3D Graphics and Virtual Reality (Answers)
Section A. (4 marks)
Assign 1 mark for each major component described (up to a maximum of 4 marks). Sample components and descriptions are :
Section B. (4 marks)
One mark for each description of the four terms. Maximum marks allocated is 4.
Section C. (6 marks)
Assign 1 mark for each adequate description of the terms translation, rotation and scaling. Assign 1 mark for each adequate example for these terms. Maximum marks allocated is 6.
Section D. (6 marks)
Allocate 1 mark for the correct description of the transformation. 1 mark for applying the transformation correctly (i.e. multiplying each vertex in turn or as a single matrix multiplication). 1 mark for each correct coordinate and finally 1 mark for a correct sketch of the new object’s position.
The transformation shown is a scaling operation. The scaling factor is 1.25 along the X axis and 0.5 along the Y axis.
You can either apply the transformation to each of the object’s vertices separately, or form a single 3*3 matrix containing all 3 coordinates.
The first method :
Vertex 1. 
Vertex 2. 
Vertex 3. 



The second method :
The new coordinates for each of the vertices are thus :
Vertex 
Coordinate 
1 
0.0, 2.0 
2 
2.5, 0.5 
3 
2.5, 0.5 
The new position of the object is shown in the figure below.