Questions about explicit functions expressed in terms of independent variables, i.e. parameters. Including approaches for rewriting functions using different parameterizations.

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0
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0answers
25 views

How do I change a 3d bspline curve to a polygon based graphic?

I have a graphics image generated with bsplines: Graphics3D[Tube[BSplineCurve[pts], 2]] I want to export this to a .stl file. To do so I know I need to modify ...
6
votes
1answer
127 views
+100

Is it possible to speed up the user-defined function CAGDBezierSurface?

For given control net of points $P_{i,j}, \quad i=0,2, \cdots m, \quad j=0,2,\cdots, n$,the Bézier surface is defined by the following equation: ...
9
votes
2answers
321 views

A problem about the implementation of Bezier curve

I implemented the Bezier curve like built-in BezierCurve as follow: SplineDegree -> d specifies that the underlying ...
3
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1answer
86 views

How to change parameters to equations of physical properties they belong to in an equation?

First off, I want to apologize for my poor English as I am not a native speaker. In my physics research, I had to solve a system of equations, from which I would get a solution for the speed of an ...
-2
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1answer
40 views

Plot the result of NIntegrate for different parameter values

I want to plot the result of a numerical integration containing a parameter in terms of the parameter. The code is: ...
0
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0answers
37 views

How to solve algebra equations containing integration and parameters?

I'm trying to solve two nonlinear algebra equations for two unknown parameters, U and Tf. Since some terms in these equations contain integration, and the integration also contains U and Tf. The main ...
1
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2answers
215 views

Plotting a parametric function containing an integral [closed]

I need to plot this expression $$ \phi(s; H,B)=\left(\int_{0}^{s}\frac{1+B\ \sin2H\ t}{\sqrt{1+B^2+2B\sin2H\ t}} \text{d} t,\ \frac{1}{2H}\sqrt{1+B^2+2B\sin2H\ s}\right)$$ for $H=0.5$, $B=0, 0.5, 1, ...
1
vote
1answer
62 views

Adding a fading color only to 3D curves going outside a cylinder

I'm having a problem with color shades on multi curves drawn with the Mathematica 7.0 code below. All the curves with both their endpoints inside the unit cylinder (green circle on the picture below) ...
1
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1answer
62 views

Adding a fading color to multiple lines in 3D

I would like to add a fading color to all the 3D lines I'm drawing with the code below, but I'm having difficulties with implementing the idea. The curves are starting on a unit sphere, and extend in ...
6
votes
1answer
302 views

Dipolar magnetic field lines inside a cylinder

I'm drawing the magnetic field lines of a rotating dipole (magnetic field distorded by emission of radiation). Currently, my Mathematica 7.0 code is fully working, but I'm having a constraint which I ...
0
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1answer
55 views

Colors on a 3D curve not working

I'm having troubles applying colors to a simple 3D curve plot. Here's the code : ...
14
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2answers
379 views

Symbolic area calculation for a parametric self-intersecting closed curve

The parametric equation of the curve is: $$\begin{cases} x &= -9 \sin (2 t)-5 \sin (3 t) \\[6pt] y & = 9 \cos (2 t)-5 \cos (3 t) \end{cases}\quad t\in[0,2\pi]$$ which can be easily ...
4
votes
2answers
162 views

How to obtain the area enclosed by such a curve?

The desired curve is defined as curve02 below : ...
4
votes
1answer
253 views

Using ParametricNDSolve and NMinimize to find accurate interplanetary trajectory arrival periapse radius

I have an interplanetary trajectory simulation that calculates the required velocity (using a Lambert solver) and escape angle for a spacecraft to travel from Earth to Mars. This model does not use a ...
6
votes
1answer
115 views

ParametricNDSolve[ ] and NMinimize[ ] in Combination

I have the following code that is used to simulate a spacecraft orbiting Mars, and uses ParametricNDSolve to vary the spacecraft's initial conditions using a parameter value ...
0
votes
3answers
75 views

Confusing “Part::pspec” and “Part::partw” following call to ParametricPlot3D

The problem I'm having is that the function definition given below continually gives me baffling error messages. I'm trying to turn a list of 3D points into a function that approximates a curve by ...
2
votes
1answer
98 views

Minkowski sum and product of 2D-regions

Let $A_j$, $j=1,\dots,n$ be subsets of $\mathbb C$ defined by $$ A_j=\{z\,|\,f_j(z)\geq0\} $$ where $f_j:\mathbb C\to\mathbb R$ are given functions. I am interested in the following subsets of ...
0
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0answers
38 views

ParametricNDSolve of differential equation with singularity

I have a differential equation I would like to solve with the ParametricNDSolve. However, the coefficients in the differential equation are singular at a certain value, so sometimes NDSolve crashes ...
5
votes
3answers
191 views

Finding the conditions for degenerate solutions to a cubic equation

I have a cubic equation (corresponding to the band structure of a physical system) given by w in the code below. ...
1
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1answer
72 views

How to convert a rational parametric plane curve into implicit form?

This problem is generated from another Green's theorem related question of mine. And here is a forward of the same problem in math.stackexchange. The original equation of the plane curve is not in ...
2
votes
0answers
51 views

ParametricNDSolveValue has a problem with complex numbers

Edited: I have simplified the example compared to before and narrowed the problem down a bit. I would like to use ParametricNDSolveValue as function for data ...
0
votes
2answers
68 views

Create a moving plot along a parametric plot using Manipulate?

I have been looking through Manipulate examples and haven't been able to create a working plot yet. I have a parametric plot defined: ...
0
votes
1answer
83 views

KdV equation - wavebreaking and Galerkin method

I want to show how a wave given by the initial condition: $$ \begin{equation*} \begin{split} u(x, 0) = \left\{\def\arraystretch{1.2}% \begin{array}{@{}c@{\quad}l@{}} 1 - x^2 & \text{for ...
4
votes
1answer
96 views

Substituting ParametricNDSolve for NDSolve

This is my first post so let me know if I need to format things differently. I have been using NDSolve for most problems which optimize parameters for ODEs. I believe that ParametricNDSolve would be ...
0
votes
1answer
80 views

Functions behaving weirdly

The following code f[k_, n_] := Sum[2*(1 + Sum[f[k - j, n - m - j], {j, 1, k - 1}]), {m, 1, n - k + 1}] f[4, 7] f[4, n] gives the output: ...
1
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1answer
54 views

Change input parameter order in a function

I'm a beginner in Mathematica programming and I'm trying to understand how input parameters work in Mathematica's function. I encountered a problem with the sequence/order of the input parameters of ...
5
votes
1answer
154 views

Fitting a Parametric Curve

I apologize if this question is obvious or simple. I'm in high school and have started playing around with Mathematica only recently. For my Calculus Final, I am supposed to use rotation about the ...
5
votes
1answer
119 views

How to fill the closed region by ParametricPlot with solid color?

I am interested in the following implicit curve with parametric equation: $$ \left\{\quad \begin{array}{rl} x=& 9 \sin 2 t+5 \sin 3 t \\ y=& 9 \cos 2 t-5 \cos 3 t \\ \end{array} \right. $$ ...
2
votes
1answer
47 views

How to plot points using ParametricPlot3D?

I have the following Mathematica code: ParametricPlot3D[{{0 + 0*t, 10 - 1*t, 9 - 1*t}, {7 - t, 7 - t, 6 - t}, {0, 0, -1}}, {t, 12, -20}] The last "parametric ...
1
vote
1answer
45 views

Multiplying two parametric solutions

I'm solving two (1-parameter) differential equations and I want to plot the product of their solutions, how do I do this? Here's the code, ...
3
votes
3answers
309 views

Finding intersections of two parametric curves

I am dealing with the root finding of two parametric data curves (data below). I have already checked Parametric Interpolation of 2D data, which I found useful for plotting, though it is not adequate ...
-2
votes
1answer
64 views

Sign of a symbolic expression as a function of parameter values

I need to know the sign of the following expression for p[t] = z/(1-a), as a function of the parameters {a, b, c, z}: ...
1
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2answers
92 views

Plot ParametricNDSolve

I am trying to plot the probability of a molecule being in a certain state via the numerical solution of the Schrödinger's equation of molecule in an oscillating electric field (in a rotating system). ...
0
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1answer
141 views

How to convert a system of parametric equations?

I have a system of parametric equations (t is a parameter) ...
0
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1answer
87 views

How to plot trajectory for a differential equation in polar coordinates? [duplicate]

I have a differential equation for dr/dt and d[Theta]/dt in terms of r and theta, and I am trying to plot the trajectory in the x-y plane for a given initial condition (r,theta). ...
1
vote
2answers
242 views

How to Fit experimental data with 4D ParametricNDSolve?

Let me first explain the background problem. I'm trying to solve a problem with a projectile motion in 4D such that the position vector is: $\boldsymbol{r}(t)=\boldsymbol{r}[x(t),y(t),z(t)]$ I have ...
8
votes
3answers
221 views

How to combine ParametricPlot and RegionPlot?

I have two implicitly defined equations. I plot the implicit curve using parametric plot. ...
4
votes
1answer
139 views

ParametricPlot3D of Boy's surface

I'm trying to visualize Boy's surface using Bryant's parametrization, as per the MathWorld article. However, I'm not sure I understand the parametrization, and I don't know how to implement it when ...
0
votes
1answer
77 views

Plot curves like equation problems

I'm proving to plot and edit some wolfram alpha laminae, but when I try it, I don't have any result, for example: (from:http://blog.wolframalpha.com/data/uploads/2013/07/Curvespt31.cdf) ...
-2
votes
1answer
56 views

Solve on parametric equation produces inequal results

I have a parametric (parameter t) equation in two dimensions (vectors). s = Solve[pt[t] == qt[t], {a, b}] Both pt and qt are parametric lines using a and b as ...
0
votes
1answer
45 views

Error Exporting STL --insufficient elements to export

I am trying to export the following code as an STL file: ...
0
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1answer
58 views

Unable to Solve (for arclength parametrization)

I am having trouble with Mathematica while trying to re-parametrize a curve with respect to its arclength. I need to get the old parameter s written in terms of arclength a so the code is ...
0
votes
0answers
44 views

Formating in Mathematica 10 Find the point of intersection of a plane

Hi all i am new here and i am trying to figure out how to correctly format in Mathematica 10...Finding the point of intersection of a line to a plane. I know how to do it by hand. 1) Find the ...
1
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1answer
90 views

Plot a parametric equation in cylindrical coordinates

I'm looking for a way to plot this parametric equation on cylindrical coordinates. r = e^t theta = t+1 z = e^2t Any help would be appreciated
2
votes
2answers
81 views

Why is there always a horizontal tail line on the parametric curve?

I am trying to create a smooth, piecewisely continuous and differentiable curve by using Mathematica's Floor function, which is as in: ...
1
vote
1answer
130 views

Eliminating parameter from parametric equation [closed]

In Mathematica Online I tried: Eliminate[{x == t + t^3, y == t - t^3, z == 1 + t^4}, {t}] ...
0
votes
0answers
68 views

ParametricPlot3D doesn't work with components of a vector input

I can't understand why ParametricPlot3D works, when the input is a vector and does not work, when the input is separated components of the vector (it returns an empty plot). The same happens for ...
0
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1answer
51 views

What's wrong with the code?

The following code doesn´t fill the base of the picture. ¿Why? ...