Pen & Paper

Due: Wednesday, May 10st 2019, 23:55

No late submissions / grace days allowed!!

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Please note:

This assignment has to be submitted in Moodle

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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

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

Task 2

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.

Task 3

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 4

For many Virtual Reality installations, the COP can be at any point and the projection plane can be at any orientation. Derive the projection matrix for this general case.

Task 5

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 graphics? Name at least two and explain them using the above mentioned triangle.

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Submission

Please submit a single pdf-file (no zip!) containing all the solutions to the provided tasks in Moodle.

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Last modified: April 21st, 2020

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