Phong Lighting Model

Topic Overview

Three Components of Surface Lighting

In 1975, Bui Tuong Phong published a model that broke real-time lighting into three terms. It is empirical, not physically based, but fast and convincing enough to dominate games for three decades before PBR took over.

1. Ambient: constant indirect light so surfaces are never pure black
2. Diffuse (Lambertian): max(0, N dot L) where N is surface normal, L is light direction
3. Specular: shiny highlight toward the viewer

Blinn-Phong Variant

The Blinn-Phong specular term uses a half-angle vector instead of a reflection vector:

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For example, a surface with normal (0,0,1), light at (2,2,5), and eye at (0,0,5) produces a bright specular lobe when N dot H is near 1. Diffuse depends only on light angle; specular depends on both light and view angles.

• Ambient: material ambient * light color
• Diffuse: matte scatter, no view dependence
• Specular: shininess controls highlight tightness (32 is moderately glossy)

For This Exercise

You will implement Blinn-Phong lighting for a single surface point with given normal, light position, eye position, and material constants. This task asks you to compute L, V, H, and print the final RGB color. Even PBR renderers retain the same N dot L diffuse structure introduced here.

Your Task

Shade surface points with the Phong and Blinn-Phong reflection models, using point lights with colour and distance attenuation. For each light, print the geometric terms (distance, N·L, and the specular cosine R·V or N·H) and the resulting diffuse and specular contributions. Then print the final colour, both unclamped and as 8-bit RGB.

You may use <math.h>: the task compiles with -lm.

Input

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Rules

With N normalized, V = normalize(camera - P), and for each light L = normalize(light - P) and d = |light - P|:

• Diffuse: max(0, N·L).
• Specular, only when N·L > 0:
  • Blinn-Phong: H = normalize(L + V) and s = max(0, N·H)^shininess.
  • Phong: R = 2(N·L)N - L and s = max(0, R·V)^shininess.
  • When N·L ≤ 0, the cosine is reported as 0.
• Colour, per channel k: ka·albedoₖ + Σ att·lightₖ·(kd·diffuse·albedoₖ + ks·s). Specular highlights take the light's colour, not the surface's.
• 8-bit: clamp each channel to [0, 1], then (int)(c·255 + 0.5).

Output

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• Numbers use %.4f, and a value with |x| < 0.00005 prints 0.0000.
• Per-light terms: "diffuse" is kd·diffuse and "specular" is ks·s, both before attenuation and colour. The label is R.V under Phong. A light with N·L ≤ 0 adds (facing away).
• Unclamped colour: the values in parentheses may exceed 1.
• Errors:
  • material: KA KD KS SHININESS(1-256), albedo: R G B (0-1)
  • light: NAME X Y Z R G B, light: at most 4 lights
  • attenuation: CONSTANT LINEAR QUADRATIC (not all zero)
  • camera: X Y Z, model: phong|blinn
  • shade: PX PY PZ NX NY NZ, shade: the normal must not be zero
  • unknown command X

Example

Input:

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Output:

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Requirements

1. Normalize every direction before a dot product. An unnormalized normal silently scales the lighting.
2. Gate specular on N·L > 0, so a surface facing away from a light gets no highlight from it.

Hidden tests cover two coloured lights with attenuation (one behind the surface), a tilted normal, Phong versus Blinn-Phong on the same point, over-exposure clamping, a zero normal, and argument errors.