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

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0
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0answers
40 views

Find the height(h) of a Circular segment based on Radius and Length(c) [on hold]

I have found the formula for calculating the R of a circle, based on a circular segment, which is; R=h/2+c^2/(8h) Where, R is ...
42
votes
2answers
1k views

Numerically solving Helmholtz equation in 3D for arbitrary shapes

Context While studying manifold Learning I got interested in finding the eigenvectors of the Laplacian. (also in connection to this problem of solving the heat equation) Following this and that ...
-1
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0answers
22 views

Distance between a circle and a line [migrated]

Find the distance between the circle $(x-3)^2+(y+2)^2=4$ and the line $x + 2y = 9$.
3
votes
1answer
55 views

Angle between two vectors in spherical coordinates [closed]

I have two vectors: H = {1, 0, π/4}; EA = {1, 0, 0}; Which I want to be in {r, Phi, Theta} - which would should give an angle between the two vectors as ...
1
vote
1answer
85 views

Draw Vectors in Spherical Shell and then Animate

I want to draw three vectors inside a spherical shell. One of the vectors will be moving, the others will be stationary. However, the animation is the next step. For now, I would like to get the ...
2
votes
2answers
128 views

HIghlight intersection of two disks [duplicate]

I tried this: reg1 = Disk[{0, 0}, 1]; reg2 = Disk[{1, 0}, 1]; reg3 = RegionIntersection[reg1, reg2]; Then this: ...
0
votes
0answers
14 views

Solve the Angle [migrated]

My background in Trigonometry and Geometry is very basic. I am doing a a study and need to work out the angle of a wire; I would also like to know it relative to vertical. I have attached a basic ...
2
votes
1answer
131 views

geodesics' on torus

Is it possible to draw geodesics between the points in a path on a torus - toroidal surface? geodesics: generalization of the notion of a "straight line" to "curved spaces" ...
1
vote
0answers
79 views

Intersection of two volumes

I would like to know the volume of the intersection of a cone and a cuboid : ...
14
votes
2answers
270 views

How to export textures?

Is there any object geometry format for which Mathematica supports the exporting of textures for external (non-Mathematica) use ? If not does anyone know of work arounds? All the texture primitives ...
14
votes
0answers
130 views

Bug in RegionMember?

RegionMember (new in V10) appears to have a bug. For some polygons it finds points that are clearly outside to be "members" of the region. This depends on the shape ...
3
votes
1answer
101 views

hippocrates moons for any shape

Can someone help me create code for a hippocrates moons on random shape with given amount of edges? I want to make something like this: when you press button, it asks you for the amount of ...
1
vote
0answers
70 views

Intersecting ellipsoids

First of all I know that findng whether two ellispoids intersect is complicated and there are specific algorithms created for this purpose (see, for instance, [1]. Actually, I am trying to follow this ...
22
votes
6answers
2k views

Drawing a square root spiral

Here is a start. I'm looking for a nice way to draw it. ...
2
votes
0answers
66 views

Wolfram alpha algorithm for geometric packing in 2D [closed]

Is there any way to gain access to the algorithm that wolfram alpha uses? More specifically, I want to pack small circles in hex and square patters in a larger cicle ...
7
votes
1answer
257 views

Unexpected behavior of GeometricTransformation

Bug introduced in 8.0 or earlier and persisting through 10.3 or later I have the following mapping on the complex plane: $$ z \mapsto \tau \mu z-1, $$ where $\mu$ is complex, $\tau$ is real ...
2
votes
2answers
171 views

intersecting cylinders

I try to replicate the two figures of two intersecting cylinders from here. I tried ...
2
votes
1answer
127 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 ...
8
votes
1answer
403 views

How to use Undocumented Functions Prism, Tetrahedron and Hexahedron

Taking a look at this question and this one, I checked to see if Mathematica really does not have a Prism primitive. To my surprise the function ...
4
votes
1answer
100 views
30
votes
3answers
1k 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 ...
1
vote
3answers
102 views

How do I tell if two sets of dots are in some way similar?

I have two sets of dots (x,y coordinates) and I'd like to figure out if there's a way to find out if the second set of dots is (more or less) "close" to the first one. I may plot these two sets in ...
1
vote
0answers
74 views

Easy way to get the boundary of a geometric object [closed]

I am trying to define von Neumann boundary conditions for a prism. To do so I need the boundary of the geometric object. I can't seem to find an easy way to do this. I have tried to hard code a ...
15
votes
3answers
488 views

How to manipulate a circle in GeoGebra style?

I want to emulate the GeoGebra app. I want to get an effect like this in Mathematica. I don't know how to move whole circle without changing the radius of the circle. My sample code: ...
1
vote
0answers
58 views

Find volume of a translated and rotated ellipsoid below xy (horizontal) plane

I am trying to find the volume of the lower part (above horizontal plane) of an ellipsoid that is clipped by the horizontal (or x-y) plane. This ellipsoid is also translated (i.e. origin is not at ...
5
votes
1answer
96 views

Minimal perimeter of all possible polygons

We had a fun problem for a student activity today: Let $P(z) = z^8 + \left(4\sqrt{3} + 6\right)z^4 - \left(4\sqrt{3} + 7\right)$. What is the minimum perimeter among all the $8$-sided polygons in the ...
5
votes
3answers
153 views

Simple triangular meshes of primitive shapes

I'd like to generate triangular meshes or a cylinder and sphere primitives as part of a lattice meshing program I am writing to experiment with Mathematica. Consider the following snippet: ...
0
votes
1answer
75 views

How do I create a function to rotate a rectangle about its origin? [closed]

I am new to Mathematica and was trying some new things. I wanted to rotate a rectangle using a rotation matrix by any angle theta from say o to 2pi. I could do it using predefined Mathematica ...
3
votes
3answers
326 views

intersection between polygon. Algorithm to check it [closed]

I'm working on an algorithm which should check if two polygons, described by their vertex coordinates, are: one inside the other, are intersecting or are separated image below describe this three ...
2
votes
0answers
110 views

Animate FromQuarternionTo3DRotation nb file with 4 quarternion values

I have a csv file. Inside the csv file, there are few rows of 4 quartenion values. I would like to animate the quarternion nb in http://demonstrations.wolfram.com/FromQuaternionTo3DRotation/ I ...
1
vote
0answers
35 views

Creating a triangle from the difference of two points [closed]

I'm attempting to create a triangular area from the difference of two points. I basically have a straight line that could be the length of 1. I would like to create points on both of the sides of the ...
6
votes
1answer
148 views

Symbolic geometry not working?

Bug fixed in 10.0.0+2014080602 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 ...
1
vote
0answers
91 views

How to plot several small circles in a bigger circle [closed]

I want to plot several small circles in a bigger one with constraint minimization. The distance between any two small circles must be >= to 2*the radius in order not to enter one another. When I ...
3
votes
1answer
68 views

How to determine the value of an angle starting from an image? [duplicate]

I have two lines drawn with Mathematica, how do I calculate the angle between these two lines to have the numeric value of that angle? Thank you
28
votes
2answers
1k views

How can I pack circles of different sizes into a spiral?

Given a list of circles of different areas, I need to arrange them tangentially in order of increasing area and spiraling outward. An example of the type of packing I'm attempting is shown by the ...
15
votes
3answers
496 views

Solve a trig equation system

Background of the problem In the same plane, P is a fixed point, A,B,C are moving point, PA=a, PB=b, PC=c, find the maximize perimeter of △ABC. let ∠BPC=A, ∠CPA=B, ∠APB=2*Pi-A-B, then the ...
4
votes
3answers
152 views

Reflect point over a line in 3D

I'd like to sample points on a triangle randomly. The following code yields points that are uniformly distributed on a quadrilateral: ...
4
votes
4answers
328 views

Picking points in a plane under a curve given by a list

Suppose that I have a set of points in a plane, which range from $x\in [0,20]$ and $y\in[0,10]$, and a curve given by a list of points in the same region: ...
7
votes
1answer
390 views

How to create a Poincaré disk type kaleidoscope in Mathematica?

Creating a kaleidoscope in Mathematica is not a new topic at all, examples can be found from the links like Wolfram reference and Wolfram demonstrations. My question is how to create Poincaré disk ...
12
votes
5answers
1k 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 ...
0
votes
0answers
33 views

How to put n circles on a sphere [duplicate]

I have a piece of code that generates a circle on a sphere, but the problem is, this code creates only one circle. How can I change it in order to create n circles on the same sphere? Do I have to put ...
13
votes
4answers
219 views

Administrative Divisions bordering a geographic region (e.g. an ocean)

Update 3 I've worked out a solution that is bearable for a small number of subregions in the neighbour and added it as an answer. I'm going to make a post for optimisation help. Update 2 For a ...
19
votes
3answers
1k 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 ...
6
votes
7answers
960 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 ...
7
votes
2answers
141 views

How do I get ConvexHullMesh to return polygons instead of triangle as surface mesh?

I would need to identify the types of regular polygons forming the surface of a convex hull of 3D points. If I e.g. take the following example of a regular polyhedron ...
3
votes
1answer
63 views

MaxCellMeasure fails in 3D?

Question How come MaxCellMeasure works in 2D but fails in 3D? Indeed if I try ...
1
vote
1answer
77 views

How can I plot a sector of an ellipse using the central angle and not the Eccentric Anomaly?

It would appear that the Disk function, when asked to produce the sector of an ellipse between two angles treats those angles as Eccentric Anomalies (i.e. arguments ...
20
votes
7answers
2k views

Find intersection of pairs of straight lines

I have a list of 24 points, in which two consecutive points (1st and 2nd, 3rd and 4th, …) are supposed to form a line: ...
2
votes
2answers
184 views

How do I rotate a curve?

I have a circular segment defined as: ParametricPlot[5 {Sin[ϕ], 1 - Cos[ϕ]}, {ϕ, -0.2, 0.8}, PlotRange -> All] which I have to rotate around point ...