Parametric equation for a space curve
With reference to the following image:
the blue curve has trivially a parametrization:
$$(x, y, z) = (costheta, , sintheta, , 0) ; ; ; text{with} ; theta in [0,,2pi)$$
I would like to determine the parametric equations of the red curve, very badly drawn in Paint, where I mean a sinusoidal curve along the blue circumference.
Although I thought about it a lot, I still could not figure out how to derive these parametric equation. Any ideas?
curves parametrization
edited 28 mins ago
dmtri
1,4181521
asked 1 hour ago
TeM
415315
add a comment |
With reference to the following image:
the blue curve has trivially a parametrization:
$$(x, y, z) = (costheta, , sintheta, , 0) ; ; ; text{with} ; theta in [0,,2pi)$$
I would like to determine the parametric equations of the red curve, very badly drawn in Paint, where I mean a sinusoidal curve along the blue circumference.
Although I thought about it a lot, I still could not figure out how to derive these parametric equation. Any ideas?
curves parametrization
edited 28 mins ago
dmtri
1,4181521
asked 1 hour ago
TeM
415315
1
It looks like a curve of the form $$ r(theta) = r_0 + A cos{(omega theta )} $$ But it's not very clear what you mean with the hand-drawn curve. Is it supposed to come out of the $z=0$-plane?
– Matti P.
57 mins ago
1
@MattiP.: Yes, it must exit the $z = 0$ plane and have the circumference as the average line.
– TeM
36 mins ago
add a comment |
With reference to the following image:
the blue curve has trivially a parametrization:
$$(x, y, z) = (costheta, , sintheta, , 0) ; ; ; text{with} ; theta in [0,,2pi)$$
I would like to determine the parametric equations of the red curve, very badly drawn in Paint, where I mean a sinusoidal curve along the blue circumference.
Although I thought about it a lot, I still could not figure out how to derive these parametric equation. Any ideas?
curves parametrization
edited 28 mins ago
dmtri
1,4181521
asked 1 hour ago
TeM
415315
With reference to the following image:
the blue curve has trivially a parametrization:
$$(x, y, z) = (costheta, , sintheta, , 0) ; ; ; text{with} ; theta in [0,,2pi)$$
I would like to determine the parametric equations of the red curve, very badly drawn in Paint, where I mean a sinusoidal curve along the blue circumference.
Although I thought about it a lot, I still could not figure out how to derive these parametric equation. Any ideas?
curves parametrization
curves parametrization
edited 28 mins ago
dmtri
1,4181521
asked 1 hour ago
TeM
415315
edited 28 mins ago
dmtri
1,4181521
asked 1 hour ago
TeM
415315
edited 28 mins ago
dmtri
1,4181521
edited 28 mins ago
dmtri
1,4181521
edited 28 mins ago
dmtri
1,4181521
1,4181521
asked 1 hour ago
TeM
415315
asked 1 hour ago
TeM
415315
asked 1 hour ago
TeM
415315
415315
1
It looks like a curve of the form $$ r(theta) = r_0 + A cos{(omega theta )} $$ But it's not very clear what you mean with the hand-drawn curve. Is it supposed to come out of the $z=0$-plane?
– Matti P.
57 mins ago
1
@MattiP.: Yes, it must exit the $z = 0$ plane and have the circumference as the average line.
– TeM
36 mins ago
add a comment |
1
It looks like a curve of the form $$ r(theta) = r_0 + A cos{(omega theta )} $$ But it's not very clear what you mean with the hand-drawn curve. Is it supposed to come out of the $z=0$-plane?
– Matti P.
57 mins ago
1
@MattiP.: Yes, it must exit the $z = 0$ plane and have the circumference as the average line.
– TeM
36 mins ago
1
1
It looks like a curve of the form $$ r(theta) = r_0 + A cos{(omega theta )} $$ But it's not very clear what you mean with the hand-drawn curve. Is it supposed to come out of the $z=0$-plane?
– Matti P.
57 mins ago
It looks like a curve of the form $$ r(theta) = r_0 + A cos{(omega theta )} $$ But it's not very clear what you mean with the hand-drawn curve. Is it supposed to come out of the $z=0$-plane?
– Matti P.
57 mins ago
1
1
@MattiP.: Yes, it must exit the $z = 0$ plane and have the circumference as the average line.
– TeM
36 mins ago
@MattiP.: Yes, it must exit the $z = 0$ plane and have the circumference as the average line.
– TeM
36 mins ago
add a comment |
1 Answer
1
active
oldest
votes
You can try$$thetamapstoleft(costheta,sintheta,frac{cos(8theta)}8right),$$for instance.
answered 57 mins ago
José Carlos Santos
150k22121221
It's exactly what I wanted, thank you! Could you tell me how you managed to understand it?
– TeM
29 mins ago
2
The $z$ coordinate had to be a waving line again, and so I thought about $cos(8theta)$, but then the waves would go too high and too low. That's why I divided by $8$.
– José Carlos Santos
25 mins ago
Perfect! Before closing I also wanted to ask how to get the parametric equations of the red curve if it lay in the $z = 0$ plane. Is it better that I open a new question or change the request?
– TeM
15 mins ago
No need for that. Just consider:$$thetamapstoleft(costheta+frac{cos(8theta)}8,sintheta,0right).$$
– José Carlos Santos
8 mins ago
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
You can try$$thetamapstoleft(costheta,sintheta,frac{cos(8theta)}8right),$$for instance.
answered 57 mins ago
José Carlos Santos
150k22121221
It's exactly what I wanted, thank you! Could you tell me how you managed to understand it?
– TeM
29 mins ago
2
The $z$ coordinate had to be a waving line again, and so I thought about $cos(8theta)$, but then the waves would go too high and too low. That's why I divided by $8$.
– José Carlos Santos
25 mins ago
Perfect! Before closing I also wanted to ask how to get the parametric equations of the red curve if it lay in the $z = 0$ plane. Is it better that I open a new question or change the request?
– TeM
15 mins ago
No need for that. Just consider:$$thetamapstoleft(costheta+frac{cos(8theta)}8,sintheta,0right).$$
– José Carlos Santos
8 mins ago
add a comment |
You can try$$thetamapstoleft(costheta,sintheta,frac{cos(8theta)}8right),$$for instance.
answered 57 mins ago
José Carlos Santos
150k22121221
It's exactly what I wanted, thank you! Could you tell me how you managed to understand it?
– TeM
29 mins ago
2
The $z$ coordinate had to be a waving line again, and so I thought about $cos(8theta)$, but then the waves would go too high and too low. That's why I divided by $8$.
– José Carlos Santos
25 mins ago
Perfect! Before closing I also wanted to ask how to get the parametric equations of the red curve if it lay in the $z = 0$ plane. Is it better that I open a new question or change the request?
– TeM
15 mins ago
No need for that. Just consider:$$thetamapstoleft(costheta+frac{cos(8theta)}8,sintheta,0right).$$
– José Carlos Santos
8 mins ago
add a comment |
You can try$$thetamapstoleft(costheta,sintheta,frac{cos(8theta)}8right),$$for instance.
answered 57 mins ago
José Carlos Santos
150k22121221
You can try$$thetamapstoleft(costheta,sintheta,frac{cos(8theta)}8right),$$for instance.
answered 57 mins ago
José Carlos Santos
150k22121221
edited 32 mins ago
answered 57 mins ago
José Carlos Santos
150k22121221
answered 57 mins ago
José Carlos Santos
150k22121221
answered 57 mins ago
José Carlos Santos
150k22121221
150k22121221
It's exactly what I wanted, thank you! Could you tell me how you managed to understand it?
– TeM
29 mins ago
2
The $z$ coordinate had to be a waving line again, and so I thought about $cos(8theta)$, but then the waves would go too high and too low. That's why I divided by $8$.
– José Carlos Santos
25 mins ago
Perfect! Before closing I also wanted to ask how to get the parametric equations of the red curve if it lay in the $z = 0$ plane. Is it better that I open a new question or change the request?
– TeM
15 mins ago
No need for that. Just consider:$$thetamapstoleft(costheta+frac{cos(8theta)}8,sintheta,0right).$$
– José Carlos Santos
8 mins ago
add a comment |
It's exactly what I wanted, thank you! Could you tell me how you managed to understand it?
– TeM
29 mins ago
2
The $z$ coordinate had to be a waving line again, and so I thought about $cos(8theta)$, but then the waves would go too high and too low. That's why I divided by $8$.
– José Carlos Santos
25 mins ago
Perfect! Before closing I also wanted to ask how to get the parametric equations of the red curve if it lay in the $z = 0$ plane. Is it better that I open a new question or change the request?
– TeM
15 mins ago
No need for that. Just consider:$$thetamapstoleft(costheta+frac{cos(8theta)}8,sintheta,0right).$$
– José Carlos Santos
8 mins ago
It's exactly what I wanted, thank you! Could you tell me how you managed to understand it?
– TeM
29 mins ago
It's exactly what I wanted, thank you! Could you tell me how you managed to understand it?
– TeM
29 mins ago
2
2
The $z$ coordinate had to be a waving line again, and so I thought about $cos(8theta)$, but then the waves would go too high and too low. That's why I divided by $8$.
– José Carlos Santos
25 mins ago
The $z$ coordinate had to be a waving line again, and so I thought about $cos(8theta)$, but then the waves would go too high and too low. That's why I divided by $8$.
– José Carlos Santos
25 mins ago
Perfect! Before closing I also wanted to ask how to get the parametric equations of the red curve if it lay in the $z = 0$ plane. Is it better that I open a new question or change the request?
– TeM
15 mins ago
Perfect! Before closing I also wanted to ask how to get the parametric equations of the red curve if it lay in the $z = 0$ plane. Is it better that I open a new question or change the request?
– TeM
15 mins ago
No need for that. Just consider:$$thetamapstoleft(costheta+frac{cos(8theta)}8,sintheta,0right).$$
– José Carlos Santos
8 mins ago
No need for that. Just consider:$$thetamapstoleft(costheta+frac{cos(8theta)}8,sintheta,0right).$$
– José Carlos Santos
8 mins ago
add a comment |
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1
It looks like a curve of the form $$ r(theta) = r_0 + A cos{(omega theta )} $$ But it's not very clear what you mean with the hand-drawn curve. Is it supposed to come out of the $z=0$-plane?
– Matti P.
57 mins ago
1
@MattiP.: Yes, it must exit the $z = 0$ plane and have the circumference as the average line.
– TeM
36 mins ago