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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29 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 ...
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1answer
116 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: ...
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5answers
423 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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4answers
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 ...
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1answer
64 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 ...
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1answer
98 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 $e=1/2$. ...
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4answers
97 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 ...
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1answer
78 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 ...
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212 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 ...
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2answers
56 views

Legend for two parametric surfaces

I have the plot of two surfaces given by ...
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34 views

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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1answer
52 views

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 ...
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1answer
66 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 ...
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3answers
59 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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1answer
67 views

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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1answer
48 views

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 ...
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1answer
47 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][[1]]] and got Sphere[{11/2, Sqrt[11]/2}, Sqrt[11]/2] But, I cannot get the result when I used ...
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3answers
268 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 ...
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5answers
438 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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2answers
95 views

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 ...
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1answer
51 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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2answers
71 views

Divide `Graphics` `Line` into `i` equal lengths

I have a line given by ...
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2answers
45 views

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) ...
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3answers
230 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 (...
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44 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,...
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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: ...
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46 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 ...
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2answers
136 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: ...
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55 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.
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2answers
103 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: ...
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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 ...
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1answer
56 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.
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1answer
123 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 ...
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1answer
110 views

Area of Generalized Koch Snowflake

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 - ...
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1answer
96 views

Minimum path on a rectangular prism

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 ...
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3answers
366 views

How to do this Padovan spiral using Mathematica?

how to do this unusual pendovan spriral? can anyone help me ?
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1answer
121 views

Numerical simulation for density of strings in a ball

I am trying to numerically reproduce the Mathematica result for the density of strings in a sphere as explained here. The program is to generate random, uniformly distributed pair points on a unit ...
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0answers
31 views

RegionDifference not working with one Cuboid and large number of embedded cylinders

I am trying to create a Cuboid with embedded hollow cylindrical regions. It seems to work fine when I use a relatively small number of cylinders (about 20) but does not work when I use a large number ...
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68 views

Find two points (of maximum distance) lying on perpendicular intersecting polygon border

On a randomly generated convex hull, I found the two points of maximum distance on the region's perimeter (the points in black). I would like to find two points that lie on the perpendicular to this ...
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3answers
59 views

Checking whether the line is parallel to the plane

I have tried to write a code to check whether a line is parallel to the plane in Mathematica. Using that a plane has the normal vector of $\vec{n}=(a,b,c)$ and a line has a direction vector $\vec{L}=(...
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0answers
31 views

Table with two functions to output matrix with values

So I have a wing modeled as an .STL and I am analyzing its structure so I need its cross sectional area and moment of inertia at points along its span. I do this by moving an infinite plane across the ...
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0answers
29 views

How to generate a list of values related to calculating angles of a polygon? (One solution already created) [duplicate]

I want to generate this exact list I have this code and it works perfectly however I want to do it in a different way without using these functions, can someone please help me do this? ...
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1answer
204 views

Plotting cities with Callout labels on a globe?

This question essentially amounts to implementing a very basic version of GeoGraphics3D: ...
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1answer
170 views

Creating 2d-HexagonalLattice and 3d-HexagonalClosePacking lattice with LatticeData function

I found here a solution by s0rce on how one can for example create a 3d FaceCenteredCubic lattice structure: ...
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1answer
103 views

Derive a polygon from the midpoints of the sides of a given polygon [closed]

Write a function that creates a new figure (a new broken line) out of a given broken line. It would take as parameter a list of (max) 20 points representing the closed broken line. The output must be ...
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19 views

How to find a,b, and R for the given circle [duplicate]

Given the three points (x1,y1), (x2,y2),(x3,y3) find a,b,and R for the circle (x-a)^2 +(y - b)^2 =R that passes through them. Notice that the solutions have the same denominator or its square. What ...
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1answer
299 views

Packing arbitrary shapes

I'm looking for a general method of packing any set of 2D glyphs. For example, say I had 30 randomly transformed english characters: ...
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1answer
71 views

From Free-Form linguistic input to function expression to calculate spheroid surface

I need to calculate the surface area of an oblate spheroid. My first step is to get the surface equation from Free-Form input. But I have trouble converting to a WM function and replace the focus ...
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2answers
96 views

Trouble with Calculating Area of Parametric Region

This question stems from an attempt to solve the following question: How to calculate specific area on surface of sphere? First, I parametrize a circular loop: ...
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0answers
71 views

How to calculate specific area on surface of sphere?

I am trying to calculate the solid angle subtended by arbitrary-shaped loops on a sphere's surface. First, I parametrize circular loops by: $$\theta(t,k_{x0},r) = k_{x_0} + r \cos(t);$$ $$\phi(t,k_{...