Lab 2

Pen & Paper

Due: Wednesday, Nov 21st 2018, 23:59

No late submissions / grace days allowed!!

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Please note:

This assignment has to be turned in twice:

• one digital copy, which you have to upload in Moodle at the above mentioned deadline
• one physical (printed) copy, which you have to bring with you to class on Thursday, Nov 22nd 2018

Both have to be turned in! If one of them is missing, no points can be awarded for this assignment!

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Tasks

The following are based on exercises from the book Interactive Computer Graphics A Top-Down Approach with WebGL 7th edition.

Task 1

Using barycentric coordinates, how do you calculate an arbitrary point P in a triangle formed by the Vertices V₁, V₂, V₃? What are some of the practical applications for barycentric coordinates in computer grahics? Name at least two and explain them using the above mentioned triangle.

Task 2

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)?

Task 3

Derive the perspective projection matrix when the COP can be at any point and the plane can be at any orientation.

Task 4

Show how to compute u and v directions from the VPN, VRP, and VUP using only cross products.

Task 5

Consider a highly reflective sphere centered at the origin with a unit radius. If a viewer is located at P, describe the points she would see reflected in the sphere at a point on its surface.

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Submission

Please submit a single pdf-file (no zip!) containing all the solutions to the provided tasks in Moodle. Bring a hard copy to class, which will also have to be turned in.

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Last modified: November 11, 2018

Manfred Klaffenboeck / manfred DOT klaffenboeck AT univie DOT ac DOT at