Gouraud Shading

• Gouraud shading interpolates colours across a polygon from the vertices.
• Lighting calculations are only performed at the vertices.
• Works well for triangles
• Barycentric combinations are also affine combinations...
  Triangular Gouraud shading is invariant under affine transformations.

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• To implement, use repeated affine combination

  Similar to scan conversion of triangles

  (picture)

• Gouraud shading is well-defined only for triangles
  
• For polygons with more than three vertices:
  • Sort the vertices by y coordinate.
  • Slice the polygon into trapezoids with parallel top and bottom.
  • Interpolate colours along each edge of the trapezoid...
  • Interpolate colours along each scanline.

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• Gouraud shading gives bilinear interpolation within each trapezoid.
• Since rotating the polygon can result in a different trapezoidal decomposition, n-sided Gouraud interpolation is not affine invariant.
• Highlights can be missed or blurred.
• Common in hardware renderers; model that OpenGL supports.
• Exercise: Provide an example of the above effect.
• Exercise: Prove the above algorithm forms a barycentric combination on triangles.