How to get circle points in 3d given a radius and a vector orthogonal to the circle area?
$begingroup$
I already know how to get a point on a circle (here), but I need a circle in 3d which should be the orthogonal to a given vector.
I got:
- Angle in degree/radians
- Circle radius
- Orthogonal vector
I think, I need to rotate the 2d circle positions to be orthogonal to the given vector, but I do not how how to do that.
vectors circle 3d
asked Aug 14 '15 at 8:40
Janmm14Janmm14
62
$endgroup$
add a comment |
$begingroup$
I already know how to get a point on a circle (here), but I need a circle in 3d which should be the orthogonal to a given vector.
I got:
- Angle in degree/radians
- Circle radius
- Orthogonal vector
I think, I need to rotate the 2d circle positions to be orthogonal to the given vector, but I do not how how to do that.
vectors circle 3d
asked Aug 14 '15 at 8:40
Janmm14Janmm14
62
$endgroup$
$begingroup$
What does the given angle specify? Where is the center of the circle? What kind of result do you expect/need?
$endgroup$
– coproc
Aug 17 '15 at 6:55
$begingroup$
The angle is the angle on the circle needing to calculate a point on the circle in 2d. The result should be a 3d point (x,y,z). The center of the circle should be at (0,0,0).
$endgroup$
– Janmm14
Aug 21 '15 at 14:00
add a comment |
$begingroup$
I already know how to get a point on a circle (here), but I need a circle in 3d which should be the orthogonal to a given vector.
I got:
- Angle in degree/radians
- Circle radius
- Orthogonal vector
I think, I need to rotate the 2d circle positions to be orthogonal to the given vector, but I do not how how to do that.
vectors circle 3d
asked Aug 14 '15 at 8:40
Janmm14Janmm14
62
$endgroup$
I already know how to get a point on a circle (here), but I need a circle in 3d which should be the orthogonal to a given vector.
I got:
- Angle in degree/radians
- Circle radius
- Orthogonal vector
I think, I need to rotate the 2d circle positions to be orthogonal to the given vector, but I do not how how to do that.
vectors circle 3d
vectors circle 3d
asked Aug 14 '15 at 8:40
Janmm14Janmm14
62
asked Aug 14 '15 at 8:40
Janmm14Janmm14
62
asked Aug 14 '15 at 8:40
Janmm14Janmm14
62
asked Aug 14 '15 at 8:40
Janmm14Janmm14
62
asked Aug 14 '15 at 8:40
Janmm14Janmm14
62
62
$begingroup$
What does the given angle specify? Where is the center of the circle? What kind of result do you expect/need?
$endgroup$
– coproc
Aug 17 '15 at 6:55
$begingroup$
The angle is the angle on the circle needing to calculate a point on the circle in 2d. The result should be a 3d point (x,y,z). The center of the circle should be at (0,0,0).
$endgroup$
– Janmm14
Aug 21 '15 at 14:00
add a comment |
$begingroup$
What does the given angle specify? Where is the center of the circle? What kind of result do you expect/need?
$endgroup$
– coproc
Aug 17 '15 at 6:55
$begingroup$
The angle is the angle on the circle needing to calculate a point on the circle in 2d. The result should be a 3d point (x,y,z). The center of the circle should be at (0,0,0).
$endgroup$
– Janmm14
Aug 21 '15 at 14:00
$begingroup$
What does the given angle specify? Where is the center of the circle? What kind of result do you expect/need?
$endgroup$
– coproc
Aug 17 '15 at 6:55
$begingroup$
What does the given angle specify? Where is the center of the circle? What kind of result do you expect/need?
$endgroup$
– coproc
Aug 17 '15 at 6:55
$begingroup$
The angle is the angle on the circle needing to calculate a point on the circle in 2d. The result should be a 3d point (x,y,z). The center of the circle should be at (0,0,0).
$endgroup$
– Janmm14
Aug 21 '15 at 14:00
$begingroup$
The angle is the angle on the circle needing to calculate a point on the circle in 2d. The result should be a 3d point (x,y,z). The center of the circle should be at (0,0,0).
$endgroup$
– Janmm14
Aug 21 '15 at 14:00
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Let us denote the angle by $theta$, the radius by $r$ and the orthogonal vector by $vec a$ ("axis"); furthermore let us assume the length of $vec a$ is 1.
First you must define which point is defined by $theta=0$. If $vec a$ is not parallel to the $xy$-plane then there is a unique vector $vec v_0 = (x_0, 0, z_0)$ orthogonal to $vec a$ with length $r$ and $x_0 > 0$. (Otherwise you need a different choice for $vec v_0$. In 3D there is no obvious way to define such a $vec v_0$ for any $vec a$.)
Then all you need to do is rotate the vector $vec v_0$ around $vec a$ by the angle $theta$. The formula is:
$$ cos theta vec v_0 + (1-cos theta)(vec a cdot vec v_0)vec a + sin theta vec a times vec v_0$$
answered Aug 21 '15 at 18:20
coproccoproc
977514
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add a comment |
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1 Answer
1
active
oldest
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1 Answer
1
active
oldest
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active
oldest
votes
active
oldest
votes
$begingroup$
Let us denote the angle by $theta$, the radius by $r$ and the orthogonal vector by $vec a$ ("axis"); furthermore let us assume the length of $vec a$ is 1.
First you must define which point is defined by $theta=0$. If $vec a$ is not parallel to the $xy$-plane then there is a unique vector $vec v_0 = (x_0, 0, z_0)$ orthogonal to $vec a$ with length $r$ and $x_0 > 0$. (Otherwise you need a different choice for $vec v_0$. In 3D there is no obvious way to define such a $vec v_0$ for any $vec a$.)
Then all you need to do is rotate the vector $vec v_0$ around $vec a$ by the angle $theta$. The formula is:
$$ cos theta vec v_0 + (1-cos theta)(vec a cdot vec v_0)vec a + sin theta vec a times vec v_0$$
answered Aug 21 '15 at 18:20
coproccoproc
977514
$endgroup$
add a comment |
$begingroup$
Let us denote the angle by $theta$, the radius by $r$ and the orthogonal vector by $vec a$ ("axis"); furthermore let us assume the length of $vec a$ is 1.
First you must define which point is defined by $theta=0$. If $vec a$ is not parallel to the $xy$-plane then there is a unique vector $vec v_0 = (x_0, 0, z_0)$ orthogonal to $vec a$ with length $r$ and $x_0 > 0$. (Otherwise you need a different choice for $vec v_0$. In 3D there is no obvious way to define such a $vec v_0$ for any $vec a$.)
Then all you need to do is rotate the vector $vec v_0$ around $vec a$ by the angle $theta$. The formula is:
$$ cos theta vec v_0 + (1-cos theta)(vec a cdot vec v_0)vec a + sin theta vec a times vec v_0$$
answered Aug 21 '15 at 18:20
coproccoproc
977514
$endgroup$
add a comment |
$begingroup$
Let us denote the angle by $theta$, the radius by $r$ and the orthogonal vector by $vec a$ ("axis"); furthermore let us assume the length of $vec a$ is 1.
First you must define which point is defined by $theta=0$. If $vec a$ is not parallel to the $xy$-plane then there is a unique vector $vec v_0 = (x_0, 0, z_0)$ orthogonal to $vec a$ with length $r$ and $x_0 > 0$. (Otherwise you need a different choice for $vec v_0$. In 3D there is no obvious way to define such a $vec v_0$ for any $vec a$.)
Then all you need to do is rotate the vector $vec v_0$ around $vec a$ by the angle $theta$. The formula is:
$$ cos theta vec v_0 + (1-cos theta)(vec a cdot vec v_0)vec a + sin theta vec a times vec v_0$$
answered Aug 21 '15 at 18:20
coproccoproc
977514
$endgroup$
Let us denote the angle by $theta$, the radius by $r$ and the orthogonal vector by $vec a$ ("axis"); furthermore let us assume the length of $vec a$ is 1.
First you must define which point is defined by $theta=0$. If $vec a$ is not parallel to the $xy$-plane then there is a unique vector $vec v_0 = (x_0, 0, z_0)$ orthogonal to $vec a$ with length $r$ and $x_0 > 0$. (Otherwise you need a different choice for $vec v_0$. In 3D there is no obvious way to define such a $vec v_0$ for any $vec a$.)
Then all you need to do is rotate the vector $vec v_0$ around $vec a$ by the angle $theta$. The formula is:
$$ cos theta vec v_0 + (1-cos theta)(vec a cdot vec v_0)vec a + sin theta vec a times vec v_0$$
answered Aug 21 '15 at 18:20
coproccoproc
977514
answered Aug 21 '15 at 18:20
coproccoproc
977514
answered Aug 21 '15 at 18:20
coproccoproc
977514
answered Aug 21 '15 at 18:20
coproccoproc
977514
977514
add a comment |
add a comment |
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$begingroup$
What does the given angle specify? Where is the center of the circle? What kind of result do you expect/need?
$endgroup$
– coproc
Aug 17 '15 at 6:55
$begingroup$
The angle is the angle on the circle needing to calculate a point on the circle in 2d. The result should be a 3d point (x,y,z). The center of the circle should be at (0,0,0).
$endgroup$
– Janmm14
Aug 21 '15 at 14:00