# Tagged Questions

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

0answers
58 views

### Plot all points that satisfy a condition [closed]

I'm interested in plotting various curves directly from their definitions, but I have no idea which function I'd use for that. For example, I'd try plotting a circle by telling Mathematica that a ...
1answer
75 views

### Arbitrary hollow cylinders in mathematica 9

I'm having trouble displaying a hollow cylinder in Mathematica 9. A hollow cylinder looks like this: I tried to use RevolutionPlot3D with a step function. It ...
5answers
444 views

### Plot a partition of the sphere given vertices of polygons

I saw in this question that Mathematica can draw spherical triangles. I guess something similar can be done to plot a spherical polygon. I am interested in something similar: I have a set of ...
1answer
114 views

### Distinguishing left from right adjacent triangles in triangle mesh

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 ...
2answers
102 views

This code: ...
2answers
310 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, ...
1answer
35 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: ...
0answers
45 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 ...
1answer
92 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 ...
1answer
232 views

### xCoba: evaluate tensor quantities, given an explicit metric [closed]

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 ...
3answers
618 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 ...
1answer
681 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 $S^2$ ...
0answers
56 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 ...
2answers
224 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 ...
1answer
259 views

### A problem on generating convex hull

For example, I typed the following: ...
3answers
217 views

### Unable to compute the area of region

For a set of data: ...
0answers
57 views

### How to plot a ternary plot? [duplicate]

Does anybody know how to plot a ternary plot (equilateral triangle)? Suppose, I have a list of lists like this (triplets): ...
2answers
154 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: ...
1answer
111 views

### Symbolic geometry not working?

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 ...
1answer
38 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 ...
0answers
39 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 ...
2answers
158 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. ...
3answers
882 views

### Approximating an ornamental curve

How do I go about approximating this ornamental curve? Note variable thickness typical in calligraphy. Handbook and Atlas of Curves by E.V. Shikin (1995) contains many directions, including curve ...
1answer
174 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., ...
2answers
100 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: ...
3answers
355 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. ...
2answers
147 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 ...
1answer
172 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}] ...
2answers
203 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 ...
3answers
707 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 ...
2answers
282 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 ...
1answer
125 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: ...
1answer
233 views

### Generate a set of 3D coordinates subject to constraints

Generating a set of random 3D coordinates is ok, e.g. ...
5answers
3k views

### How to draw a great circle on a sphere?

I apologize for the text description, but new users are not allowed to post images. I want to draw a circle that cuts through the center of a sphere and has an inclination of 15 degrees with the ...
2answers
126 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 ...
1answer
185 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 ...
1answer
145 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 ...
3answers
972 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 ...
2answers
209 views

### Constructing a list of Cartesian coordinates of the Icosahedron

Iâ€™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 ...
2answers
120 views

### Controlling PointSize in a RegionPlot

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

### Labeling named point in Mathematica 10 [closed]

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 ...
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 ...
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 ...
4answers
834 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 ...
6answers
547 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 ...
5answers
2k views

### Generating evenly spaced points on a curve

In the KnotData package a simple command such as points = Table[KnotData[{3, 1}, "SpaceCurve"][t], {t, 0, 2 Pi, 0.1}]; will ...
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 ...
1answer
156 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, ...
2answers
758 views

### How can I plot a loxodrome?

Can someone show me how to plot a rhumb line (loxodrome) in Mathematica via the ParametricPlot function? Here is what I got so far: ...
4answers
8k views

### Finding unit tangent, normal, and binormal vectors for a given r(t)

For my Calc III class, I need to find $T(t), N(t)$, and $B(t)$ for $t=1, 2$, and $-1$, given $r(t)=\{t,t^2,t^3\}$. I've got Mathematica, but I've never used it before and I'm not sure how to coerce ...