Phong Lighting Model

Write a C program that implements the Blinn-Phong lighting model for a single point on a surface.

Requirements:

• Define a surface point at origin (0, 0, 0) with normal N = (0, 0, 1)
• Define a point light at position L_pos = (2, 2, 5) with color (1.0, 1.0, 1.0)
• Define the camera/eye at E = (0, 0, 5)
• Material properties: ambient = (0.1, 0.1, 0.1), diffuse = (0.7, 0.2, 0.2), specular = (0.8, 0.8, 0.8), shininess = 32
• Compute:
  • Light direction L = normalize(L_pos - surface_point)
  • View direction V = normalize(E - surface_point)
  • Half-angle H = normalize(L + V)
  • Ambient = material.ambient * light.color
  • Diffuse = material.diffuse * light.color * max(0, N dot L)
  • Specular = material.specular * light.color * pow(max(0, N dot H), shininess)
  • Final = Ambient + Diffuse + Specular
• Print each component (ambient, diffuse, specular) as RGB values
• Print the final color
• Test with three shininess values: 8, 32, 128, showing how the specular highlight tightens
• Implement vector helpers: dot, normalize, add, subtract
• Use 3 decimal places for output