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.
...
- 114k
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 ...
- 39.3k
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 ...
- 5,776
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 ...
- 3,807
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 ...
- 264k
14
votes
Accepted
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.
...
- 8,342
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 ...
- 62.4k
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
...
- 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-...
- 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 ...
- 26.8k
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.:
...
- 55k
12
votes
Logarithmic scale in an ParametricPlot obtained from ODE boundary conditions
You can use ScalingFunctions. It appears in red but works.
...
- 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 ...
- 58.2k
11
votes
Accepted
Oval or Bunimovich stadium
My defined function next find {nextpoint, nextdirection} value from ...
- 5,085
11
votes
11
votes
Accepted
11
votes
Parametric plot on multi-dimensional domain
Method 1: unconstrained regions
You can easily do it with regions:
...
- 42.8k
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:
...
- 95k
11
votes
Accepted
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 ...
- 58.2k
11
votes
Accepted
11
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 ...
- 349k
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*)
- 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 ...
- 36.3k
10
votes
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}...
- 2,788
10
votes
Accepted
How to combine ParametricPlot and RegionPlot?
To fill with a solid color, you can post-process the Line primitive into a Polygon
...
- 349k
10
votes
Fitting a Parametric Curve
Your data is appended at the end this answer.
Setting up (parametrizing your curve):
...
- 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.
...
- 106k
Only top scored, non community-wiki answers of a minimum length are eligible