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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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6
votes
1answer
47 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 ...
0
votes
2answers
38 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 ...
0
votes
1answer
55 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
0
votes
1answer
44 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 ...
2
votes
1answer
46 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 ...
4
votes
3answers
264 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 ...
8
votes
5answers
423 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, ...
0
votes
2answers
93 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 ...
1
vote
1answer
48 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 $(x,y)\mapsto (\sqrt x,\sqrt y)$). ...
3
votes
2answers
71 views

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

I have a line given by ...
1
vote
2answers
38 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) ...
5
votes
3answers
221 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 (...
0
votes
0answers
42 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,...
0
votes
0answers
27 views

parametric to cartesian equation of a paraboloid

I need to found the cartesian equation of the parametric equation of a paraboloid. The following equations describe parallel paraboloids: ...
0
votes
0answers
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: ...
1
vote
0answers
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 ...
5
votes
2answers
135 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: ...
0
votes
0answers
54 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.
4
votes
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: ...
0
votes
0answers
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 ...
0
votes
1answer
55 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.
1
vote
1answer
118 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 ...
3
votes
1answer
108 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 - ...
3
votes
1answer
92 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 ...
6
votes
3answers
357 views

How to do this Padovan spiral using Mathematica?

how to do this unusual pendovan spriral? can anyone help me ?
1
vote
1answer
114 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 ...
1
vote
0answers
30 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 ...
0
votes
0answers
65 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 ...
0
votes
3answers
57 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}=(...
0
votes
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 ...
2
votes
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? ...
11
votes
1answer
186 views

Plotting cities with Callout labels on a globe?

This question essentially amounts to implementing a very basic version of GeoGraphics3D: ...
2
votes
1answer
153 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: ...
0
votes
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 ...
0
votes
0answers
18 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 ...
12
votes
1answer
291 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: ...
1
vote
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 ...
1
vote
2answers
94 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: ...
4
votes
0answers
64 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_{...
1
vote
2answers
109 views

How to calculate arbitrary 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_{...
1
vote
0answers
54 views

Create a Weighted Region

I am trying the make (not super accurate, just for fun really) simulations of light curves, as just circles with various sizes and temperatures, then computing the ...
1
vote
2answers
68 views

How can I make an arrow's shaft more visible?

{Graphics[{Arrowheads[.1], Arrow[{{0, 0}, {2, 1}}]}], Graphics[{Arrowheads[.1], Arrow[BezierCurve[{{0, 0}, {1, 1}, {2, 0}}]]}]} say I have the above code. Can I ...
0
votes
1answer
83 views

Make Arrows Smaller

I have the following program that describes a 3D curve in space with an osculating circle and TNB vectors moving with the curve. The arrows indicating the TNB vectors are way too large making it seem ...
2
votes
1answer
69 views

Perpendicular chord lengths from the boundary points of an arbitary 2D shape

Let's generate an arbitrary convex domain with smooth boundaries: Graphics[BSplineCurve[{{1, 4}, {5, 3}, {9, 4}, {5, 5}, {8, 7}}, SplineClosed -> True]] I'...
8
votes
3answers
547 views

Find bounding box of arbitrary 3d graphics?

What's the best workaround for this limitation: RegionBounds[ BoundaryDiscretizeGraphics[Graphics3D[{Cone[], Cuboid[]}]]]
3
votes
0answers
88 views

How to implement projective geometry in MMA?

I'd like to implement 2D projective geometry in Mathematica, making use of the FindEquationalProof command. Up to Wiki ru.wikipedia.org (This topic is better ...
0
votes
1answer
107 views

How can I make a convex catenoid (minimum surface of revolution that closes on -1 and 1? [closed]

In Wolfram MathWorld I see the catenoid (minimum surface of revolution which is concave and open ended, but I want the one where the sides are convex and close on the long axis (say z) at -1 and 1. I ...
2
votes
1answer
77 views

How to use Normal to recover translated points [duplicate]

I'm working through a coding exercise to program a matrix of Lissajour Curves in Mathematica but have encountered an obstacle when trying to recover the translated ...
12
votes
2answers
191 views

How to Interpolate a 3D MeshRegion?

If you were given some discrete MeshRegion called r (you don't know R): ...
2
votes
1answer
105 views

Plotting 2-dimensional polytopes embedded in n-dimensional Euclidean spaces

My minimal working example is Graphics3D[Polygon[{{0, 0, 2}, {0, 3, 4}, {0, -1, 2}}]] How can I plot the polygon I have listed above on a 2-dimensional plane (...