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

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1
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1answer
66 views

Implicit region is not “valid” in ParamatricNDSolveValue function?

I am trying to solve a geometric problem with relation to my Schrodinger equation and its boundaries. Here is my code: ...
2
votes
1answer
149 views

Surface Plot 3D of a strongly concave shape

I have a list of {x,y,z} points that all lie on the surface of an object (model output from COMSOL). I would like to generate a graphics object that reproduces the surface. Ideally, I would like ...
2
votes
1answer
103 views

Contourplot gives inaccurate ellipses

I'm trying to draw a family of ellipses with pre-defined foci as follows: ...
1
vote
0answers
100 views

Implementation of Lubaehevsky-Stillinger Algorithm to pack hard spheres

To generate a model of a polycrystalline material with specified grain size distribution (e.g coming from a Monte Carlo Grain Growth simulation) the Paper "Effects of grain size distribution and ...
5
votes
2answers
353 views

Calculate area under a polyline

Consider the following code: tmp = {{0, 0}, {1, 1}, {2, 1}, {3, 2}, {1, 0.5}}; ListLinePlot[tmp, Filling -> Axis] Is there any easy way to compute filled ...
1
vote
1answer
124 views

Implicit region misses subset?

Context I am interested in integrating a 2D function over lines defined implicitely Attempt Let me just start by integrating the identify on such sets of lines which a defined using ...
35
votes
3answers
1k views

Can Mathematica solve Plateau's problem (finding a minimal surface with specified boundary)?

Given a closed curve $\mathcal C$ in three dimensions, is it possible to use Mathematica's built-in functionality to compute a minimal surface whose boundary is $\mathcal C$? For simplicity, let us ...
2
votes
1answer
281 views

Distinguishing left from right adjacent triangles in triangle mesh [closed]

What I'm trying to do: I'm trying to create a path-drawing function which will produce a path like the one I-P in the diagram below. The way this path was generated requires me to swap between the ...
27
votes
2answers
354 views

Bug in ArcLength?

fixed in 10.1 (windows) With Mathematica 10.0.2: ArcLength[Line[{{0, 0}, {1, 0}, {2, 0}}]] ArcLength[Line[{{0}, {1}, {2}}]] (* 2 *) (* 2 *) However, ...
7
votes
3answers
274 views

Unable to compute the area of region

For a set of data: ...
1
vote
2answers
201 views

Only show part of a cube below an intersecting plane

I plot a cube and a plane. I just want to show the part below the plane. The code: ...
0
votes
1answer
42 views

Computing $V(p_1, p_2)$ and determining whether $V(p_1) \subset V(p_2)$

Say I have two homogeneous polynomials $p_1, p_2 \in \mathbb{C}[x_0, \dots, x_n]$. In other words, they cut out co-dimension 1 varieties in $\mathbb{P}^n$. I would like to know how to compute two ...
22
votes
6answers
4k views

Drawing a square root spiral

Here is a start. I'm looking for a nice way to draw it. ...
6
votes
1answer
151 views

Symbolic geometry not working?

Bug fixed in 10.0.0+2014080602 I have Mathematica 10 on the Raspberry Pi. (wolfram-engine version 10.0.0+2013112003) According to the "What's New in Mathematica 10" page ...
1
vote
0answers
53 views

Coding the Gibbons-Hawking metric

I am studying the Gibbons-Hawking metric, which is $ g= U^{-1}(d\tau + \omega.dx)^2 + U.dx.dx$ where $U = \sum_{s=1}^n \frac{1}{|x-P_n|}$. It is a family of metrics defined on a four-dimensional ...
6
votes
2answers
242 views

Building bounded polygon around heatmap (or points)

I have a set of data for world marine piracy. I'd like to build polygons encircling areas of active piracy. So to start with I get piracy data and make a heatmap from it. ...
6
votes
1answer
279 views

Obtain polygons describing all intersections of many polygons

I have 6894 polygons describing zones in a state plane (i.e., cartesian) coordinate system. Most are not very complex, and I believe none have holes. A random example is Polygon[{{351633., ...
1
vote
2answers
129 views

Draw Multiple Polygons Given Their Vertices

Hi I have a very simple question but I haven't been able to find a set answer. How would I draw a bunch of polygons on one graph. The following does not work: ...
8
votes
1answer
449 views

How to create a Poincaré disk type kaleidoscope in Mathematica?

Creating a kaleidoscope in Mathematica is not a new topic at all, examples can be found from the links like Wolfram reference and Wolfram demonstrations. My question is how to create Poincaré disk ...
4
votes
2answers
186 views

Compute the average distance from the base of a rectangular pyramid to its apex

How can I compute the average distance from the base of a rectangular pyramid to its apex? For example, if the base of the pyramid is 30 feet by 8 feet, and the height of the pyramid is 12 feet, then ...
4
votes
2answers
327 views

Equation of a transformed (roatted) ellipsoid

Given an ellipsoid with semi-axis {a,b,c} and cantered at {a,0,0}, how do I use ...
2
votes
1answer
171 views

Mean curvature of Sphere

I am trying to calculate mean curvature of a parametric surface(like sphere), and I wrote this code based on this discussion. Here is my code: ...
4
votes
2answers
445 views

Plane Geometry Diagrams With Labels

I can make some basic diagrams in Mathematica (stolen from their pages, for example see the below: LaminaData["FilledIsoscelesTriangle", "Diagram"] However, I'm ...
2
votes
2answers
184 views

Finding the area bounded by a logspiral curve and two straight lines

I'm facing some trouble with finding the area of a region which is described by x-y coordinates (or line equations) and a curved line represented by logspiral. I tried my best in coming up with the ...
7
votes
3answers
476 views

Finding volume of a segment

I'm still pretty new to Mathematica, so I would like to seek advice regarding a geometrical problem. I am currently trying to define that as an extra condition in the Mathematica code below. ...
7
votes
1answer
236 views

Getting the coordinates of GeoDisk[] and similar Mathematica 10 GeoObjects

I'm a big fan of the new Mathematica 10 geographic capabilities and functions such as GeoDisk[], GeoCircle[] and others. One limitation of these functions, however, is the transformation of the actual ...
0
votes
1answer
309 views

Order contour points in clockwise

I want to describe shape of an object using contour points descriptor. Given a silhouette (image black white of an object), I extrait the contour points using EdgeDetect[] fonction. After that, I need ...
4
votes
3answers
855 views

Computing Gaussian curvature

Can Gaussian curvature $K$ be computed from WolframAlpha or any other available Mathematica program? Please indicate the program or its reference. If input ...
3
votes
2answers
275 views

Constructing a list of Cartesian coordinates of the Icosahedron

I’m learning Mathematica and I need the coordinates of the Icosahedron vertices. This is my attempt at writing a program for it. The vertex coordinates are simply all cyclic permutations and ...
2
votes
2answers
174 views

Controlling PointSize in a RegionPlot

I have a "named" point in Mathematica 10 and am plotting it like this using RegionPlot: ...
0
votes
1answer
240 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}] ...
14
votes
3answers
2k 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 ...
12
votes
3answers
905 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 ...
15
votes
3answers
519 views

How to manipulate a circle in GeoGebra style?

I want to emulate the GeoGebra app. I want to get an effect like this in Mathematica. I don't know how to move whole circle without changing the radius of the circle. My sample code: ...
35
votes
6answers
2k 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 ...
2
votes
1answer
195 views

Plotting a Partially Filled Ellipse

I would like to plot a partially filled/shaded ellipse. The code below shades the whole ellipse. However, I only want to shade the part of the ellipse to the right of the vertical line where x > ...
13
votes
5answers
1k 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 ...
29
votes
1answer
779 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 $S^2$ ...
30
votes
5answers
3k 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
229 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
3answers
314 views

Matrix containing ellipse

I have to make a matrix which contains elements in an ellipse shaped region, but I need to make ellipse region in such a way that larger axis of ellipse is inclined with angle θ with horizontal. With ...
8
votes
1answer
562 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 ...
6
votes
1answer
262 views

Generating cylindrical geometry via extruding a section

Toady I want to build geometry as shown below: I know the Mathematica owns the built-in like Cylinder[], Sphere[] and so on, ...
2
votes
0answers
240 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 ...
3
votes
0answers
334 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: ...
7
votes
4answers
1k views

How to find all data points within closed curve

I want to find all data points inside curve as given below: ...
5
votes
4answers
1k views

An easier way to find the properties of an ellipse from its equation?

In this Q&A about fitting an ellipse to a set of points, there are multiple answers that generated general equations of the ellipse, like this one by @ubpdqn: However, the steps to find out the ...
3
votes
1answer
104 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 ...
20
votes
7answers
2k views

Find intersection of pairs of straight lines

I have a list of 24 points, in which two consecutive points (1st and 2nd, 3rd and 4th, …) are supposed to form a line: ...
2
votes
1answer
145 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 ...