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

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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
425 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
780 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 ...
1
vote
0answers
246 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
513 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
279 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
657 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
354 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
659 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
464 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
780 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
953 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
734 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
703 views
5
votes
1answer
499 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
240 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
284 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
194 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
217 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
324 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
263 views
8
votes
1answer
313 views

How to compile Heike's winding number function?

Heike gave the following function for winding number: ...
6
votes
1answer
279 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
500 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 ...
10
votes
5answers
571 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
880 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
477 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
909 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
481 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
981 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
590 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 ...
6
votes
1answer
174 views

Why is FindInstance failing when I relax a set of constraints?

I'm attempting to use FindInstance to generate coordinate sets for plausible triangles with edge length distance constraints. E.g.: ...
4
votes
1answer
210 views

Is there a fast way to trilaterate a point?

I have a point in 2D or 3D space at an unknown coordinate, $p_0$, and I'd like to determine its position using distances from known coordinates $(p_1, p_2, p_3)$. Beyond using ...
5
votes
2answers
721 views

Triangle mapped on a sphere in $\mathbb R^3$?

How can I map a triangle on a sphere? I want to visualize (plot or animate) it for my student in Non-Euclidean geometry. I have no restrictions on the triangle's kind or on the sphere in $\mathbb ...
0
votes
3answers
244 views

Cover a rectangle with size constrained rectangular regions

I have a big grid (indicated on the image in grey) that is divided in several blocks (each with a maximum width of 3 units). Now I would like to divide a region (indicated on the grid in red) by the ...
8
votes
2answers
445 views

How to punch a hole in some 3D distribution of points

Suppose we have a long list of 3D Cartesian coordinates, defining a distribution of random points in 3D space. How could we remove all the points inside a sphere of radius ...
0
votes
0answers
78 views

How to define the tangent gradient operator? [duplicate]

I would like to define a new differential operator that is the tangent gradient for a curve $\Sigma$. This is defined as $$\nabla_\Sigma=\mathbf{P}\nabla$$ where $\mathbf{P}$ is the projection ...
6
votes
2answers
2k views

Calculating a minimum bounding box for a set of 3-space coordinates / spheres

I have a set of 3-space coordinates for the atoms of a molecule (I could also transform them into spheres with radii corresponding to the atoms they represent). I would like to place this molecule ...
22
votes
7answers
3k views

Distance between point and line segments

How would you determine the shortest distance between a point and one or more segments? For example, what is the shortest distance between the point and the two segments below? Clearly the point is ...
2
votes
1answer
686 views

Drawing a quadrilateral inscribed within a circle

I would like to draw a quadrilateral inscribed within a circle. How can I construct this figure, taking into account arbitrary (specified) side lengths, while still ensuring that the vertices of the ...