Transforming Tilt and Azimuth in one coordinate space to another

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I have two different 3D coordinate spaces where I am using affine transformations to convert points between one coordinate space to the other. My problem is that these points also include tilt and azimuth as well. How can I transform these tilt and azimuth values? Can I make use of the 4×4 affine transformation that I have for converting the $x,y,z$ points?



So to begin, I have 8 points in coordinate space one, with the corresponding 8 points in coordinate space two. What I calculate is the Affine transformation matrix that can transform points in coordinate space 1 to coordinate space 2, like this Affine Transformation Matrix:
$$beginbmatrixX_p\Y_p\Z_p\1endbmatrix=beginbmatrixM_11&M_12&M_13&M_14\M_21&M_22&M_23&M_24\M_31&M_32&M_33&M_34\0&0&0&1endbmatrixbeginbmatrixX\Y\Z\1endbmatrix$$
Where $X_p,Y_p,Z_p$ is projected points and $X,Y,Z$ are original points. Last row of the transformation matrix can actually be ignored cause we know $w$ is always equal to 1. $M_11$ through $M_34$ are the coefficients for the transformation matrix.



So all I have to do to transform a point in coordinate system 1 is multiply by transformation matrix. But I also have tilt and azimuth, how can I convert these values? Can I use my transformation matrix or do I need to handle tilt and azimuth separately?




linear-algebra linear-transformations




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  • Your transformation won’t preserve angles unless it’s a similarity. If it is, you can decompose it to isolate its rotation component.
    – amd
    Jul 26 at 3:26














up vote
2
down vote

favorite












I have two different 3D coordinate spaces where I am using affine transformations to convert points between one coordinate space to the other. My problem is that these points also include tilt and azimuth as well. How can I transform these tilt and azimuth values? Can I make use of the 4×4 affine transformation that I have for converting the $x,y,z$ points?



So to begin, I have 8 points in coordinate space one, with the corresponding 8 points in coordinate space two. What I calculate is the Affine transformation matrix that can transform points in coordinate space 1 to coordinate space 2, like this Affine Transformation Matrix:
$$beginbmatrixX_p\Y_p\Z_p\1endbmatrix=beginbmatrixM_11&M_12&M_13&M_14\M_21&M_22&M_23&M_24\M_31&M_32&M_33&M_34\0&0&0&1endbmatrixbeginbmatrixX\Y\Z\1endbmatrix$$
Where $X_p,Y_p,Z_p$ is projected points and $X,Y,Z$ are original points. Last row of the transformation matrix can actually be ignored cause we know $w$ is always equal to 1. $M_11$ through $M_34$ are the coefficients for the transformation matrix.



So all I have to do to transform a point in coordinate system 1 is multiply by transformation matrix. But I also have tilt and azimuth, how can I convert these values? Can I use my transformation matrix or do I need to handle tilt and azimuth separately?




linear-algebra linear-transformations




share|cite|improve this question





















  • Your transformation won’t preserve angles unless it’s a similarity. If it is, you can decompose it to isolate its rotation component.
    – amd
    Jul 26 at 3:26












up vote
2
down vote

favorite









up vote
2
down vote

favorite











I have two different 3D coordinate spaces where I am using affine transformations to convert points between one coordinate space to the other. My problem is that these points also include tilt and azimuth as well. How can I transform these tilt and azimuth values? Can I make use of the 4×4 affine transformation that I have for converting the $x,y,z$ points?



So to begin, I have 8 points in coordinate space one, with the corresponding 8 points in coordinate space two. What I calculate is the Affine transformation matrix that can transform points in coordinate space 1 to coordinate space 2, like this Affine Transformation Matrix:
$$beginbmatrixX_p\Y_p\Z_p\1endbmatrix=beginbmatrixM_11&M_12&M_13&M_14\M_21&M_22&M_23&M_24\M_31&M_32&M_33&M_34\0&0&0&1endbmatrixbeginbmatrixX\Y\Z\1endbmatrix$$
Where $X_p,Y_p,Z_p$ is projected points and $X,Y,Z$ are original points. Last row of the transformation matrix can actually be ignored cause we know $w$ is always equal to 1. $M_11$ through $M_34$ are the coefficients for the transformation matrix.



So all I have to do to transform a point in coordinate system 1 is multiply by transformation matrix. But I also have tilt and azimuth, how can I convert these values? Can I use my transformation matrix or do I need to handle tilt and azimuth separately?




linear-algebra linear-transformations




share|cite|improve this question













I have two different 3D coordinate spaces where I am using affine transformations to convert points between one coordinate space to the other. My problem is that these points also include tilt and azimuth as well. How can I transform these tilt and azimuth values? Can I make use of the 4×4 affine transformation that I have for converting the $x,y,z$ points?



So to begin, I have 8 points in coordinate space one, with the corresponding 8 points in coordinate space two. What I calculate is the Affine transformation matrix that can transform points in coordinate space 1 to coordinate space 2, like this Affine Transformation Matrix:
$$beginbmatrixX_p\Y_p\Z_p\1endbmatrix=beginbmatrixM_11&M_12&M_13&M_14\M_21&M_22&M_23&M_24\M_31&M_32&M_33&M_34\0&0&0&1endbmatrixbeginbmatrixX\Y\Z\1endbmatrix$$
Where $X_p,Y_p,Z_p$ is projected points and $X,Y,Z$ are original points. Last row of the transformation matrix can actually be ignored cause we know $w$ is always equal to 1. $M_11$ through $M_34$ are the coefficients for the transformation matrix.



So all I have to do to transform a point in coordinate system 1 is multiply by transformation matrix. But I also have tilt and azimuth, how can I convert these values? Can I use my transformation matrix or do I need to handle tilt and azimuth separately?





linear-algebra linear-transformations





share|cite|improve this question












share|cite|improve this question




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edited Jul 26 at 1:08









Parcly Taxel

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asked Jul 26 at 1:04









Jamis Moy

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  • Your transformation won’t preserve angles unless it’s a similarity. If it is, you can decompose it to isolate its rotation component.
    – amd
    Jul 26 at 3:26
















  • Your transformation won’t preserve angles unless it’s a similarity. If it is, you can decompose it to isolate its rotation component.
    – amd
    Jul 26 at 3:26















Your transformation won’t preserve angles unless it’s a similarity. If it is, you can decompose it to isolate its rotation component.
– amd
Jul 26 at 3:26




Your transformation won’t preserve angles unless it’s a similarity. If it is, you can decompose it to isolate its rotation component.
– amd
Jul 26 at 3:26















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