Questions tagged [simplex]

An n-dimensional simplex is a subspace of R^n with codimension 1, therefore n-1 coordinates are enough to represent any point on the simplex. A 2D simplex can be plotted as a ternary plot.

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Discretizing higher dimensional region (simplex)

I want to create an evenly distributed set of $N$ points inside a d-dimensional simplex ($d>3$), i.e. I want to have $N$ vectors $\vec{a}=\{a_1,a_2,...,a_d\}$ such that $0\leq a_j \leq 1$ for all $...
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Numeric integration and RegionDilation in higher dimensions

I would like to integrate over a dilationed region in higher dimensions. In 3 dimensions it works well. ...
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Simulation of a discrete pdf

I have 3 random variables (b,c,d) that capture a discrete pdf over 4 possible realizations. In every period, they evolve according to the random process described in the code below. I would like to ...
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3 votes
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Ternary Diagram: Plotting Lines, Areas, Conditions

I am trying to replicate the diagram below with grid lines, lines, areas, and labels (corners, coordinates, lines, and areas). The blue line can be characterized by a line between the points {0.5,0,0....
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Integrate of simple equation but is not solving!

I have this simple integral but I don't know why Mathematica can't solve it?! FullSimplify[Integrate[x/(-x^2 + a x + b)^(1/2), {x, Sqrt[b], Sqrt[R^2 + b]},Assumptions -> {a > 0, b > 0}]]
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Triangulation of Point Configuration

I was going through the documentation of Mathematica but couldn't find any built-in function that can find all possible triangulations for a given set of points. For example, if I have the following ...
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Computing possibles values (range) for an (polynomial) expression that takes values from two 2-simplex

Let $(p,q) \in \Delta_2$ and $(k,m) \in \Delta_2$, where $\Delta_2$ is the 2-simplex, that is, $0\leq p\leq 1$, $0\leq q\leq 1$, and $0\leq 1-p-q\leq 1$. Consider the expression ...
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Plotting maxima within a simplex

I am trying to draw a particular maximum plot within a simplex. I have functions based on two variables: Write p,q for the two variables where p,q \geq 0 and p + q \leq 1. This defines the simplex ...
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Split $n$-dimensional prism into simplices

Are there standard geometry or graph functions that allow to, say, construct a $n$-dimensional prism by it's $(n-1)D$ base and height and split it into simplices (without creating new points)? Extra ...
Vsevolod A.'s user avatar
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Test regularity of Simplex

A simplex is regular if its all edges have the same length. How to test in Mathematica whether a Simplex is regular or not, without checking all the edges manually?...
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Plot a trajectory in a simplex [duplicate]

I would like to plot the make-up of a population over time as it changes its composition. For this, I'd like to make a simplex plot, a classic method in some fields - such as this example from a paper ...
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Plotting a manifold within an existing surface

I have a dynamical system $\textbf{x}'=\textbf{f(x)}$ where $x\in \mathbb{R}^4$. However, $x_1 +x_2 +x_3 + x_4 =1$ and $0\leq x_i \leq 1$ for $i = 1,2,3,4$, meaning the system lives on the Tetrahedron....
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region plot in a 2-simplex

I want to plot a 2-dimensional region with constraint $x+y\le N$, i.e., I want to plot a sub-region inside a 2-simplex. As an example: ...
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Manipulate Controller - Simplex

Imagine you have three numbers a, b and c, and using ...
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Plot in a 2-dimensional simplex

I have a row vector as $P=(p_1,p_2,p_3)$ which should be obtained from the following constraints: $a_1p_1 + a_2p_2 + a_3p_3 = b_1p_1 + b_2p_2 + b_3p_3$ ($a_i$'s and $b_i$'s are known) $p_1 + p_2 + ...
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How to plot ternary density plots?

How can I get a ternary density plot just like the plots from OriginLab? ContourPlot and DensityPlot seemingly can accept the <...
Scott Wang's user avatar
6 votes
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Generate regularly spaced points from the surface of simplexes

I need to generate regularly spaced samples (points) from the surface of unit simplexes with 2 or greater vertices or end points. I can generate random samples pretty straightforwardly: ...
Jagra's user avatar
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12 votes
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How to plot a barycentric line

I want to plot a barycentric function on an equilateral triangle (ternary plot). For example f1 = {Abs[Sin[x]], Mod[x, 2], Abs[Cos[x]]}; At the moment I evaluate ...
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