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CSCE 452: Question Set 1

CSCE 452: Question Set 1. Spatial Descriptions Homogeneous Transformations: Mapping and Operator Three Angle Rotation Representations. Last lecture: Homogeneous Transform Interpretations. Homogeneous Transformation for Mapping. Transformation Operator. Rotation Representations.

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CSCE 452: Question Set 1

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  1. CSCE 452: Question Set 1 Spatial Descriptions Homogeneous Transformations: Mapping and Operator Three Angle Rotation Representations

  2. Last lecture: Homogeneous Transform Interpretations

  3. Homogeneous Transformation for Mapping

  4. Transformation Operator

  5. Rotation Representations • Rotation Matrix • Fixed Angle Rotation • Euler Angle Rotation • Angle-Axis Representation • Euler Parameters

  6. Q1 • A vector is rotated aboutby θdegrees and is subsequently rotate about by φdegrees. Given the rotation matrix that accomplishes these rotations in the given order.

  7. Q1 Answer • A vector is rotated aboutby θdegrees and is subsequently rotate about by φdegrees. Given the rotation matrix that accomplishes these rotations in the given order.

  8. Q2 • What is the corresponding operator T for Q1 in matrix format?

  9. Q2-Answer • What is the corresponding operator T for Q1 in matrix format?

  10. Q3 • A frame {B} is initially coincident with a frame {A}. We rotate {B} aboutby θ degrees, and then we rotate the resulting frame about by φdegrees. Given the rotation matrix that changes the description of the vectors from to .

  11. Q3 -Answer • A frame {B} is initially coincident with a frame {A}. We rotate {B} aboutby θ degrees, and then we rotate the resulting frame about by φdegrees. Given the rotation matrix that changes the description of the vectors from to .

  12. Q4 • What is the transformation matrix for the that of Q2? How to compute

  13. Q4 –Answer: • What is the transformation matrix for the that of Q2? How to compute

  14. Q5 • A vector is undergoing the following transformation in sequence: • Translate by vector • Rotate about by θdegrees • Translate by another vector • Rotate about about by φdegrees • Please compute transform operator T for each step and a single transform operator matrix that can perform the above sequence. What is new ?

  15. Q5 - Answer • A vector is undergoing the following transformation in sequence: • Translate by vector • Rotate about by θdegrees • Translate by another vector • Rotate about about by φdegrees • Please compute transform operate T for each step and a single transform operator matrix that can perform the above sequence. What is new ? • , , • , ,

  16. Q6 • A frame {B} is initially coincident with a frame {A}. We transform frame {B} according to the following sequence • Translate by vector to form frame {B’} • Rotate about by θdegrees to form frame {B’’} • Translate by another vector to from frame {B’’’} • Rotate about about by φdegrees to form final frame {B} • What is frame mapping matrices for each step. What is the final matrix ?

  17. Q6 - Answer • A frame {B} is initially coincident with a frame {A}. We transform frame {B} according to the following sequence • Translate by vector to form frame {B’} • Rotate about by θdegrees to form frame {B’’} • Translate by another vector to from frame {B’’’} • Rotate about about by φdegrees to form final frame {B} • What is frame mapping matrices for each step. What is the final matrix ? • ,, • ,,

  18. Q7 • We have the following frames {U}, {1}, {2}, {3}, {4} with known frame mapping matrices , , , , how to obtain and ?

  19. Q7 - Answer • We have the following frames {U}, {1}, {2}, {3}, {4} with known frame mapping matrices , , , , how to obtain and ? • =

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