20 votes
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How to add a fading trail effect in Animate?

ColorFunction and Epilog were around in version 7. However, ColorFunction did get an update ...
Edmund's user avatar
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20 votes
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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 ...
MelaGo's user avatar
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16 votes
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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 ...
Mr.Wizard's user avatar
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14 votes
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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 ...
Jason B.'s user avatar
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14 votes
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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" ...
J. M.'s eventual burnout's user avatar
13 votes

Logarithmic scale in an ParametricPlot obtained from ODE boundary conditions

You can use ScalingFunctions. It appears in red but works. ...
Sumit's user avatar
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13 votes
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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 ...
Chris K's user avatar
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12 votes
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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.: ...
ubpdqn's user avatar
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12 votes
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Plotting the image of a curve under a flow

...
Dr. belisarius's user avatar
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 ...
bbgodfrey's user avatar
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12 votes
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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 ...
kglr's user avatar
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12 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 ...
Ulrich Neumann's user avatar
11 votes
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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: ...
Jens's user avatar
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11 votes
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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 ...
Michael Seifert's user avatar
11 votes
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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 ...
bbgodfrey's user avatar
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11 votes
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Shading the surface of the 3D plot

Perhaps, this is what you had in mind. ...
bbgodfrey's user avatar
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11 votes
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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*)
yarchik's user avatar
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11 votes

Obtaining the curve parallel to the function a/(x^2+b)

Use FrenetSerretSystem. ...
cvgmt's user avatar
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11 votes

2D cross-section of ParametricPlot3D

We can use the MeshFunctions options and extract the slice data accordingly. ...
Greg Hurst's user avatar
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10 votes

Plotting Limit Cycle

Hopf bifurcation analysis The differential system: ...
E. Chan-López's user avatar
10 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 ...
e.doroskevic's user avatar
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9 votes
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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: ...
march's user avatar
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9 votes

My 3D plot of a Klein bottle doesn't look right

This is just to give a solution based on minimal correction of the OP's code. ...
m_goldberg's user avatar
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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 ...
J. M.'s eventual burnout's user avatar
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): ...
b3m2a1's user avatar
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9 votes

How to visualize a 4-dimensional parametric surface?

A simple minded possibility is to use a perspective projection (similar to what I did here). Applied to the 4D Klein bottle, we have ...
J. M.'s eventual burnout's user avatar
9 votes

Solving a non-linear ODE system with ParametricNDSolveValue

This problem has a solution. It is given below ...
Alex Trounev's user avatar
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9 votes
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RevolutionPlot3D: get graphics primitives

Use Cases to extract the GraphicsComplex from the plot: ...
Jason B.'s user avatar
  • 68k
9 votes
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Solve can't solve my trigonometric equation—why?

Solve, NSolve as well as FindRoot can solve this equation, one should only remember several ...
Artes's user avatar
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9 votes
Accepted

Olympic Athletics Track

Here's my attempt without using formulae but using a StadiumShape discretization instead, mainly to show another way to do it for better performance: ...
flinty's user avatar
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