written 3.1 years ago by | • modified 3.1 years ago |

**Find the coordinates of the rotated figure.**

**Mumbai university > mechanical engineering > sem 7 > cad/cam/cae**

**Marks: 10M**

**Difficulty: Easy**

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The pyramid defined by the coordinates A(0,0,0), B(1,0,0), C(0,1,0) and D(0,0,1) is rotated 45 deg about the line L that has the direction V = J + K and passing through point C(0,1,0).

written 3.1 years ago by | • modified 3.1 years ago |

**Find the coordinates of the rotated figure.**

**Mumbai university > mechanical engineering > sem 7 > cad/cam/cae**

**Marks: 10M**

**Difficulty: Easy**

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written 3.1 years ago by |

Step 1: Translating line (i.e Point C) to the origin O(0,0,0)

{tx = 0, ty = -1, tz =0}

Step 2: Aligning with Positive z-axis

On comparing with V = ai + bj + ck ; a = 0, b =1, c =1

also

and

Now,

Step 3: Rotation of the object about z-axis by an angle of θ= 45 deg in CCW direction

Step 4: Aligning Z with V

Step 5: Inverse Translation

Now,

The combined transformation matrix,

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[T] = [Tr] [R] [M] [R]^{-1} [Tr]^{-1}

Now, new resultant coordinates are:

[X'] = [X] [T]

Hence,

A' = (0.5, 0.15, -0.146)

B' = (1.207, 0.6, -0.646)

C' = (0, 1, 0)

D' = (1, 0.296, 0.704)

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