1
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1answer
64 views

Parametric equation of a circle given starting point.

Find the parametric equations of a circle with radius of $5$ where you start at point $(5,0)$ at $v=0$ and you travel clockwise with a period of $3$. So, I know that I require to have a $x(v)$ and ...
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1answer
44 views

x(u,v), y(u,v), z(u,v) parametric equations for a special cycloid

I'm trying to find out a 3d parametric equations for a cycloid I know that a cycloid is a 2d curve it is generated by a point on a rolling circle. but my circle is rolling around another circle both ...
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2answers
81 views

Paramtrizing a counterclockwise circle vs. a clockwise one

Does it make a different when you parametrize a counterclockwise full circle and a clockwise circle in the complex plane? For example, I am looking at computing an integral $\int_\gamma ...
0
votes
1answer
164 views

Intersection of a parametric curve and a circle

Given a curve defined by a parametric equation $x(t)$ and $y(t)$, how might one calculate the point of intersection with a circle? The derivatives $x'(t)$ and $y'(t)$ are also available if they prove ...
1
vote
1answer
64 views

Determine if a point is contained in the circle in 3d space

I have a problem where I need to determine if a point is contained in the area of a circle in 3d space. For my circle, I have the radius (R), the position of the center (C) and a normal vector to the ...
1
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3answers
213 views

Equation of a Circle from parametric functions of sin and cos

Given: x = 2 cos (t/2) y = 2 sin (t/2) How do we find the equation of the circle? I know that x^2 + y^2 = 1, where x = cos(t) y = sin(t) so x^2 = (2 cos (t/2))^2 y^2 = (2 sin (t/2))^2 How do ...
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votes
1answer
112 views

Circle wrapped on a cylinder

I'd like to know the parametric equations of a circle(r) wrapped on a cylinder(R). $x(t)= r\times cos(t)$ $y(t)=?$ $z(t)=?$ Which are the parametric equations? Thanks
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1answer
116 views

Ray Disk intersection

So if I have a ray parameterized as $O + tD$ where $O$ is the origin, $D$ is the direction and $t$ is the parameter variable and a flat circular disk with a center point $P$ in 3D space and a radius ...
4
votes
2answers
124 views

Circumference parametrization

Let $C=\{(x,y)\in \Bbb R^2: (x-x_0)^2+(y-y_0)^2=r^2\}$ and let $\varphi :[0,2\pi]\to \mathbb{R}^2$, $\theta \mapsto (x_o+r\cos \theta, y_0+r\sin \theta)$, with $r>0$. I'm trying to prove that ...
0
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1answer
169 views

equation for the region inside a circle

What equation or group of equations fill the entire or part of a region inside a circle without using inequalities? Update I don't know if this problem is already solved, I'm trying to find the ...
1
vote
2answers
251 views

A circle on the plane [duplicate]

Possible Duplicate: Parametric Equation of a Circle in 3D Space? I know that, for example, if a circle is on a plane with counter-clockwise orientation, and with center $(a,b)$ and radius ...
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5answers
14k views

Parametric Equation of a Circle in 3D Space?

So, my dilemma here is... I have an axis. This axis is given to me in the format of the slope of the axis in the x,y and z axes. I need to come up with a parametric equation of a circle. This circle ...