The parametric tag has no wiki summary.
5
votes
2answers
36 views
Parametrizing a given line and equations
1) Parametrizethe given line contraining the points (3,2) and (-5,6).
2) Find the parametric equations for the segment joining the given points (2,3) and (5,5) where $0\leq t \leq 1$.
...
0
votes
1answer
14 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 ...
0
votes
1answer
30 views
Find position on surface of a lens
If I have a lens with coordinates UV on the lens surface where U, V are [-1, 1] and I want to find the real-world (x,y,z) coordinates of the UV point, how would I do that if I have the following ...
0
votes
1answer
36 views
Shortest distance between a 3D parametric surface and a point
Right now I'm working on a library for finding the distances between objects in Lua. I've had some trouble finding the distance between a point and a bounded plane. I'm using these parametric ...
0
votes
1answer
31 views
parabola in homogeneous coordinates
So if I have the parabola Y = X^2, how do I go about representing this homogeneously? I know I can parameterize it as F(t) = (t, t^2), but then what?
The reason I ask is because I have a 3*3 matrix ...
0
votes
1answer
61 views
Converting parametric equations in a numerical equation
Is it possible convert this parametric equations in a numerical equation?
$$
\begin{cases}
\displaystyle x(t)=tv_0\cos(\theta)\\
\displaystyle y(t)=tv_0\sin(\theta)-\frac{1}{2}gt^2+h
\end{cases}
$$
...
0
votes
1answer
31 views
Represent sorting position by a parametric form
Given a set of random integers {0,5,100,65,...,0,1,2}, is there a mathematical method existing to construct a parametric form $f$ (the number of parameters $<<$ the number of integers) so that ...
0
votes
1answer
130 views
Is this valid parametric equation to create control points for a helix in 3D space?
Is this a valid way to compute new points that are on a helix and if not what is it wrong?
The Cartesian coordinates of each new helix control point could be described by the following ...
6
votes
0answers
54 views
Find a parametric formula to $n=(a^2+1)(b^2+1)$ in three distinct ways
I mentioned that the number $4420$ is expressible in the form $(a^2+1)(b^2+1)$ (where $a,b$ are positive integers) in three distinct ways,here is a list of these numbers:
...
2
votes
0answers
180 views
Parametrization of square to calculate Dot-product in line-integrals and area-integrals, electric field from $\frac{dB}{dt}$?
I am calculating 3A of Tfy-0.1064 in Aalto University. I realized here that I am misunderstanding something in vector calculus: the thing market in green particularly.
I know
$$\nabla\times E= ...
2
votes
0answers
388 views
Explain Triangle perimeter in polar coordinates
The question is to give a formula in $x$ and $y$ that gives all three sides of an equilateral triangle. The formula should not be true for points that are not part of the perimeter of the triangle. ...
1
vote
0answers
44 views
Tangent Vectors in a Surface
As of recent, I've been studying Differential Geometry per the Dover Publication on the subject, and I've ran into a bit of an issue with tangent vectors to a parametric surface $ \mathbf{x}(u^1,u^2) ...
1
vote
0answers
28 views
Vector Tangent to Curve of Intersection
I am having problems solving this.
Find a vector tangent to the curve of intersection of $z = 4x^2 + y^2$ and $z=(27-x^2-y^2)^{1/2}$ at the point $(1,1,5)$.
I'm able to do this kind of thing using ...
1
vote
0answers
35 views
$\frac{dy}{dx}$ of a parametric curve
Given $x = sin^2(t)$, $y = cos^2(t)$, I need to find $\frac{dy}{dx}$ in every non-singular point of the curve.
So $\frac{dy}{dt} = -2sin(t)cos(t)$ and $\frac{dx}{dt} = sin(2t)$.
To find the ...
1
vote
0answers
45 views
Computing the surface area of a (piecewise) polynomial parametric surface
I'm wondering what kind of numerical integration (e.g. Gauss-Legendre quadrature) I should use to compute the surface area of a (piecewise) polynomial parametric surface. There are two cases.
Case ...
1
vote
0answers
41 views
Maximum value for parameter
I am facing the following problem:
A number of a adults, b children older than 12, and c children younger than twelve attend an event. The sum of all people a+b+c=100. The prices are \$6 per adult, ...
1
vote
0answers
94 views
Distance between point and a spiral
I'm trying to work out an algorithm where, given the equation for a spiral in polar coordinates, $r(\theta)$, and a point rectilinear coordinates, $P(x,y)$, I can work out the minimum distance between ...
1
vote
0answers
128 views
Motion on a parametric surface
Please excuse what will surely turn into a long rambling question, full of incorrect terminology.
I'm trying to figure out the mathematics of moving on a parametric surface - that is, for some ...
1
vote
0answers
27 views
MLE estimation of parameters, converting normalized observations to integers and back
I am fitting a model's parameters to grouped data by maximizing the likelihood equation:
$L(\theta)=N!\prod_{i=1}^{G}\frac{p_i(\theta)^{n_i}}{n_i!}$
$\theta$ is the vector of parameters. $n_i$ is ...
0
votes
0answers
35 views
parametric equation derivative question: can someone help me understand this question?
I am given $x$ and $y$ coordinates in parametric form with equations...
$x(t)$ and $y(t)$.
The questions asks to calculate $f'(x)$ for when $x = x(2\pi/5)$.
Now am I first to calculate the ...
0
votes
0answers
13 views
Can one characterize which surfaces are capable of being described by a closed-form parameterization?
Speaking intuitively, I can visualize a lot of surfaces in my mind; but it seems that some of the ones I can imagine are not capable of being described by the 'usual suspects', i.e., elementary ...
0
votes
0answers
27 views
0
votes
0answers
47 views
Torus equation in terms of tangent
So if I have an equation for a torus in $F(a,b) = (X, Y, Z)$ where $X = (R + r\cos a)\cos b$ and $0 < r < R$, how would I go about rewriting this equation for $X$ in terms of $\tan(a/2)$ and ...
0
votes
0answers
79 views
Finding parametric equations
I am trying to understand volume and surface integrals. I do get the idea of the process (find a parametric equation of the volume/surface, integrate afterwards). But I just cannot make up parametric ...
0
votes
0answers
63 views
complex circular motion
Assume the planet orbits its star in a circular orbit of 100 units with period 360 days. The moon in turn orbits its planet at a radius of 10 units and period 28 days. Finally the moon rotating, we ...
0
votes
0answers
437 views
Converting standard equation for a paraboloid to a parametric one
I have the equation for a hyperbolic paraboloid in $x$, $y$, and $z$:
$$\frac{z}{c} = \frac{x^2}{a^2} + \frac{y^2}{b^2}$$
I also have the parametric equations for the same parabaloid:
$$x = a u ...
0
votes
0answers
251 views
Distance between two parametric curves
I have two parametric planar curves.
The curves are not self-intersecting.
Curve $C_0$ is inside $C_1$.
With $t \in [0..1]$
$ C_0:x = f_0(t); y = g_0(t) $
$ C_1:x = f_1(t); y = g_1(t) $
Now ...
-1
votes
0answers
24 views
Flux integrals, parameterization
let S be the cylinder x^2 + z^2 = 9 where -2 /ge y /le 2
parameterization: thi(u,v)= <3cosv, u, 3sinv> where -2 /ge y /le 2 and 0 /ge v /le 2pi
(thi is the symbol of I with the circle in the ...
