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. ...
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19 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 ...
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  • 39.3k
18 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 ...
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  • 5,776
16 votes
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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 ...
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  • 3,807
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 ...
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  • 264k
14 votes
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How to create these famous surfaces in topology with the desired color effects?

Concerning the comment about creating the surfaces, sure: Mathematica is one of the best tools available for that. Here's the Klein bottle, for example. ...
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  • 8,342
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 ...
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13 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" ...
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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 ...
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  • 17.6k
12 votes

How to create these famous surfaces in topology with the desired color effects?

I just finished blog post about the creation of nice graphics from Mathematica Graphics3D using the Blender render framework: http://wolfig-techblog.blogspot.de/2015/04/blender-as-shader-for-...
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  • 323
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 ...
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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.: ...
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  • 55k
12 votes

Logarithmic scale in an ParametricPlot obtained from ODE boundary conditions

You can use ScalingFunctions. It appears in red but works. ...
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  • 15.5k
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 ...
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  • 58.2k
11 votes
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Oval or Bunimovich stadium

My defined function next find {nextpoint, nextdirection} value from ...
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  • 5,085
11 votes

How to combine ParametricPlot and RegionPlot?

Probably this match your plot: ...
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11 votes
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How to fill the closed region by ParametricPlot with solid color?

...
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  • 349k
11 votes

Parametric plot on multi-dimensional domain

Method 1: unconstrained regions You can easily do it with regions: ...
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  • 42.8k
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: ...
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  • 95k
11 votes
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Plotting the image of a curve under a flow

...
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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 ...
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  • 58.2k
11 votes
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Shading the surface of the 3D plot

Perhaps, this is what you had in mind. ...
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  • 58.2k
11 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 ...
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  • 349k
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*)
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  • 15.7k
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 ...
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10 votes

Spherical parametric plot

If you have version 9+ you can use: ...
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  • 10.6k
10 votes

Spherical parametric plot

covert your spherical parametrized curve into cartesian parametrized curve with formulas: $$\begin{cases} x&=r\sin\theta\cos\varphi\\ y&=r\sin\theta\sin\varphi\\ z&=r\cos\theta \end{cases}...
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  • 2,788
10 votes
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How to combine ParametricPlot and RegionPlot?

To fill with a solid color, you can post-process the Line primitive into a Polygon ...
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  • 349k
10 votes

Fitting a Parametric Curve

Your data is appended at the end this answer. Setting up (parametrizing your curve): ...
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  • 55k
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. ...
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