Questions on the application of Mathematica to geometric problems. You might also consider adding the [graphics] tag, if appropriate.

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2
votes
2answers
77 views

Controlling PointSize in a RegionPlot

I have a "named" point in Mathematica 10 and am plotting it like this using RegionPlot: ...
-1
votes
1answer
48 views

Labeling named point in Mathematica 10 [on hold]

I have a "named" point in Mathematica 10 defined like this: point["camp location"] = Point[{latitude, longitude}]; I assume there is some way to make the name of ...
0
votes
1answer
101 views

How to construct new geometrical shapes in Mathematica?

In this question of mine I asked for how to implement a 2D random walk within a bounded area. In the provided solution one can use Rectangle[{-10, -10}, {10, 10}] ...
11
votes
2answers
427 views

Fitting ellipse to 5 given points on the plane

Five points are required to define a unique ellipse. An ellipse has five degrees of freedom: the $x$ and $y$ coordinates of each focus, and the sum of the distance from each focus to a point on the ...
10
votes
3answers
545 views

Finding the surface area of a 3D convex hull

I have noted several instances here and here where ConvexHullMesh, introduced in v10 has been used to greatly simplify some geometry problems. Determining the ...
27
votes
6answers
1k views

Finding length of intersection of two surfaces

I would like to know how we find the length of the intersection of two surfaces. For instance, in the following example,a surface intersects with a plane: How do we find the length of intersection ...
0
votes
0answers
28 views

DelaunayTriangulation in Mathematica V 7.01.0 [duplicate]

I have a list of 2D point coordinates in the form of {...,{xi,yi},...} and want to make a triangular mesh for it. By using DelaunayTriangulate function in Mathematica V7, it gives me something that ...
10
votes
4answers
701 views

To inscribe a circle in a given triangle

I am trying to to inscribe a circle in a given triangle but it isn't working. I've used GeoGebra with this construction and worked but as I'm new to Mathematica I am missing something. It can't be so ...
17
votes
0answers
437 views

Proving the hairy ball theorem using xAct

I would like to formally prove the hairy ball theorem in Mathematica, initially just for $S^2$, and then see about generalizing. An approach I thought about to use the xAct package to define $S^2$ ...
22
votes
5answers
2k views

2D random walk within a bounded area

I want to simulate a random walk on two dimension in a bounded area such as a square or circle. I am thinking of using If statement to define a boundary. Is there a ...
1
vote
1answer
125 views

Is it necessary to introduce ImplicitRegion and ParametricRegion in version 10?

In version 10.0, Mathematica introduced a new function about region plotting: ImplicitRegion. But I'm wondered that haven't this function been already existed in the older version? That is, ...
3
votes
1answer
89 views

xCoba: evaluate tensor quantities, given an explicit metric

I am new to xAct packages and I'm having some problems to compute tensor quantities with xCoba. I defined a manifold and a metric. I computed All quantities of ...
5
votes
1answer
174 views

How to generate nonperiodic tilings?

I need to generate nonperiodic tilings which are similar to the attached figure (kite-domino tiling). I was thinking the code is similar to the code for the Penrose tiling. However, that code is too ...
4
votes
1answer
139 views

Construct a function that can generate a geometry by extruding a section

Toady I want to construct a geometry shown as below: I know the Mathematica has the functions like Cylinder, Sphere and so ...
1
vote
1answer
112 views

Generating and plotting hypocycloids [closed]

Hypocycloids are curves generated by following a fixed point on a smaller circle rolling around the inside of a larger circle. The following code is from the recent book of P. Wellin (with modified ...
2
votes
0answers
66 views

VoronoiMesh for 3D points

I believe that this is a doc error in V10 (this was programmed to be but not implemented). The new VoronoiMesh should work for 3D set of points. The ...
1
vote
0answers
75 views

Death of parallel sub-kernels

EDIT : Finally, the new Mathematica 10.0 seems to fix it. I have a little parallelization problem. I wrote a code to generate a quasicrystal by dynamical generation. Here the code: ...
3
votes
1answer
74 views

Symbolic Output after numerical computation

I have a small question about the symbolic output. I started to write a program that generates the coordinates of n-dimensional polytopes by Wythoff construction. For crystallographic groups, all is ...
1
vote
1answer
84 views

how to find iso-cost contours on a 2d plot efficiently

Consider a 2D plot in which dimension 1 and 2 represent quantity 1 and 2 respectively ranging over 0 to 100. Each point in the space corresponding to (x,y) represent cost of choosing quantity 1 as x ...
3
votes
1answer
233 views

How to map vertex points from the surface of a straight pipe onto 2D plane

How to map vertex points from the surface of a straight pipe onto 2D plane. The 3D surface points of the straight pipe can be found here: data Working code: ...
0
votes
1answer
74 views

How do I show cross sections of a basic shape using calculus? [closed]

Assume I have an object whose radius is modeled by the function $x^2$. Using calculus and circular cross-sections, the object's volume is given by $\pi\int_a^b(x^2)^2dx$. But given an arbitrary ...
1
vote
1answer
123 views

Generate a set of 3D coordinates subject to constraints

Generating a set of random 3D coordinates is ok, e.g. ...
11
votes
2answers
607 views

Rebuild a polygon so it doesn't self intersect

If you consider the following Polygon: ...
0
votes
1answer
114 views

Height average between 4 points

I have a $3D$ space, if I had a square in this space: square = {{ 0, 0, 100}, { 100, 100, 50}, { 0, 100, 22}, { 100, 0, 86}}; how could I get the average height ...
6
votes
2answers
610 views

Distribution of 10 points within a unit square

Related to some packing problems, following problem arose: Distribute 10 points within a square of sides 1, so that minimal distance between them is maximized. With the help of random simulation, or ...
0
votes
0answers
106 views
17
votes
3answers
551 views

Creating sculptural forms using graphics primitives

This is a question based on this answer by halirutan. Some amazing images can be created with this code, and I was wondering whether it was possible to extend the principle to different shapes. I ...
3
votes
2answers
337 views

Intersection of surface with parallel planes

Consider the code (adapted from here) ...
0
votes
1answer
184 views

Area of a convex polygon with a set of points [duplicate]

I have a set of points Pts[a_,b_,c_]:={{a, b}, {b, a}, {c, a}, {a, c}, {b, c}, {c, b}} which define a convex polygon and I would like to find its area. There is ...
5
votes
6answers
321 views

Choosing $n$ equidistant points on a circle with given radius and center

I would like to have a function circle which takes two inputs: a tuple {x,y} and a real number ...
1
vote
1answer
144 views

How to get the dimensions of a rectangle?

Suppose I create a Rectangle of dimensions 1 and 3. Is there any function in Mathematica that I can use to recover the dimensions of the original rectangle? If there is no such a function, is there a ...
2
votes
0answers
232 views

Visualising Special Relativity

Mathematica newbie learning by doing (or not so far, in this case). Problem: Special Relativity - consider two inertial frames $A$ & $A'$ in relative motion. At a time $t0$ as measured in $S$, ...
1
vote
0answers
100 views

Extract coefficients of differential form in package RGTC

I am using the Package RGTC to do some calculations in Supergravity. It allows to define differential forms after specifying a co-frame. I am working in with the 10d coordinates ...
9
votes
2answers
259 views

Counting and extracting hit circles/triangles for randomly chosen points

Below, you see a triangle in which the incircle was inscribed. As we know, the center of this circle is the intersection of the angle bisectors. At this point, one could go further and find the ...
1
vote
1answer
350 views

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 + ...
23
votes
5answers
993 views

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 solve the ...
1
vote
1answer
130 views

Return “true” if point is in Convex Hull [duplicate]

I have a set of points Z: Z = {{x1,y1},{x2,y2},..,} I would like to obtain a function that returns ...
4
votes
1answer
195 views

Plot a cone in spherical co-ordinates

As we all know in spherical coordinates a function phi = π/3 gives us a cone. The cone makes an angle of π/3 with the imagined ...
6
votes
1answer
310 views

Imposing a Periodic Boundary Condition in Nearest Neighbour Search

I am trying to find first nearest neighbour distributions of randomly dispersed point-like objects in an infinite system. To do this I make a finite sized box unit cell with a chosen concentration of ...
9
votes
1answer
482 views

Uniformly distributed n-dimensional probability vectors

What's the right way to generate a random probability vector $p={p_1,\ldots,p_n} \in {(0,1)}^n$ where $\sum_i p_i=1$, uniformly distributed over the $(n-1)$-dimensional simplex? What I have is ...
11
votes
1answer
560 views

Solving Killing equations

Is it possible to solve Killing equations in Mathematica for a general vector? I am looking for a way to create Killing equations and then find what the vectors are, but I have a problem with this. ...
2
votes
1answer
286 views
0
votes
2answers
106 views

How can I plot the integral of a unit tangent vector? [closed]

The questions states: Let r[t_]:= {E^(-t), 3t^2, 4 Sin[t]} Plot and compare r[t] and the integral of ...
8
votes
4answers
637 views

Plotting an epicycloid

I am fairly new to Mathematica and I cannot figure out how to plot an epicycloid. I have plotted some neat looking things in my attempts, but can't make one. I am not looking to make an animation, ...
11
votes
2answers
441 views

Is there a triangle like this?

I want to find the numbers $a$, $b$, $c$, $d$ of the function $y = \dfrac{a x + b}{c x + d}$ so that the triangle $ABC$ with three points $A$, $B$, $C$ have integer coordinates and lies on the graph ...
4
votes
2answers
151 views

Assumptions for RotationMatrix

I'm making C++ program, and in my program I need a rotation matrix around any vector. I wanted to extract RotationMatrix[fi,{x,y,z}] output and put it in my ...
0
votes
1answer
128 views

Are there built in functions to perform a geometric transform to rotate a set of points around an arbitrary point?

I have a list of points {{4,5},{6,7},{9,8},...} in two-dimensions. I'd like to rotate these points some number of degrees $\theta$ around an arbitrary anchor point ...
1
vote
1answer
163 views

Efficiently determining if a morphological component overlaps a polygon with vertices at real number coordinates

I have a list of morphological components $m$, a set of vertices for a polytope $P$ (at real number coordinates), and I'd like to be able to calculate a list of morphological components $m'$ that ...
3
votes
0answers
169 views

Generating an obstacle-avoiding closed-curve with a fixed perimeter and a target area

I was wondering if there was a neat way to solve the following problem in Mathematica v9 - Provided a binarized image (where we call black pixels "obstacles" or vice versa, whichever is most ...
19
votes
4answers
2k views

How do I calculate the area of a polygon given its coordinates?

I have a polygon: Polygon[{{0, 200 }, {200, 100}, {500, 300}, {100, 700}}] How can I figure out its area? The docs page does not have any example. So far I've ...