Questions below are asked in Computer Graphics lecture.
1. Mark either True or False:
If you want a rotation of 270 degrees around the z-axis, the value in the first (top) row, second column should be sin(270).
True/False:
2. True/False:
The cross product of two parallel 3D vectors is the zero vector (0, 0, 0).
True/False:
3. True/False:
Rigid transformations include the scaling and shear transformation.
True/False:
4. Any affine transformation in a 3D space can be described by a 3x3 matrix.
True/False:
5. For any two transformations, A and B, we get the same result if we apply A before B as if we apply B before A.
True/False:
2. Find an implicit equation for the plane containing the triangle (vi, Vi, Vs). The equation should have the form:
f(p) = N(p - q) = 0
where N is a normal to the plane and q is a point in the plane.
Find N and q in terms of the triangle vertices. Show your steps.
3. (10 points) What are the ray parameters of the intersection points between ray (2, 2, 2) + t (-1, -1, -1) and the sphere centered at the origin with radius 1? Outline your approach, show the steps, but you do not need to compute the final t value.
