Differentiate Between Ambient Light and Diffuse Reflection & Phong Shading Algorithm

Part A: Difference Between Ambient Light and Diffuse Reflection

Parameter	Ambient Light	Diffuse Reflection
Definition	Constant background illumination that uniformly lights all surfaces regardless of position or orientation	Light reflected equally in all directions from a surface based on the angle of incoming light
Direction Dependency	Independent of light source direction and viewer position	Depends on the angle between light source direction and surface normal
Formula	$I_{ambient} = K_a \cdot I_a$	$I_{diffuse} = K_d \cdot I_l \cdot \cos\theta = K_d \cdot I_l \cdot (\hat{N} \cdot \hat{L})$
Surface Normal	Not required for computation	Required to calculate the angle of incidence
Appearance	Produces flat, uniform illumination with no shading variation	Produces shading that varies across the surface based on orientation
Realism	Low — no depth perception	Moderate — gives sense of 3D shape
Light Source	Simulates indirect/scattered light in environment	Simulates direct light hitting a rough/matte surface
Shadow Effect	No shadows produced	Surfaces facing away from light appear darker
Example	Light in a room with no visible source	A chalk piece or matte wall under a bulb

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Part B: Algorithm for Phong Shading (Per-Pixel Shading)

Phong Shading is an interpolation method where the surface normal is interpolated across the polygon, and the illumination model is applied at each pixel to produce smooth, realistic highlights.

Steps of the Algorithm:

• Step a: For each polygon, compute the normal vectors at each vertex ($\hat{N}_1, \hat{N}_2, \hat{N}_3$) using the average of normals of adjacent polygons.

• Step b: For each scan line that intersects the polygon, determine the boundary edges (left and right intersection points).

• Step c: Interpolate normals along polygon edges — For each edge, linearly interpolate the vertex normals to get the normal at each edge intersection point on the scan line:

$$\hat{N}_a = \frac{y - y_2}{y_1 - y_2} \hat{N}_1 + \frac{y_1 - y}{y_1 - y_2} \hat{N}_2$$

• Step d: Interpolate normals along the scan line — For each pixel between left and right edge, interpolate the normal:

$$\hat{N}_p = \frac{x_{right} - x}{x_{right} - x_{left}} \hat{N}_a + \frac{x - x_{left}}{x_{right} - x_{left}} \hat{N}_b$$

• Step e: Normalize the interpolated normal at each pixel: $\hat{N}_p = \frac{\hat{N}_p}{|\hat{N}_p|}$

• Step f: Apply the Phong illumination model at each pixel using the interpolated normal:

$$I = K_a I_a + K_d I_l (\hat{N}_p \cdot \hat{L}) + K_s I_l (\hat{R} \cdot \hat{V})^n$$

Where:

• $K_a, K_d, K_s$ = ambient, diffuse, specular reflection coefficients

• $\hat{R}$ = reflection vector

• $\hat{V}$ = viewer direction vector

• $n$ = shininess exponent

• Step g: Assign the computed intensity value to the pixel and move to the next pixel.

• Step h: Repeat for all scan lines until the entire polygon is rendered.

Advantages of Phong Shading:

• Produces realistic specular highlights that appear smooth and correctly positioned
• Eliminates Mach band effect seen in Gouraud shading
• Gives high-quality rendering for curved surfaces

Disadvantage:

• Computationally expensive since illumination model is evaluated at every pixel

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Conclusion: Ambient light provides basic uniform visibility while diffuse reflection adds depth based on surface orientation. Phong Shading combines both along with specular reflection at every pixel to produce the most realistic rendering among polygon shading methods.