Lab 3

Transformations, Illumination

Due: Tuesday, December 9th 2014, 13:15 (in class)

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Individual Effort:

No team participation is really encouraged in the case of the homework or the labs. If you fail to do so, it will be treated as academic misconduct.

Late Submission:

In general late submission is not encouraged/accepted unless there is a very good reason.

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Tasks:

Make sure that you do not copy statements from anywhere without an acknowledgment (reference + quotes). The homeworks are meant as an exercise for you to express ideas and concepts in your own words. Hence keep quotes to a bare minimum. All necessary drawings are to be done by hand with a pencil. Briefly describe the method you used to create your figures.

The exercises are taken from the book ...

• Edward Angel, Dave Shreiner Interactive Computer Graphics with WebGL 7th edition, Addison-Wesley, 2015. Publishers link

1. Do exercise 4.32 in the book:
   Show that the sum
   P = α₁ P₁ + α₂ P₂ + ... + α_n P_n
   is defined if and only if
   α₁ + α₁₂ + ... + α_n = 1.
   Hint: Start with the first two terms and write them as
   P = α₁ P₁ + α₂ P₂ + ... = α₁ P₁ + (α₂ + α₁ - α₁)P₂ + ...
   = α₁(P₁ - P₂) + (α₁ + α₂)P₂ + ... ,
   and then proceed inductively.
   
   
2. Do exercise 5.12 in the book:
   How do the WebGL projection matrices change if the COP is not at the origin?
   Assume that the COP is at (0, 0, d) and the projection plane is z = 0.
   
   
3. Do exercise 5.17 in the book:
   Find the projection of a point onto the plane ax + by + cz + d = 0 from a light source located at infinity in the direction (d_x, d_y, d_z).
   
   
4. Do exercise 6.7 in the book:
   Show that if v lies in the same plane as l, n, and r then the halfway angle satisfies
   2ψ = Φ.
   What relationship is there between the angles if v is not coplanar with the other vectors?

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Last modified: November 20, 2014

Sebastian Klaassen / sebastian dot klaassen at univie DOT ac DOT at