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

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2
votes
1answer
388 views

Generate a set of 3D coordinates subject to constraints

Generating a set of random 3D coordinates is ok, e.g. ...
16
votes
2answers
1k views

Rebuild a polygon so it doesn't self intersect [duplicate]

If you consider the following Polygon: ...
0
votes
1answer
157 views

Height average between 4 points

I have a $3D$ space, if I had a square in this space: square = {{ 0, 0, 100}, { 100, 100, 50}, { 0, 100, 22}, { 100, 0, 86}}; how could I get the average height ...
6
votes
2answers
840 views

Distribution of 10 points within a unit square

Related to some packing problems, following problem arose: Distribute 10 points within a square of sides 1, so that minimal distance between them is maximized. With the help of random simulation, or ...
5
votes
4answers
949 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: ...
21
votes
3answers
846 views

Creating sculptural forms using graphics primitives

This is a question based on this answer by halirutan. Some amazing images can be created with this code, and I was wondering whether it was possible to extend the principle to different shapes. I ...
8
votes
1answer
427 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
2answers
1k views

Intersection of surface with parallel planes

Consider the code (adapted from here) ...
0
votes
1answer
495 views

Area of a convex polygon with a set of points [duplicate]

I have a set of points Pts[a_,b_,c_]:={{a, b}, {b, a}, {c, a}, {a, c}, {b, c}, {c, b}} which define a convex polygon and I would like to find its area. There is ...
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 ...
1
vote
1answer
161 views

How to get the dimensions of a rectangle?

Suppose I create a Rectangle of dimensions 1 and 3. Is there any function in Mathematica that I can use to recover the dimensions of the original rectangle? If there is no such a function, is there a ...
2
votes
0answers
430 views

Visualising Special Relativity

Mathematica newbie learning by doing (or not so far, in this case). Problem: Special Relativity - consider two inertial frames $A$ & $A'$ in relative motion. At a time $t0$ as measured in $S$, ...
1
vote
3answers
795 views

Draw generalized k-ellipse using “the locus of points so that sum of the distances to the foci is constant” deffinition

My goal is to draw a family (for different distances) of 3-ellipse for equilateral set of foci. 3-ellipse definition is: "the locus of points so that sum of the distances to the three foci is ...
2
votes
1answer
270 views

Extract coefficients of differential form in package RGTC

I am using the Package RGTC to do some calculations in Supergravity. It allows to define differential forms after specifying a co-frame. I am working in with the 10d coordinates ...
9
votes
2answers
536 views

Counting and extracting hit circles/triangles for randomly chosen points

Below, you see a triangle in which the incircle was inscribed. As we know, the center of this circle is the intersection of the angle bisectors. At this point, one could go further and find the ...
0
votes
1answer
282 views

Plotting a line segment from the degenerate case of an ellipse [duplicate]

An ellipse degenerates into a line segment when the defining constant distance from the two foci is the actual distance between the two foci. The ellipse closes into a line segment. The following ...
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 ...
1
vote
1answer
665 views

Plot in a 2-dimensional simplex

I have a row vector as $P=(p_1,p_2,p_3)$ which should be obtained from the following constraints: $a_1p_1 + a_2p_2 + a_3p_3 = b_1p_1 + b_2p_2 + b_3p_3$ ($a_i$'s and $b_i$'s are known) $p_1 + p_2 + ...
36
votes
6answers
3k 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 ...
2
votes
1answer
359 views

Return “true” if point is in Convex Hull [duplicate]

I have a set of points Z: Z = {{x1,y1},{x2,y2},..,} I would like to obtain a function that returns ...
17
votes
2answers
687 views

How to simulate the true reflective movement of a particle bouncing around in an ellipse?

Please help me to simulate the movement of a particle inside a region with elliptical walls such that particle is reflected from the walls and continues to move. A friend was able write code to ...
4
votes
1answer
478 views

Plot a cone in spherical co-ordinates

As we all know in spherical coordinates a function phi = π/3 gives us a cone. The cone makes an angle of π/3 with the imagined ...
9
votes
1answer
790 views

Imposing a Periodic Boundary Condition in Nearest Neighbour Search

I am trying to find first nearest neighbour distributions of randomly dispersed point-like objects in an infinite system. To do this I make a finite sized box unit cell with a chosen concentration of ...
15
votes
1answer
969 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 ...
13
votes
1answer
742 views

Ellipse counting from image

I have hundreds of images similar to this image: I'm looking to count the number of ellipses as well as their major and minor diameters. The ellipses are touching, hence, ...
12
votes
1answer
1k views

Solving Killing equations

Is it possible to solve Killing equations in Mathematica for a general vector? I am looking for a way to create Killing equations and then find what the vectors are, but I have a problem with this. ...
2
votes
1answer
760 views
5
votes
1answer
505 views

How to make a filled Ellipsoid?

I want to make a filled Ellipsoid, but it seems Filling options doesn't work in Graphics ...
11
votes
4answers
2k views

Plotting an epicycloid

I am fairly new to Mathematica and I cannot figure out how to plot an epicycloid. I have plotted some neat looking things in my attempts, but can't make one. I am not looking to make an animation, ...
11
votes
2answers
497 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 ...
5
votes
3answers
242 views

Assumptions for RotationMatrix

I'm making C++ program, and in my program I need a rotation matrix around any vector. I wanted to extract RotationMatrix[fi,{x,y,z}] output and put it in my ...
0
votes
1answer
297 views

Are there built in functions to perform a geometric transform to rotate a set of points around an arbitrary point?

I have a list of points {{4,5},{6,7},{9,8},...} in two-dimensions. I'd like to rotate these points some number of degrees $\theta$ around an arbitrary anchor point ...
1
vote
1answer
196 views

Efficiently determining if a morphological component overlaps a polygon with vertices at real number coordinates

I have a list of morphological components $m$, a set of vertices for a polytope $P$ (at real number coordinates), and I'd like to be able to calculate a list of morphological components $m'$ that ...
3
votes
0answers
220 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 ...
22
votes
4answers
4k views

How do I calculate the area of a polygon given its coordinates?

I have a polygon: Polygon[{{0, 200 }, {200, 100}, {500, 300}, {100, 700}}] How can I figure out its area? The docs page does not have any example. So far I've ...
0
votes
1answer
250 views
1
vote
1answer
329 views

A problem on generating convex hull

For example, I typed the following: ...
6
votes
4answers
1k views

Identifying and counting closely spaced particles

Following in the footsteps of this blog post: http://blog.wolfram.com/2011/09/09/building-a-microscopy-application-in-mathematica/, I took a microscope picture of some particles on a surface, and ...
1
vote
1answer
264 views
8
votes
1answer
314 views

How to compile Heike's winding number function?

Heike gave the following function for winding number: ...
6
votes
1answer
280 views

Generate regularly spaced points from the surface of simplexes

I need to generate regularly spaced samples (points) from the surface of unit simplexes with 2 or greater vertices or end points. I can generate random samples pretty straightforwardly: ...
1
vote
1answer
503 views

Understanding the computation of the geometric median

In the Wolfram Demonstration Fermat Point for Many Points, it appears that the geometric median is being calculated for an arbitrary set of five manipulable points. How might one extend this ...
11
votes
5answers
573 views

How to choose three points on the circle so that the triangle is not a right triangle?

I want to choose three points $A$, $B$, $C$ has integer coordinates on the circle $$(x+2)^2 + (y+1)^2 = 25$$ so that the triangle is not a right triangle. But I can not. I tried ...
4
votes
1answer
895 views

How to draw a Circle in a graph with Log Y Scale

I've programmed drawing tools for graph images and am experiencing a problem with the coordinates of an Ellipse on a graph with a Log Y axis. It's quite easy to work out the Y Axis coordinates for ...
4
votes
2answers
479 views

Create polygon using edge lengths and area

Four-sided convex land plots are usually denoted with edge lengths and area. How do I create a Polygon Object with these parameters in Mathematica ?
8
votes
2answers
927 views

How can I plot a loxodrome?

Can someone show me how to plot a rhumb line (loxodrome) in Mathematica via the ParametricPlot function? Here is what I got so far: ...
0
votes
1answer
485 views

Using LatticeData to fill a space with spheres in a face-centered cubic (fcc) lattice packing arrangement

I have a large sphere of radius $R_1$ which I would like to pack with $N$ smaller radius of radius $r_2<R_1$ arranged in a face-centered cubic (fcc) packing arrangement (i.e. Kepler's optimal ...
6
votes
1answer
991 views

How can I draw a polygon from a set of angles?

In recreational mathematics, polytans are polygons formed by edge-connecting isosceles right triangles. Order-n polytans are those constructed from n such triangles. My question is this: Given a ...
7
votes
4answers
592 views

How can I shorten this code to rotate a line segment around its center?

I have a list of line segments stored in the form: { {{x11,y11},{x12,y12}} , {{x21,y21},{x22,y22}} , ... , {{xn1,yn1},{xn2,yn2}} } Now I want to rotate all of ...
0
votes
0answers
54 views

How to judge if a point is in the interior of a closed curve or not? [duplicate]

For example: pts = {{0, 1}, {-(Sqrt[3]/2), -(1/2)}, {Sqrt[3]/2, -(1/2)}}; trig=JoinedCurve[Line[pts], CurveClosed -> True]; Then ...