3D Graphics and Virtual Reality (Answers)

Section A. (10 marks)

Part A(i) (3 marks)

Part A(ii) (3 marks)

Part A(iii) (4 marks)

One example could be Architectural an walk-through. Here the emphasis is on gaining a realistic impression of what a building will look like when finished. User movement and interaction are of lesser importance, visual realism is paramount.

Flight simulators do require as high visual realism as possible, however most important of all is the system’s response and realism of response and interaction. Undue latency must be kept to an absolute minimum, at the sacrifice of visual realism.

Section B. (10 marks)

Part B(i) (3 marks)

To produce a compound transformation which will scale about any given point (SP), we must perform the following operations. First, transform an object from the specified point, back to the origin (T-P). Second, perform a scale operation on the object, centred about the origin (SO). Third, transform the object back to the specified point (TP). This equates to…

SP = TP.SO.T-P

Part B(ii) (3 marks)

Expanding the above equation with the full transformations….

OR

Part B(iii) (4 marks)

You can either apply the transformation to each of the object’s vertices separately, or form a single 3*3 matrix containing all 3 co-ordinates. Firstly, filling in the matrix with the values for Px, Py, Sx and Sy gives….

The first method :

Vertex 1.

Vertex 2.

Vertex 3.

The second method :

The new co-ordinates for each of the vertices and the new position of the object are shown in the table and figure below.

Vertex

Co-ordinate

1

1.0, 1.5

2

-2.0, -1.0

3

4.0, -1.0