersection points, for pixel x_p:

   I_p = ((x_b − x_p)/(x_b − x_a))·I_a + ((x_p − x_a)/(x_b − x_a))·I_b

   (Incremental form along the scan line: I_{p+1} = I_p + (I_b − I_a)/(x_b − x_a).)

5. Fill each pixel with I_p.

 I1 o
    |\
  Ia o--o Ib    I_p interpolated between Ia and Ib
    |    \
 I2 o-----o I3

Advantages

• Removes the faceted look and gives smooth shading.
• Much faster than Phong shading, since the illumination model is applied only at the vertices and the interpolation is linear and incremental.

Disadvantages

• Specular highlights inside a polygon may be missed or appear wrong, because only vertex intensities are used.
• The Mach-band effect (visible bright or dark bands) can appear at polygon boundaries.
• The silhouette still looks polygonal.
• Results depend on the orientation of the polygon on the screen.