Question

1. A tetrahedron originally has coordinates given in the table below. Assume the tetrahedron is to...

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.

Homework Answers

Answer #1

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.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Find a 3x3 matrix that performs the 2D transformation in homogeneous coordinates: a) Reflects across the...
Find a 3x3 matrix that performs the 2D transformation in homogeneous coordinates: a) Reflects across the y-axis and then translates up 4 and right 3. b) Dilate so that every point is twice as far from the point (-2,-1) in both the x direction and the y direction.
Find the rectangular coordinates of the point whose spherical coordinates are given. (a) (1, 0, 0)...
Find the rectangular coordinates of the point whose spherical coordinates are given. (a) (1, 0, 0) (x, y, z) = (b) (14, π/3, π/4) (x, y, z) =
1) Convert the point (x,y,z)=(−2,5,3) to spherical coordinates. Give answers as positive values, either as expressions,...
1) Convert the point (x,y,z)=(−2,5,3) to spherical coordinates. Give answers as positive values, either as expressions, or decimals to one decimal place. (ρ,θ,ϕ)= 2) Convert the point (r,θ,z)=(2,2π,4) to Cartesian coordinates. Give answers either as expressions, or decimals to at least one decimal place. (x,y,z)= 3) Convert the point (ρ,θ,ϕ)= (5,5π/3,3π/4) to Cartesian coordinates. Give answers either as expressions, or decimals to at least one decimal place. (x,y,z) =
A table of values is given for a function f(x, y) defined on R = [1,...
A table of values is given for a function f(x, y) defined on R = [1, 3] × [0, 4]. 0 1 2 3 4 1.0 2 0 -3 -6 -5 1.5 3 1 -4 -5 -6 2.0 4 3 0 -5 -8 2.5 5 4 3 -1 -4 3.0 7 8 6 3 0 Estimate f(x, y) dA R using the Midpoint Rule with m = n = 2 and estimate the double integral with m = n =...
1-Find two positive numbers satisfying the given requirements. The product is 238 and the sum is...
1-Find two positive numbers satisfying the given requirements. The product is 238 and the sum is a minimum. (smaller value) ? (larger value)? 2-Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter: 176 meters length m width m 3-Find the points on the graph of the function that are closest to the given point. f(x) = x2, (0, 4) (x, y) =   (smaller x-value) (x, y) =   (larger x-value)
1. Find the distance between the point and the line given by the set of parametric...
1. Find the distance between the point and the line given by the set of parametric equations. (Round your answer to three decimal places.) (8, -1, 4); x = 2t, y = t − 3, z = 2t + 2 I had put 6.87 but it shows as it being wrong. 2. Consider the following planes. −6x + y + z = 6 24x − 4y + 6z = 36 Find the angle between the two planes. (Round your answer...
1. (5pts.) Compute the derivative dy/dx for y = 7√ 9π + x ^5 /6 +...
1. (5pts.) Compute the derivative dy/dx for y = 7√ 9π + x ^5 /6 + 27e^x . 3. (5pts.) Write the equation of the tangent line to the graph of y = 3 + 8 ln x at the point where x = 1. 4. (5pts.) Determine the slope of the tangent line to the curve 2x^3 + y^3 + 2xy = 14 at the point (1, 2). 5. (5pts.) Compute the derivative dw/dz of the function w =...
Age #Bathrooms #Rooms #BedRooms Age #FirePlaces sellingPrice in $100 42 1 7 4 42 0 4.9176...
Age #Bathrooms #Rooms #BedRooms Age #FirePlaces sellingPrice in $100 42 1 7 4 42 0 4.9176 62 1 7 4 62 0 5.0208 40 1 6 3 40 0 4.5429 54 1 6 3 54 0 4.5573 42 1 6 3 42 0 5.0597 56 1 6 3 56 0 3.891 32 1 6 3 32 0 5.6039 32 1 6 3 32 0 5.8282 30 1 6 3 30 0 5.3003 30 1 5 2 30 0 6.2712 32...
1. A truck with 24-in.-diameter wheels are traveling at 60 mi/h. Find the angular speed of...
1. A truck with 24-in.-diameter wheels are traveling at 60 mi/h. Find the angular speed of the wheels in rad/min:    rad/min How many revolutions per minute do the wheels make?    rpm 2. Without using a calculator, compute the sine and cosine of 300∘300∘ by using the reference angle. (Type sqrt(2) for √22 and sqrt(3) for √33.) What is the reference angle?  degrees. In what quadrant is this angle?  (answer 1, 2, 3, or 4) sin(300∘)=sin(300∘)=    cos(300∘)= 3. Find an angle θθ with 0∘<θ<360∘ that...
PLEASE USE MAT LAB ONLY. THANK YOU (a) Create and plot the signals listed below and...
PLEASE USE MAT LAB ONLY. THANK YOU (a) Create and plot the signals listed below and save your Matlab code in a script file. i) Cosine signal of frequency 100 Hz over the range [0,0.1] seconds and samples spaced 10^- 4 seconds apart with a phase of pi/2 and an amplitude of 1.   PLEASE USE MAT LAB ONLY. THANK YOU ii) A square wave that oscillates between 0 and 1 every five samples, plot 3 periods of the waveform. iii)...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT