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

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14
votes
3answers
2k views

Fitting ellipse to 5 given points on the plane

Five points are required to define a unique ellipse. An ellipse has five degrees of freedom: the $x$ and $y$ coordinates of each focus, and the sum of the distance from each focus to a point on the ...
12
votes
3answers
920 views

Finding the surface area of a 3D convex hull

I have noted several instances here and here where ConvexHullMesh, introduced in v10 has been used to greatly simplify some geometry problems. Determining the ...
15
votes
3answers
542 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: ...
35
votes
6answers
2k views

Finding length of intersection of two surfaces

I would like to know how we find the length of the intersection of two surfaces. For instance, in the following example,a surface intersects with a plane: How do we find the length of intersection ...
2
votes
1answer
196 views

Plotting a Partially Filled Ellipse

I would like to plot a partially filled/shaded ellipse. The code below shades the whole ellipse. However, I only want to shade the part of the ellipse to the right of the vertical line where x > ...
13
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 ...
29
votes
1answer
786 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 $S^2$ ...
30
votes
5answers
3k views

2D random walk within a bounded area

I want to simulate a random walk on two dimension in a bounded area such as a square or circle. I am thinking of using If statement to define a boundary. Is there a ...
0
votes
1answer
254 views

Is it necessary to introduce ImplicitRegion and ParametricRegion in version 10?

In version 10.0, Mathematica introduced a new function about region plotting: ImplicitRegion. But I'm wondered that haven't this function been already existed in the older version? That is, ...
3
votes
3answers
315 views

Matrix containing ellipse

I have to make a matrix which contains elements in an ellipse shaped region, but I need to make ellipse region in such a way that larger axis of ellipse is inclined with angle θ with horizontal. With <...
8
votes
1answer
623 views

How to generate nonperiodic tilings?

I need to generate nonperiodic tilings which are similar to the attached figure (kite-domino tiling). I was thinking the code is similar to the code for the Penrose tiling. However, that code is too ...
6
votes
1answer
277 views

Generating cylindrical geometry via extruding a section

Toady I want to build geometry as shown below: I know the Mathematica owns the built-in like Cylinder[], Sphere[] and so on, ...
2
votes
0answers
259 views

VoronoiMesh for 3D points

I believe that this is a doc error in V10 (this was programmed to be but not implemented). The new VoronoiMesh should work for 3D set of points. The ...
4
votes
0answers
354 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: ...
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: ...
5
votes
4answers
1k views

An easier way to find the properties of an ellipse from its equation?

In this Q&A about fitting an ellipse to a set of points, there are multiple answers that generated general equations of the ellipse, like this one by @ubpdqn: However, the steps to find out the ...
3
votes
1answer
104 views

Symbolic Output after numerical computation

I have a small question about the symbolic output. I started to write a program that generates the coordinates of n-dimensional polytopes by Wythoff construction. For crystallographic groups, all is ...
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
1answer
146 views

how to find iso-cost contours on a 2d plot efficiently

Consider a 2D plot in which dimension 1 and 2 represent quantity 1 and 2 respectively ranging over 0 to 100. Each point in the space corresponding to (x,y) represent cost of choosing quantity 1 as x ...
3
votes
1answer
396 views

How to map vertex points from the surface of a straight pipe onto 2D plane

How to map vertex points from the surface of a straight pipe onto 2D plane. The 3D surface points of the straight pipe can be found here: data Working code: ...
2
votes
1answer
413 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
161 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
872 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
978 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
866 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
442 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 ...
5
votes
2answers
1k views

Intersection of surface with parallel planes

Consider the code (adapted from here) ...
0
votes
1answer
511 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
162 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 ...
1
vote
3answers
806 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
296 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 $\{t,x,y,z,r,\phi_1,\...
9
votes
2answers
571 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 points,...
0
votes
1answer
288 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 ...
8
votes
1answer
252 views

Law of Cosines to determine angle change along spiral

The Spiral I'm trying to place circles along the outside of an Archimedean spiral. Shown below: ...
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
685 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 + ...
39
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
381 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
713 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
495 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 <...
0
votes
1answer
635 views

Code to give center of circle given three points in 2D? [duplicate]

does anyone know how to make a function C(p1,p2,p3)=center of circle that goes through p1, p2, and p3? This is in 2D Sorry this is poorly written but I ...
9
votes
1answer
809 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
1k 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
760 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, ...
2
votes
1answer
801 views
5
votes
1answer
516 views

How to make a filled Ellipsoid?

I want to make a filled Ellipsoid, but it seems Filling options doesn't work in Graphics ...
14
votes
5answers
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 I still can't make one. I am not looking to make an ...
11
votes
2answers
498 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 ...