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

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4
votes
1answer
107 views
1
vote
3answers
108 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
78 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
519 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
62 views

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

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
111 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
168 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
92 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
384 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
125 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
40 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
151 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
102 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
73 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
550 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
216 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
334 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: ...
8
votes
1answer
449 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 ...
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 ...
14
votes
4answers
250 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
1k 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
178 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
74 views

MaxCellMeasure fails in 3D?

Question How come MaxCellMeasure works in 2D but fails in 3D? Indeed if I try ...
1
vote
1answer
97 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
224 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 ...
13
votes
0answers
414 views

Circle with negative radius?

Why does this work: Graphics[{Circle[{0, 0}, -Pi/4]}] But this doesn't? Graphics[{Circle[{0, 0}, N[-Pi/4]]}] Telling me: ...
11
votes
2answers
324 views

How to make geometric intersection faster for geographic borders?

I have developed a solution to identify geographic regions bordering a region in this post (94723). Can this functionality be made to execute any faster? Find which entities in a set border other ...
5
votes
3answers
356 views

Rotating a circle about a larger circle

I've got some wonderful answers this morning on Mathematica Stack Exchange. See Diagonals of a regular octagon and Determine the height of a box packed with spheres. I'm just smiling with the amount I ...
6
votes
2answers
294 views

Diagonals of a regular octagon

We had a little activity after school today and one of the questions was: All diagonals are drawn in a regular octagon. At how many distinct points in the interior of the octagon (not on the ...
10
votes
2answers
396 views

Determine height of box packed with spheres

I got such a wonderful answer regarding The Diagonals of a Regular Octagon, so I thought I'd try asking another question we had on our Pizza and Problem quiz activity at College of the Redwoods. The ...
0
votes
1answer
141 views

4D rotations of 600-cell to make cell centered stereographic projection

I have made a 600-cell wireframe model from Eric Weinsteins' 2/13/14 600-cell notebook (600-cell: a regular polytope, 4D, analogous to the icosahedron, with 600 tetrahedral cells, 120 vertices, 720 ...
1
vote
1answer
93 views

Recursive calculation is very slow

I've got a recursive definition of Arcs that shares equal length and a several other dependencies to each respective predecessor. (Imagine a book being bent.) I formulated all necessary things here: ...
11
votes
1answer
210 views

Is DiscretizeRegion not yet ready ro discretize 3D-solids?

In the DiscretizeRegion documentation: "The region reg can be anything that is ConstantRegionQ and RegionEmbeddingDimension less than or equal to 3." With DiscretizeRegion there could be an easy way ...
5
votes
4answers
456 views

Minimal overlap area of circles

I have 20 points in the 2D plane with $(x_i,y_i)$ coordinates. I want to use Mathematica to optimally distribute 10 circles with equal radius of a given positive value $R$, i.e. to determine with the ...
3
votes
1answer
68 views

Area of a surface spanned by 2 parametric curves

I would like to find the area of a surface spanned by two parametric curves in 3D. I came up with this metric for distance between curves. The illustrations are in 2D for simplicity. ...
7
votes
4answers
1k views

How to find all data points within closed curve

I want to find all data points inside curve as given below: ...
1
vote
0answers
67 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 ...
4
votes
1answer
165 views

How can I truncate only a single vertex of a polygon?

One can truncate all the vertices of a polygon at once with Truncate. I want to do exactly that -- but only on a single vertex. Is this possible with Mathematica 9? ...
6
votes
9answers
627 views

Plotting a sequence of isosceles triangles of diminishing size

I try to plot the following graph using Graphics and Table. The graph consists of infinitely many isosceles triangles (without ...
1
vote
1answer
101 views

Create region from set of lines and arcs [duplicate]

I have a shape that is a knuckle plate with two holes cut in it, thus: ...
2
votes
3answers
120 views

Create region from polygons and tangential line segments

I have two circles and tangential line segments that I want to define a region: ...
-2
votes
1answer
79 views

Distance of a point from a line using multiplicative distance [closed]

How can we determine the multiplicative distance (http://link.springer.com/article/10.1007/s10115-014-0813-4#page-1) of a point (x0,y0) from a line (ax+by+c=0)? Let X = (x_1, x_2 ..., x_m) be a ...
6
votes
2answers
251 views

ToElementMesh problem on Ball defined by ImplicitRegion?

Bug introduced in 10.0 and fixed in 10.2 Could any one please confirm the following bug in mathematica 10.0.2 ? If I define this ball ...
4
votes
3answers
197 views

How to find points along the inner and outer edge of a ring along a specific direction

I have a set of random numbers distributed on a annular disk. I want to find points on the inner and outer edge along a particular angle. One possibility is to use ...
4
votes
2answers
177 views

Implementing AnglePath in Mathematica 10.0

Does anyone have an implementation for AnglePath (see AnglePath Documentation and example usage) in Mathematica 10.0?
46
votes
4answers
3k views

Create a torus with a hexagonal mesh for 3D-printing

I am new to Mathematica, and I'm looking for a way to create patterns on the surface of 3D objects. One thing I have not been able to do is to create a hexagonal mesh on a torus. What I would like to ...