Give the homogeneous matrix of projections











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I don't seem to fully understand how can I answer these question. So any help will be appreciated




  1. Give the homogeneous matrix of an isometric projection onto the $x$
    plane.

  2. Give the homogeneous matrix of an isometric projection onto
    the $y$ plane.

  3. Give the homogeneous matrix of an isometric projection
    onto the $xy$ plane.


I'm not quite sure how to start and a thorough explanation will be extremely helpful.



I also want to answer a different question about a vanishing point.




  1. Give the homogeneous matrix of a perspective transformation with a principle vanishing point at $(0,-5,0)$.


So far I've tried to multiply the point $(0,-5,0)$ with



$$begin{bmatrix}1 & 0 & 0 \ 0 & 1 & 0 \ frac{1}{x_0} & 0 & 1 end{bmatrix}$$



However, I'm not sure if this is the correct answer and then I don't know what to do with $x_0$ and even If this needs to be there.






matrices affine-geometry projection projection-matrices homogeneous-spaces







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    up vote
    -1
    down vote

    favorite












    I don't seem to fully understand how can I answer these question. So any help will be appreciated




    1. Give the homogeneous matrix of an isometric projection onto the $x$
      plane.

    2. Give the homogeneous matrix of an isometric projection onto
      the $y$ plane.

    3. Give the homogeneous matrix of an isometric projection
      onto the $xy$ plane.


    I'm not quite sure how to start and a thorough explanation will be extremely helpful.



    I also want to answer a different question about a vanishing point.




    1. Give the homogeneous matrix of a perspective transformation with a principle vanishing point at $(0,-5,0)$.


    So far I've tried to multiply the point $(0,-5,0)$ with



    $$begin{bmatrix}1 & 0 & 0 \ 0 & 1 & 0 \ frac{1}{x_0} & 0 & 1 end{bmatrix}$$



    However, I'm not sure if this is the correct answer and then I don't know what to do with $x_0$ and even If this needs to be there.






    matrices affine-geometry projection projection-matrices homogeneous-spaces







    share|cite|improve this question









    New contributor




    Richard is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
    Check out our Code of Conduct.






















      up vote
      -1
      down vote

      favorite









      up vote
      -1
      down vote

      favorite











      I don't seem to fully understand how can I answer these question. So any help will be appreciated




      1. Give the homogeneous matrix of an isometric projection onto the $x$
        plane.

      2. Give the homogeneous matrix of an isometric projection onto
        the $y$ plane.

      3. Give the homogeneous matrix of an isometric projection
        onto the $xy$ plane.


      I'm not quite sure how to start and a thorough explanation will be extremely helpful.



      I also want to answer a different question about a vanishing point.




      1. Give the homogeneous matrix of a perspective transformation with a principle vanishing point at $(0,-5,0)$.


      So far I've tried to multiply the point $(0,-5,0)$ with



      $$begin{bmatrix}1 & 0 & 0 \ 0 & 1 & 0 \ frac{1}{x_0} & 0 & 1 end{bmatrix}$$



      However, I'm not sure if this is the correct answer and then I don't know what to do with $x_0$ and even If this needs to be there.






      matrices affine-geometry projection projection-matrices homogeneous-spaces







      share|cite|improve this question









      New contributor




      Richard is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.











      I don't seem to fully understand how can I answer these question. So any help will be appreciated




      1. Give the homogeneous matrix of an isometric projection onto the $x$
        plane.

      2. Give the homogeneous matrix of an isometric projection onto
        the $y$ plane.

      3. Give the homogeneous matrix of an isometric projection
        onto the $xy$ plane.


      I'm not quite sure how to start and a thorough explanation will be extremely helpful.



      I also want to answer a different question about a vanishing point.




      1. Give the homogeneous matrix of a perspective transformation with a principle vanishing point at $(0,-5,0)$.


      So far I've tried to multiply the point $(0,-5,0)$ with



      $$begin{bmatrix}1 & 0 & 0 \ 0 & 1 & 0 \ frac{1}{x_0} & 0 & 1 end{bmatrix}$$



      However, I'm not sure if this is the correct answer and then I don't know what to do with $x_0$ and even If this needs to be there.






      matrices affine-geometry projection projection-matrices homogeneous-spaces




      matrices affine-geometry projection projection-matrices homogeneous-spaces






      share|cite|improve this question









      New contributor




      Richard is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.











      share|cite|improve this question









      New contributor




      Richard is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.









      share|cite|improve this question




      share|cite|improve this question








      edited 2 hours ago





















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      asked 19 hours ago









      Richard

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      Richard is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.






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