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.
...
- 115k
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 ...
- 41.5k
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 ...
- 6,831
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 ...
- 3,847
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 ...
- 269k
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 ...
- 67k
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" ...
- 123k
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
...
- 19.3k
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 ...
- 27.4k
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.:
...
- 58.3k
12
votes
Logarithmic scale in an ParametricPlot obtained from ODE boundary conditions
You can use ScalingFunctions. It appears in red but works.
...
- 15.8k
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 ...
- 60.4k
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 ...
- 377k
11
votes
Parametric plot on multi-dimensional domain
Method 1: unconstrained regions
You can easily do it with regions:
...
- 43.5k
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:
...
- 96.6k
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 ...
- 14.8k
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 ...
- 60.4k
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*)
- 17.5k
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 ...
- 47.2k
11
votes
11
votes
2D cross-section of ParametricPlot3D
We can use the MeshFunctions options and extract the slice data accordingly.
...
- 35.2k
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.
...
- 107k
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 ...
- 60.4k
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:
...
- 22.7k
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
...
- 5,899
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 ...
- 123k
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):
...
- 46.6k
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