Two Strategies on a Triangle Mesh

Both shading methods use the same illumination equation; they differ in where they evaluate it: at vertices then interpolate the color (Gouraud), or interpolate the normal then evaluate per pixel (Phong shading - distinct from Phong illumination).

Gouraud Shading (1971)

1. Compute per-vertex normal as the average of adjacent face normals.
2. Evaluate the illumination equation at each vertex -> vertex colors.
3. During rasterization, interpolate the color linearly across the triangle (using barycentric coordinates).

Pros

• Cheap: lighting once per vertex.
• Smooth color across faces, eliminates flat shading appearance.

Cons

• Highlights are missed if they fall in the middle of a triangle: the highlight only appears if a vertex happens to be near it.
• Linear color interpolation produces Mach banding at edges between triangles.
• Looks plasticky for shiny materials.

Phong Shading (1975)

1. Per-vertex normals as before.
2. During rasterization, interpolate normals across the triangle (then renormalize).
3. Evaluate the full illumination equation at every pixel.

Pros

• Sharp, correctly placed specular highlights even mid-triangle.
• Smooth shading on relatively coarse meshes.

Cons

• Cost: one lighting evaluation per pixel instead of per vertex. On modern GPUs this is the default.
• Still needs renormalization of interpolated normals (linear interpolation does not preserve unit length).

Comparison Table

Other Shading Modes Worth Knowing

• Flat (Constant) Shading: one normal per triangle, one color per triangle. Faceted look, useful for low-poly aesthetics or technical drawings.
• Blinn-Phong: replaces R.V with H.N where H = (L+V)/||L+V||, the half-vector. Cheaper and behaves better at glancing angles. Default in OpenGL fixed-function era.
• Toon / Cel: clamp diffuse and specular to a few discrete bands for a comic-book look.

Numerical Difference Sketch

Imagine a single bright triangle with a highlight near its centroid:

• Gouraud: corners might be dim because L.N near corners is moderate; centroid color is the average -> highlight invisible.
• Phong shading: per-pixel L.N at centroid is high -> highlight clearly visible.

When to Choose Which

• Gouraud: very large meshes where lighting cost dominates and material is matte.
• Phong shading: anything shiny, modern engines, mobile with deferred shading.
• Often combined: Gouraud for diffuse term + Phong for specular term to reduce cost while keeping crisp highlights.

Modern Practice

Almost all modern engines do per-pixel shading (Phong shading + PBR), with vertex-stage work limited to transform and attribute interpolation setup.