26
votes
Symbolic area calculation for a parametric self-intersecting closed curve
The plan is first get the "external" contour and then use Green's theorem to find its area.
...
20
votes
Accepted
How to add a fading trail effect in Animate?
ColorFunction and Epilog were around in version 7. However, ColorFunction did get an update ...
18
votes
Accepted
Finding a parametric curve fitting a two-dimensional dataset
A least squares approach:
model = a/((x - x01)^2 + c y^2) + a/((x - x02)^2 + c y^2)
$
\frac{a}{c y^2+(x-\text{x01})^2}+\frac{a}{c y^2+(x-\text{x02})^2}
$
If we ...
16
votes
Accepted
Plot a function for different parameters
You can use Table for this:
Plot[Evaluate@Table[f[a, b, 2, 3], {b, 0, 5, 1}], {a, 0, 1}]
And you can also put there multiple ...
16
votes
Accepted
return {} when the function is given {}
Actually, I want the output to be {} if there is anything wrong with the argument.
For this I recommend one or more definitions with patterns that only match a valid argument, and a fall-through ...
14
votes
Accepted
Solving the Frenet Serret equations for non-constant curvature and torsion, obtaining parametric equations
Okay, this'll be a short answer just to show what you can do. What you are trying for here is essentially an inverse to FrenetSerretSystem, which will give the ...
13
votes
Accepted
My 3D plot of a Klein bottle doesn't look right
Here's my slight simplification of the Klein bottle parametric equations. I believe the original parametrization is due to Stewart Dickson (whose depiction of the bottle was in the "Graphics Gallery" ...
13
votes
Accepted
Finding the Period of a Limit Cycle
Although it's primarily designed for ecological models, my EcoEvo package can help. First, you need to install it with
...
12
votes
Find eigen energies of time-independent Schrödinger equation
As in version 10.2, there is the NDEigensystem can be used to calculate the eigenstates and eigenvalues of a differential operator.
For example in the harmonic ...
12
votes
Accepted
How do I plot a parametric family of curves given a list of parameter values?
There are a number of ways to do this, e.g.:
...
12
votes
Logarithmic scale in an ParametricPlot obtained from ODE boundary conditions
You can use ScalingFunctions. It appears in red but works.
...
12
votes
Fitting experimental data by using ParametricNDSolveValue and NonlinearModelFit
A minor change to model eliminates the error cited in the question. (Replace s[t] by s in ...
12
votes
Accepted
How to draw a 3D point moving along a helical path?
You can add a moving point using a combination of options MeshFunctions, Mesh, and Method as ...
11
votes
Parametric plot on multi-dimensional domain
Method 1: unconstrained regions
You can easily do it with regions:
...
11
votes
Accepted
Continuously varying tube radius
You can take a continuous function and evaluate it at the same points that are also used by ParametricPlot3D to create the curve. Here is a way to do it:
...
11
votes
Accepted
11
votes
Accepted
Is Mathematica capable of converting parametric equations into a function? If so, how?
I suspect that there simply isn't a nice equation of the form $y = f(x)$ for these curves. As you note the equation for $x_d$ involves both algebraic and trigonometric terms, and almost all such ...
11
votes
Accepted
Finding "nice" solution for under-determined system with constraint?
If I understand the question correctly, you wish to obtain a parameterized solution {U2[U1], W2[W1]} from the equation in the question, so that you can vary that ...
11
votes
Accepted
11
votes
Accepted
Calculate Radius of Curvature
Curvature of a parabola depends on the position. To find curvature at the maximum point do
ArcCurvature[{t,fit[t]},t]/.Maximize[fit[t],t][[2]]
(*0.0170112*)
11
votes
Finding the Period of a Limit Cycle
Here is a simple approach to get the period of the unknown limit cycle.
The idea is to approximate the limitcycle by a circle (1st harmonic) around the mean of the limitcycle:
solution ...
11
votes
11
votes
2D cross-section of ParametricPlot3D
We can use the MeshFunctions options and extract the slice data accordingly.
...
10
votes
Accepted
A problem about the implementation of Bezier curve
I have reworked your code somewhat. I hope what I have done will help you with your problem.
...
10
votes
Accepted
Solve stiff system by shooting method
The goal of this question, I believe, is selecting Φ[r0] so that the solution connects smoothly to the asymptotic solution at large ...
10
votes
9
votes
Accepted
A parametrization for $\frac{\sin(x)}{x}$ as a revolution surface around $y$ axis
Perhaps something like this. Just rotate the original function about the z-axis directly:
...
9
votes
My 3D plot of a Klein bottle doesn't look right
Description
For fun, thought I give it a try. Below is an example of my attempt to Plot Kleins bottle.
Code
...
9
votes
How to plot Compressibility factor Z vs Pressure P using ParametricPlot?
The plot you were trying to reproduce is a plot of the reduced van der Waals equation; that is, it is using the reduced pressure $P_r=\frac{P}{P_c}$ and reduced temperature $T_r=\frac{T}{T_c}$ as the ...
9
votes
Issue Plotting Torus Link
Here's I think a generalization of what Ulrich gave to an arbitrary $(p, q)$ torus (if I read Wikipedia right):
...
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