Remove scale transformation from a complex transform matrix 4x4?
$begingroup$
My common task is I have a rect with coordinates of its $2$ points: $(x, y, z), (x + a, y + b, z)$. I applied a $4times4$ transform matrix to it and it became a quadrilateral. Now for some reasons I can't use it this way and must apply scaling before other transformations. The list of operations is given below (it is used in computer graphics so I don't know exactly if it is a correct order or if it should be reversed). How to solve this issue?
- perspective (
m34 = -0.0001); - translation by
z = -radius; - rotation around x axis;
- rotation around y axis;
- scale (decrease the size);
- translation by
z = radius.
This $4times4$ matrix is transposed (for example, m41 means translation by x, m42 translation by y and m43 translation by z).
matrices geometry trigonometry matrix-calculus matrix-decomposition
asked Jul 16 '15 at 7:47
Vyachaslav GerchicovVyachaslav Gerchicov
1085
$endgroup$
add a comment |
$begingroup$
My common task is I have a rect with coordinates of its $2$ points: $(x, y, z), (x + a, y + b, z)$. I applied a $4times4$ transform matrix to it and it became a quadrilateral. Now for some reasons I can't use it this way and must apply scaling before other transformations. The list of operations is given below (it is used in computer graphics so I don't know exactly if it is a correct order or if it should be reversed). How to solve this issue?
- perspective (
m34 = -0.0001); - translation by
z = -radius; - rotation around x axis;
- rotation around y axis;
- scale (decrease the size);
- translation by
z = radius.
This $4times4$ matrix is transposed (for example, m41 means translation by x, m42 translation by y and m43 translation by z).
matrices geometry trigonometry matrix-calculus matrix-decomposition
asked Jul 16 '15 at 7:47
Vyachaslav GerchicovVyachaslav Gerchicov
1085
$endgroup$
add a comment |
$begingroup$
My common task is I have a rect with coordinates of its $2$ points: $(x, y, z), (x + a, y + b, z)$. I applied a $4times4$ transform matrix to it and it became a quadrilateral. Now for some reasons I can't use it this way and must apply scaling before other transformations. The list of operations is given below (it is used in computer graphics so I don't know exactly if it is a correct order or if it should be reversed). How to solve this issue?
- perspective (
m34 = -0.0001); - translation by
z = -radius; - rotation around x axis;
- rotation around y axis;
- scale (decrease the size);
- translation by
z = radius.
This $4times4$ matrix is transposed (for example, m41 means translation by x, m42 translation by y and m43 translation by z).
matrices geometry trigonometry matrix-calculus matrix-decomposition
asked Jul 16 '15 at 7:47
Vyachaslav GerchicovVyachaslav Gerchicov
1085
$endgroup$
My common task is I have a rect with coordinates of its $2$ points: $(x, y, z), (x + a, y + b, z)$. I applied a $4times4$ transform matrix to it and it became a quadrilateral. Now for some reasons I can't use it this way and must apply scaling before other transformations. The list of operations is given below (it is used in computer graphics so I don't know exactly if it is a correct order or if it should be reversed). How to solve this issue?
- perspective (
m34 = -0.0001); - translation by
z = -radius; - rotation around x axis;
- rotation around y axis;
- scale (decrease the size);
- translation by
z = radius.
This $4times4$ matrix is transposed (for example, m41 means translation by x, m42 translation by y and m43 translation by z).
matrices geometry trigonometry matrix-calculus matrix-decomposition
matrices geometry trigonometry matrix-calculus matrix-decomposition
asked Jul 16 '15 at 7:47
Vyachaslav GerchicovVyachaslav Gerchicov
1085
asked Jul 16 '15 at 7:47
Vyachaslav GerchicovVyachaslav Gerchicov
1085
edited Jul 16 '15 at 8:41
Vyachaslav Gerchicov
asked Jul 16 '15 at 7:47
Vyachaslav GerchicovVyachaslav Gerchicov
1085
asked Jul 16 '15 at 7:47
Vyachaslav GerchicovVyachaslav Gerchicov
1085
asked Jul 16 '15 at 7:47
Vyachaslav GerchicovVyachaslav Gerchicov
1085
1085
add a comment |
add a comment |
1 Answer
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$begingroup$
I multiply by additional matrices to "neutralize" perspective and translation (first 2 transforms) one by one then I apply scale (because the rotation and scale transforms don't need to be placed in a strict order). Then I "repeat" first 2 transforms I previously "removed".
The reason I haven't found a solution previously is the perspective transform. It seems it breaks the whole matrix (or adds something like an unusual distortion) and common matrix rules may work no longer. In this case my way works if I "remove" the perspective by the first action and it won't work if I "remove" transforms from the end of the sequence.
answered Jul 16 '15 at 9:18
Vyachaslav GerchicovVyachaslav Gerchicov
1085
$endgroup$
add a comment |
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$begingroup$
I multiply by additional matrices to "neutralize" perspective and translation (first 2 transforms) one by one then I apply scale (because the rotation and scale transforms don't need to be placed in a strict order). Then I "repeat" first 2 transforms I previously "removed".
The reason I haven't found a solution previously is the perspective transform. It seems it breaks the whole matrix (or adds something like an unusual distortion) and common matrix rules may work no longer. In this case my way works if I "remove" the perspective by the first action and it won't work if I "remove" transforms from the end of the sequence.
answered Jul 16 '15 at 9:18
Vyachaslav GerchicovVyachaslav Gerchicov
1085
$endgroup$
add a comment |
$begingroup$
I multiply by additional matrices to "neutralize" perspective and translation (first 2 transforms) one by one then I apply scale (because the rotation and scale transforms don't need to be placed in a strict order). Then I "repeat" first 2 transforms I previously "removed".
The reason I haven't found a solution previously is the perspective transform. It seems it breaks the whole matrix (or adds something like an unusual distortion) and common matrix rules may work no longer. In this case my way works if I "remove" the perspective by the first action and it won't work if I "remove" transforms from the end of the sequence.
answered Jul 16 '15 at 9:18
Vyachaslav GerchicovVyachaslav Gerchicov
1085
$endgroup$
add a comment |
$begingroup$
I multiply by additional matrices to "neutralize" perspective and translation (first 2 transforms) one by one then I apply scale (because the rotation and scale transforms don't need to be placed in a strict order). Then I "repeat" first 2 transforms I previously "removed".
The reason I haven't found a solution previously is the perspective transform. It seems it breaks the whole matrix (or adds something like an unusual distortion) and common matrix rules may work no longer. In this case my way works if I "remove" the perspective by the first action and it won't work if I "remove" transforms from the end of the sequence.
answered Jul 16 '15 at 9:18
Vyachaslav GerchicovVyachaslav Gerchicov
1085
$endgroup$
I multiply by additional matrices to "neutralize" perspective and translation (first 2 transforms) one by one then I apply scale (because the rotation and scale transforms don't need to be placed in a strict order). Then I "repeat" first 2 transforms I previously "removed".
The reason I haven't found a solution previously is the perspective transform. It seems it breaks the whole matrix (or adds something like an unusual distortion) and common matrix rules may work no longer. In this case my way works if I "remove" the perspective by the first action and it won't work if I "remove" transforms from the end of the sequence.
answered Jul 16 '15 at 9:18
Vyachaslav GerchicovVyachaslav Gerchicov
1085
answered Jul 16 '15 at 9:18
Vyachaslav GerchicovVyachaslav Gerchicov
1085
answered Jul 16 '15 at 9:18
Vyachaslav GerchicovVyachaslav Gerchicov
1085
answered Jul 16 '15 at 9:18
Vyachaslav GerchicovVyachaslav Gerchicov
1085
1085
add a comment |
add a comment |
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