The parametric tag has no wiki summary.
5
votes
6answers
2k views
Is there an explicit form for cubic Bézier curves?
(See edits at the bottom)
I'm trying to use Bézier curves as an animation tool. Here's an image of what I'm talking about:
Basically, the value axis can represent anything that can be animated ...
5
votes
4answers
5k 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 ...
2
votes
4answers
409 views
Sketch a curve given parametrically by $x=2t-4t^3$ and $t^2-3t^4$
I am unable to see how to eliminate $t$. Wolfram Alpha fails at it too.
$$x=2t-4t^3$$ $$y=t^2-3t^4$$
I can guess that the curve is a polynomial equation so in principle I can write this as
$$w_1 ...
1
vote
1answer
378 views
Parametric Equation
Let $P_1$ be the plane through the origin containing the vectors $[1,2,-1]$ and $[0,1,1]$. Let $P_2$ be the plane through the point $(1,1,1)$ parallel to the vectors $[-1,2,2]$ and $[3,4,-2]$
I know ...
1
vote
3answers
111 views
How do we prove that two parametric equations are drawing the same thing?
For example, if I have
$$\begin {align}
x(t) &= r\sin t\cos t\\
y(t) &= r\sin^2 t\\
\end {align}$$
and
$$\begin {align}
x(t) &= \frac r 2 \cos t\\
y(t) &= \frac r 2 (\sin t + 1)
...
1
vote
1answer
269 views
parameterization of helical torus
A Helix is parameterized as $\langle R \cos(t), R \sin(t), \alpha t\rangle$ and one can visualize it as "wrapping" around a cylinder of radius R. I would like to accomplish the same thing but wrapping ...
1
vote
1answer
224 views
Solving Parametric Equation: Multiple coefficients of trigonomic functions
How can I solve:
$
x = 16 \sin^3(t) \\
y = 13\cos(t) - 5\cos(2t) - 2\cos(3t) - \cos(4t)
$
I've derived $t = arcsin(\frac{x^\frac{1}{3}}{16^\frac{1}{3}})$ from the first equation but I am still unsure ...
