1. A tetrahedron originally has coordinates given in the table below. Assume the tetrahedron is to be rotated 90 deg. about the x-axis (positive rotation) such that point 1 remains fixed. Compute the combined transformation matrix that performs this operation. Compute the new coordinates of points 1-4
Point 1 x=1.5, y=.20, z=1.5
Point 2 x=2.0, y=0, z=0
Point 3 x=1.0, y=0, z=0
Point 4 x=1.6, y=2.5, z=.80
2. For the tetrahedron of problem 1, compute the transformation matrix that rotates the tetrahedron about the vector direction [1,1,1] positive 45 degrees. Point 4 of the tetrahedron is to remain in its original position after the rotation. Compute the combined transformation matrix that performs this operation. Compute the new coordinates for points 1 thru 4.
for problem 1
T = [Tr] [R] [Tr]-1
this will shift point1 to origin
this will rotate the tereahedron about X axix
then apply
now get T and apply on [x y z 1] , where x,y,z are coordinates of points
we will get [x' y' z' 1] as output after applying T
x' , y' , z' are the required coordinates.
for problem 2
1)Translate (1.6, 2.5 , .80) so that the point is at origin
2) Make appropriate rotations (i.e.45 degree each about Z- axis and Y - axis Because (1,1,1) makes angle 45 degree with both axes) to make the vector (1,1,1) coincide with one of the axes, say x-axis
3)Rotate the object about x-axis by required angle
4)Apply the inverse of step 2
5)Apply the inverse of step 1
matrix will be [T] = [Tr] [R45] [R45] [R45] [R45]-1 [R45]-1 [Tr]-1 using this you can compute all the required coordinates.
Get Answers For Free
Most questions answered within 1 hours.