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CS112: Introduction to Computer Graphics

Take-Home Quiz 2, Fall 2021

Submit: Please upload your typed or scanned solution to Gradescope.

Q1 (20%). Derive the reflection vector R in terms of the normal N and the light vector L at a fixed surface point (see the following figure).

Assume all the vectors to be unit-length and point away from the surface point. (Please include step-by-step derivations.)

Q2 (40%). Below is the equation for the Blinn-Phong reflectance model:

Please define each of the ten terms on the right-hand side of this equation. Examples include diffuse coefficient, normal vector, and light intensity.

Q3 (20%). The Phong reflectance model differs from the Blinn-Phong model by using the dot product between the reflection vector R (from Q1) and the viewing direction V to capture specular reflection. Write down the specular component of the Phong model.

Q4 (20%). Answer for following questions for (a) the Gouraud and (b) the Phong shading models, respec-tively:

(i) Briefly describe how the shading model works.

(ii) When implemented using the OpenGL Shading Language (GLSL), what shader does the majority of shading computation take place in?