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

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12
votes
0answers
316 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
304 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
251 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
224 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
379 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
124 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
91 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: ...
5
votes
4answers
435 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
62 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
932 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
55 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
149 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
609 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
90 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
104 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
69 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
202 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
165 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
175 views

Implementing AnglePath in Mathematica 10.0

Does anyone have an implementation for AnglePath (see AnglePath Documentation and example usage) in Mathematica 10.0?
44
votes
4answers
2k 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 ...
10
votes
2answers
209 views

How to convert a surface into a solid

Context I am interested in converting surfaces into solids (so I can make a 3D mesh out of them using ToElementMesh) Say I have the following cool surface ...
4
votes
2answers
181 views
14
votes
1answer
890 views

Uniformly distributed n-dimensional probability vectors over a simplex

What's the right way to generate a random probability vector $p={p_1,\ldots,p_n} \in {(0,1)}^n$ where $\sum_i p_i=1$, uniformly distributed over the $(n-1)$-dimensional simplex? What I have is ...
3
votes
1answer
280 views

Visualization of Gaussian Curvature

I need to visualize Gaussian Curvature of a parametric surface. There is a solution in this math.SE post. However, I'm not sure its working because when I draw a sphere it's all white, but it should ...
6
votes
3answers
160 views

Easy way to bind rect to geometrical 2D line?

I got stuck with the following problem. For some calculation and visualization purposes I need to draw different shapes (like rectangle) with proper slope on custom line. The trivial example: ...
11
votes
2answers
495 views

Is there a triangle like this?

I want to find the numbers $a$, $b$, $c$, $d$ of the function $y = \dfrac{a x + b}{c x + d}$ so that the triangle $ABC$ with three points $A$, $B$, $C$ have integer coordinates and lies on the graph ...
7
votes
1answer
127 views

Why is RegionMeasure so slow when calculating intersection area of a 2D and a 3D object?

If you think this description is too long, you can read the problem directly I know normally when one wants to calculate an region, this guide is useful. However, when it comes to calculating an ...
16
votes
2answers
2k views

How do I split up a curve into chords of equal length?

I have a curve that is defined as f[x] and what I'm attempting to do is to divide the curve into equal straight lengths for a number of segments of my choosing that I've defined as nSeg. I've created ...
3
votes
0answers
295 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: ...
0
votes
0answers
37 views

Finding intersection of two infinitely long lines using points [duplicate]

EDITED In the Find intersection of pairs of straight lines problem, it is assumed that line are intersected by default and the purpose is to find the intersection points. In the present problem, two ...
14
votes
6answers
13k views

How to determine the center and radius of a circle given some points in 3D?

I was wondering if anyone could give me a hand with this problem I have. I have six points on a plane, and I am trying to determine if they form a circle or not. I know that any three points in 2D ...
1
vote
1answer
129 views

Calculate area from `RegionPlot` directly

I have a region plot, and I would like to calculate the area: ...
0
votes
2answers
92 views

Draw a vector with mathematica [closed]

at the risk of being trivial I would like to draw the vector $\vec{AB}$ where $A$ an d $B$ have the coordinates $(1,1,1)$ and (1,-1,2) respectively.
2
votes
1answer
172 views

Confusion with SplineFit (Angle calculation)

This question is continuation to this other one I am creating polymers (where each monomer is of equal length) using this method: ...
13
votes
1answer
352 views

How do I create a triangulated surface from points?

I have a set of points in a nx3 matrix and I would like to convert them into a surface, so that I may calculate its surface area. The function ListSurfacePlot3D creates the surface how I want it. ...
2
votes
1answer
68 views

Why are these methods giving me different results? (Trying to test SplineFit)

I am creating a polymer(where each monomer is of equal length) using this method: ...
35
votes
6answers
2k views

How to plot ternary density plots?

How can I get a ternary density plot just like the plots from OriginLab? ContourPlot and DensityPlot seemingly can accept the ...
4
votes
3answers
738 views

Computing Gaussian curvature

Can Gaussian curvature $K$ be computed from WolframAlpha or any other available Mathematica program? Please indicate the program or its reference. If input ...
2
votes
1answer
230 views

Distinguishing left from right adjacent triangles in triangle mesh [closed]

What I'm trying to do: I'm trying to create a path-drawing function which will produce a path like the one I-P in the diagram below. The way this path was generated requires me to swap between the ...
2
votes
1answer
118 views

ToElementMesh fails on DodecahedronIcosahedronCompound

Context I would like to compute the eigenmodes of a DodecahedronIcosahedronCompound. Why? Because it is cool! and I wonder how it rings… Starting with: ...
1
vote
1answer
61 views

Is there a package that can calculate the Ricci tensor from a numerically given metric?

There are many packages about general relativity or differential geometry, and they can calculate the Ricci tensor from a symbolically given metric, for example, $g_{tt}=-f(r)$, $g_{rr}=h(r)$, etc. ...
24
votes
4answers
10k views

How to calculate scalar curvature Ricci tensor and Christoffel symbols in Mathematica?

I am seeking a convenient and effective way to calculate such geometric quantities. I've used packages like TensoriaCalc, but they don't work at all time. ...
6
votes
5answers
534 views

How to draw a dodecahedron with each face modified to a pentagram?

I'd like to draw a dodecahedron with each face carved on the sides so it becomes a pentagram. I wonder how to start to do this kind of task in Wolfram language? Edit: The result should still be a ...
5
votes
4answers
837 views

Distance between two line segments in 3-space

I need to compute the distance between two line segments in a project. After googling, I found this algorithm and used it to implement a Mathematica version: ...
29
votes
1answer
760 views

Proving the hairy ball theorem using xAct

I would like to formally prove the hairy ball theorem in Mathematica, initially just for $S^2$, and then see about generalizing. An approach I thought about to use the xAct package to define $S^2$ ...
43
votes
6answers
2k views

Generating evenly spaced points on a curve

In the KnotData package a simple command such as points = Table[KnotData[{3, 1}, "SpaceCurve"][t], {t, 0, 2 Pi, 0.1}]; will ...
0
votes
2answers
297 views

Projection of triangles onto a sphere

I am trying to find the solid angle taken up by a large set of triangles around a central point. I have normalized the vertices of the triangles to a unit sphere around the central point, But the ...
9
votes
2answers
198 views

The envelope of a set of translated and rotated ellipses

I achieve a dynamic graphics by using Manipulate as follows: ...
2
votes
1answer
183 views

Calculate the total length of line segments within polygon

So we have a polygon with N vertices located on grid. All vertices are located at the intersection of cells (so their coordinates are integers). The objective is to calculate the total length of line ...