# 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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Bug introduced in 9.0 or earlier and fixed in 11.0.0 Why does this work: Graphics[{Circle[{0, 0}, -Pi/4]}] But this doesn't? ...
82 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? ...
946 views

### Minimalistic code challenge on Apollonian gaskets

I've been recently fascinated by the beauty, symmetry and mathematical richness of the Apollonian gaskets. So I felt myself challenged to see if it was possible to generate one in Mathematica with a ...
134 views

### Higher order Laplacian flows

Given disjoint surfaces $q_i$ in 3D and their 1D boundary curves $\partial q_i = \gamma_i$, I seek a surface $p$ that joins the $q_i$, where $p \cup q_i$ forms a (piecewise) $C^k$ surface that ...
290 views

### Anamorphic projection onto the corner of a room

I want to use a router to carve anamorphic projections of polyhedron wireframes onto two adjacent walls of my office. Like this: In order to do this I need to transfer the positions of the vertices ...
642 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: ...
90 views

### Need help understanding weird RegionUnion behavior

I'm trying to understand some weird behaviors of RegionUnion in a small piece of code. In particular, RegionUnion is not ...
267 views

### Volume Deformation

I want to do a volume deformation based on Bezier volumes. For example, if I have a triangle mesh, then I want to deform the mesh into a weird shape like the example image attached here. Can anyone ...
39 views

### Interpolating vertex colors with trilinear coordinates instead of barycentric

In 3D graphics, vertex attributes like vertex normals, texture coordinates, and vertex colors are interpolated over the surface of triangles using barycentric coordinates. In actual fact it's more ...
258 views

### Generating an obstacle-avoiding closed-curve with a fixed perimeter and a target area

I was wondering if there was a neat way to solve the following problem in Mathematica v9 - Provided a binarized image (where we call black pixels "obstacles" or vice versa, whichever is most ...
497 views

### How to Export to/Import from GeoGebra?

I'd like to convert geometric figures between Mathematica and GeoGebra. Does anyone know how to do that?
91 views

### Symbolic formula from GeometricScene?

I'm trying to solve the following problem with GeometricScene What is the shortest circular arc of which the altitude above its chord is one? I have the following code: ...
143 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 ...
160 views

### Finding triangles where the coordinates of vertices, centroid, orthocenter and circumcenter are all integers

I am trying to find all triangles that satisfy the following conditions: Each vertex {x, y} is a pair of integers such that -20 <= x, y <= 20. The ...
226 views

### Automated searching for maximal 2D point configurations

I have some black-box function that takes lists of 2D points, and I would like to find some practical methods of searching for collections of points that maximize it. Motivation I've come across ...
125 views

### RandomPoint not evaluating on RegionQ and ConstantRegionQ regions

When attempting to recreate and generalise the MatLab code for Random Vectors with Fixed Sum by first principles I came across a few issue with RandomPoint. ...
292 views

### How to solve or prove some plane geometry problems by Mathematica?

There are some plane geometry problems as my homework. I tried to solve one of them by Sketchpad which involved concurrent lines. I wonder if there is some way made through Mathematica? For example, ...
61 views

### Inner polygon approximation

Suppose you want to perform an inner approximation of a planar semialgebraic set by a finite set of polygons. The following is a quick way to yield an approximation but I am not convinced that it is ...
76 views

### How can I calculate the ratio of the line segments in the following geometric scene?

The following code can draw the corresponding geometric scene. By observing for many times, we can know that the length ratio of line CE and line ...
112 views

### Resolve implicit region into explicit one

Does Mathematica provide a way to take, for instance: ImplicitRegion[x^2 + y^2 <= 1, {x,y}] and convert it into a region defined explicitly in terms of x and ...
131 views

### ConvexHullMesh fails for collinear points

I've got a List of PointLists, of which some contain only collinear points. I now want to obtain all ConvexHullMeshes of my PointLists. For more than two ...
343 views

### Plotting Seifert surfaces

Is it possible to make a Seifert surface in Mathematica, such as a Seifert surface for a trefoil knot? I was thinking of taking the parametrization equations for a trefoil knot and then somehow ...
185 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 ...
31 views

### Find the ratio of two volumes of 6 x 6 positive-definite symmetric matrices

Consider the class $A$ of $6 \times 6$ positive definite matrices with real entries and unit trace (that is, the sum of the six diagonal entries is 1). (In quantum information-theoretic parlance, this ...
33 views

### Finding the shared edged between two polygons

Imagine I have two convex polygons pol1 and pol2 with a shared edge. Take, as an example, ...
44 views

### RandomInstance of GeometricScene producing unexpected result

Consider the following scene as an example: ...
37 views

### How to speedup RegionIntersection?

Consider a circle circle located at the origin of a coordinate frame and with a radius ROffAxisArb (it is parametrized by two ...
46 views

### Symmetry of Command Dot

I would like to work with the command Dot assuming symmetry. Specifically with the order D[v[t].v[t], t] I get the following output ...
37 views

### Find the (unique) 9-dimensional ellipsoid of maximum volume lying with the convex set of 4 x 4 symmetric, positive-definite (trace 1) matrices

Find the unique (JohnEllipsoid) maximum volume ellipsoid lying within the 9-dimensional convex set formed by the $4 \times 4$ symmetric, positive-definite ("density") matrices with fixed ...
86 views

### Find the intersection coordinate of a line and a 3D surface defined by a contour plot

I have two points, for instance {1, 1, 1} and {10, 11, 15} that connected to form a line. I also have an enclosed surface region ...
43 views

### An apparent bug in GeometryConvexHull2

I was replacing some usages of GeometryConvexHull2 with ConvexHullMesh and found one of my tests failing. It turned out the ...
30 views

### NearestMeshCells in Mathematica 11.3

Is there an efficient way of writing a function equivalent to NearestMeshCells (Mathematica 12.1) in Mathematica 11.3? I'm trying to write my own code, which I can ...
97 views

### How to use Mathematica to find the coordinates of 7 points?

Could anyone please help me with using Mathematica to find the coordinates of 7 equally spaced points on the unit sphere $S^3$ in $\mathbb{R}^4$? Thanks a lot!
49 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 ...
57 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 ...
65 views

### Finsler or Lagrange geometry package?

I was wondering if there exist any packages or examples of work on Finsler-Lagrange geometry. I need it to do symbolic calculations, as for example calculations of non-linear connection coefficients, ...
49 views

### Find rectangle boundries with any angle

I have a rectangle that has an angle and i need to find its boundaries in an equality form ( less than, greater than). so i guess the best way to start is to tell you what i know CENTER: (...
169 views

### Equilateral triangulation of a polyfile-defined surface

I would like to be able to make a (low fidelity) triangulation of a given surface with constant edge lengths (using equilateral triangles). This requirement limits the Gaussian curvature at each ...
37 views

### How can Integrate of conjugate transpose in mathematica?

please help me to integrate this matrix in matematica: 0 ConjugateTranspose[u[x,t]] (u_x)[x,t]+I vx,t[x,t] 0 -ConjugateTranspose[u[x,t]] (u^(1,0))[x,t]-I vx,t[x,t] 0 0 0 ...
63 views

### Rotate 120-Cell Animation

I have seen some code (https://mathematica.stackexchange.com/a/9593) to create an animation of a hypercube rotating, but I'm really struggling to understand how it works. I find it quite complicated. ...
52 views

### How can I connect and combine individual active areas in a geometric shape?

I am new in Mathematica and I do not know how I can get the following into a square. I need 4 "active areas" but in a single square which I can easily access and manipulate. Here's what I've ...
50 views

### Eliminate doesn't work

I tried to define r by the polynomials a,b,c only. The result which I want is r=4/3 a. But this eliminate doesn't work! It is continue running without stop and without any output. Eliminate[{a == x ...
29 views

### How to reorient a Sphere[] and associated point based on some arbitrary axis?

Suppose I have a unit Sphere[] sitting at the center {0,0,0}, with a point on its "north pole", like this one: ...
43 views

### 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 ...
51 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. ...
43 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 ...
100 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,...
74 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.