I have been given a piece of course work for university, see attachment. I have completed questions 1 and 2 but am completely stumped with question 3 as the 3d stuff has thrown me off and dont even know how to get the cubes cordinates in 3d for excel.
I sure this is childs play for some of the experts on here but a little help with the cordinates and transformations will be much apreciated.
thank you
ok, sorry
Question 1
Solve the matrix equation A X + I = B
where A=, B= and I is the 2x2 identity matrix.
-1 -3
2 0
Question 2
Using Excel, produce your own design of the 2D image of a building (front or side elevation) which has one of its vertices at the point with coordinates (5,4).
Rotate your image about the point (5,4) in an anticlockwise direction through an angle of 75o.Then reflect the rotated image in the straight line 2y=x+3.
Determine the single 3x3 matrix which performs this transformation and produce a plot of the original image and the transformed image on the same graph.
Marks will be awarded for the design of your building.
Question 3
A cube has vertices (0,0,0),(0,1,0),(1,1,0),(1,0,0),(1,0,1),(1,1,1),(0 ,1,1),(0,0,1).
The cube is rotated about the y-axis through an angle of 40o and then translated downwards (in the negative y direction) by 3. The image is then projected onto the viewing plane z=0 and viewed from the point (0,0,4).
Determine the overall 4x4 transformation matrix and calculate the position of the two vanishing points.
Using Excel, produce a picture showing the transformed cube and the vanishing points.
cheers