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 co-ordinate and finally 1 mark for a correct sketch of the new objectís 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 objectís vertices separately, or form a single 3*3 matrix containing all 3 co-ordinates.

The first method :

Vertex 1.

Vertex 2.

Vertex 3.

The second method :

The new co-ordinates for each of the vertices are thus :

Vertex

Co-ordinate

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.