# Questions tagged [geometry]

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

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### Torus Hex Mesh - Need Unique Hex Dimensions

I'm looking to laser cut a bunch of hexagons and assemble them into a torus (using hot glue or tape). How do I get the dimensions of the individual unique hexagons? I've seen Create a torus with a ...
55 views

### Define indicator function of mesh elements

Context I would like to (partially) answer my own question here (ok its a bit cheesy but...) Question I am interested in defining an indicator function which value would be 1 on a cell and ...
48 views

### Replacing every shape in a geometric set with another shape

Consider a Mathematica function that produces some number of identical, but separate shapes; like CantorMesh[2, 2], for example. Is there a simple way to "replace" ...
68 views

### Table of Dynamic Disks

I'm trying to create a dynamic interface to generate disks depending on 3 parameters : x-coordinate, y-coordinate and radius. The disks are generated as soon as the "export" button is pressed. I'm ...
39 views

### All positive integer points up to a certain distance from a hyperplane

I have the hyperplane $\sum_{i=1}^{d} x_i c_i = z$ for $x \in \mathbb{R}^d$, defined by the vector of postivive numerical coefficients $c_i \in \mathbb{R}, c_i > 0$, and the value $z > 0$. I ...
54 views

### Counting the number of continents

The definition of continent varies depending on: What is the minimum area that a landmass has to be to consider it to be a continent rather than an island? What is the resolution of the map you're ...
45 views

### How to use MMA to make these triangles into a Pentagon according to the equal length side?

I tried to use Polygon but failed. ...
37 views

### PlanarAngle symbolic equalities return contradictory results

PlanarAngle[OO->{A,B}]==PlanarAngle[OO->{B,A}]/.{OO->{0,0},A->{1,0},B->{1,1}} False ...
52 views

### How can i intersect a line with it´s rotated counterpart?

So, i'm trying to intersect an infinite line with a line, this is my code for now, i have been using Region Intersection, but it seems it does not work with this case i have: ...
56 views

### Order of PolygonCoordinates[] is undefined in Mathematica 12?

Probably I am missing something fundamental. I try to get a polygon's ordered coordinates, but PolygonCoordinates[] yields something pretty unordered. Am I missing some essential function? ...
278 views

### Concentric layered sphere with logarithmically scaled radius

How can I achieve a 3D visual of a concentric layered sphere (like an onion), where the radius of each layer is tick-marked using a logarithmic scale? Specifically, my project is to realize the ...
80 views

### TriangleMeasurement causing problem when used in Manipulate

On my Windows 10 machine, Manipulate with TriangleMeasurement locks up once I start changing the sliders. Even with ...
116 views

### Convert logical combinations from Reduce to a usable function

I'm working on a geometry problem and would like to create a function to create a triangle based on the logical constructs output by Reduce but cannot obtain all the constructs. Here's the problem: ...
355 views

### How do you draw a path on a parametric sphere?

Given a parameterized sphere defined by: ...
31 views

### Error in variable trying to perform SlicedVectorPlot

I have been trying to plot the normal vector over the Mobius Strip, which I know I cannot do asking it to be a well-defined continuous map, nevertheless you can do it in a small region, which I am ...
121 views

### Unable to compute the area of a polygon

I am having trouble computing the area of the following polygon. I have the following polygon: ...
480 views

### Computing the intersection area of two disks in 3D

Closely related to this question about highlighting intersection of two disks, I am trying to figure out if one can do so similarly for disks embedded in $3D$ (e.g. in a bounding box). The difference ...
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### Given a set of points in a plane, find the maximum number of the all collinear points [closed]

Given a set of points in a plane， For example:RandomInteger[{1, 10}, {50, 2}] How to find the maximum number of the all collinear points Reference link：https://blog.csdn.net/u014253011/article/...
2k views

### Is there a way to randomly distribute points within a circle on the surface of a sphere?

I'm attempting to set up a situation where on a 3D sphere, I choose a random point and construct a circle around this point with some radius. I then want to randomly distribute points within this ...
79 views

### Is it possible to plot a manifold from it's metric / line element in Mathematica?

i'm very new to using Mathematica and mostly just trying to work out what it can or can't do. I'm doing a course on differential geometry and was wondering if there might be a better way for me to ...
103 views

### How can I simplify my geometric calculation?

Here is a math problem I am dealing with right now: Given ellipse $C$: $x^2/a^2 + y^2/b^2=1$ ($a>b>0$). Ellipse $C$ passes through the point $P$: $(1,3/2)$, and has eccentricity $e=1/2$. ...
115 views

### Unable to find root for user-defined function

I created the function getSolution[xVal,yVal] for a geometry problem I'm working on and wish to solve it for getSolution[2,x]==0. I can plot it clearly showing the roots: However, when I attempt to ...
95 views

### RegionCentroid and center of mass

If we have three masses $m_1,m_2,m_3$ (assuming that are all equal to $1$) located at $r_1,r_2,r_3$ respectively, then the center of mass is at $(1.00,0.83)$. In the Wolfram Documentation page says ...
221 views

### Finding all the lines that can be defined a set of points

Input ten Points, calculate every possible straight line from each possible pair of points and check if any of the other points are on the lines. Is something like this possible in mathematica? and ...
64 views

### Legend for two parametric surfaces

I have the plot of two surfaces given by ...
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### How can I always get one option of coordinates of the points A, B, C, D, and X of the Problem 6 in IMO 2018?

This is the Problem 6 of IMO 2018 https://www.imo-official.org/problems.aspx I use the code at Mapleprimes (with some prepairs) https://www.mapleprimes.com/questions/228162-How-Can-I-Get-One-Option-...
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### Determinant of Gauss (Area of a polygon of n vertices) how to implement

A very useful procedure to find the area of ​​any irregular polygon is through the Gauss determinant. It involves drawing the figure on a Cartesian plane, setting the coordinates of each of the ...
72 views

### HalfLine to draw lines “to infinity”

I'd like to draw a simple figure illustrating geometric perspective (so-called "central-point perspective") in which perspective lines on two cubes are extended "to infinity," where they meet. Here ...
68 views

### How would I plot the inequality lines together with the intersection plot of the inequalities?

For example, I've got the following code: Plot[{x >= 5, y >= 8, x + 2y <= 64, x + y <= 40}] This would plot: Now, this is fair enough. It shows me ...
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### Using the Disk graphics primitive II

I ask again to clarify a couple more things How do I write the disk primitive to calculate these cases Cases follow this link 1 reply from @kglr thanks Using the Disk graphics primitive
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### How to obtain the positions of the points in a lattice

I want to know the positions of each point in a hexagon lattice, like I saw some posts where they obtain this lattice using a function ...
51 views

### How can I get coordinates and radius of Incirle of the triagle with the length three sides are a, b, c?

I used Insphere[SSSTriangle[5, 7, 9][]] and got Sphere[{11/2, Sqrt/2}, Sqrt/2] But, I cannot get the result when I used ...
271 views

### Using the Disk graphics primitive

Please be kind enough to give me some indication on how to use the Disk graphics primitive in any of these cases: I want to calculate the area and perimeter of the ...
461 views

### Rotating squares animation

Reference link: https://www.geogebra.org/m/RHYH3UQ8 , https://www.geogebra.org/m/xkzsqcyx , https://www.netpad.net.cn/svg.html#posts/55789 I want to generate an rotating squares animation like this, ...
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### How can reduce the code to get coordinates of vertices of tetrahedron so that O(0,0,0) is center of circumsphere?

Let be given tetrahedron $SABC$, $SA=14/3$, $SB=7*\sqrt{13}/3$, $SC=2*\sqrt{193}/3$, $AB=7$, $BC=3$, $AC=8$. I want to find the coordinates of $A, B, C, S$ so that $O(0,0,0)$ is center of circumsphere ...
53 views

### Apply non-linear transformation to graphics object

I would like to define some simple geometric primitives (e.g. points and lines) and see what happens when I transform them by a non-linear transformation (in my case $(x,y)\mapsto (\sqrt x,\sqrt y)$). ...
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### Divide Graphics Line into i equal lengths

I have a line given by ...
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### How to set up symplectic geometry without(!) metric (with xAct/xTensor)?

I want to define a symplectic manifold with symplectic form $\Omega_{[ab]}$ with $\Omega_{ab}\Omega^{ac} = \delta^c_b$, but without having a metric. I define a manifold and an antisymmetric (2,0) ...
251 views

### Color the polygons in PolyhedronData

What is the simplest method for coloring each polygon face of a polyhedron with a specified color? For instance suppose I have a list of $12$ colors (...
57 views

### Discrete Sum of Function over a Region

I might have completely missed something in my search. I want to discretely sum over a function, $f(x_i,y_j)$ multiplied by some other function $g$ over a general region $S$. \sum_{(x,y)\in S}f(x,...
16 views

### Issue connecting vertex coordinates

To make it simple, I have generated a list where sub-lists are vertex coordinates of regular or non-regular polytope. For example, here's a list that can be generated: ...
53 views

### Non-convex hull mesh from 3d points [duplicate]

I am trying to create a 3d mesh object from list of points, but the only options I see in Mathematica are ConvexHullMesh and ...
139 views

### Adjacent faces in a discrete mesh

I have a MeshRegion R and I want to extract all pairs of adjacent faces efficiently. The way that I've been computing this is demonstrated below: ...
61 views

### How can I create a Delaunay mesh in set of points inside an image?

Is there a possible way to create a Delaunay mesh inside an image given a set of points inside the image? for instance use the pixel coordinates to create the Delaunay mesh.
104 views

### How to make my code to generate polytopes more efficient?

The main purpose of my code is to generate polytopes by starting with a point. With this point, I then apply 3 actions which generates at most 3 others points: ...
39 views

### Regions detecting/counting

Recently, I solved an analytical problem on the number of possible regions in a similar figure: I conducted numerical experiments on Mathematica to verify the results. Intersection points are easy to ...
57 views

### Analytic geometry - triangle [closed]

I have three points: A[1, 2]; B[3, 5] and C[5, 7] I have some random points, like this: E [4, 4] etc. I need to check if these random point are a part of the ABC triangle, or not.
130 views

### Unfolding a polyhedron

I wanted to know how unfolding a Polyhedron in Mathematica works. I can't seem to make it work even when I have all the coordinates I need. The Polyhedron of reference is ...
I asked on the Math Stack Exchange here how I could find the area of a "generalized Koch snowflake". An $n$th generalized Koch snowflake, in my case, is formed almost the same as the Koch snowflake - ...
First of all, this is a fun question that I have seen from here. We have a rectangular prism with dimension $30\times12\times12$ cubic inches. Assume that there is an ant at the blue point 1 inch ...