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
2answers
321 views

Plane Geometry Diagrams With Labels

I can make some basic diagrams in Mathematica (stolen from their pages, for example see the below: LaminaData["FilledIsoscelesTriangle", "Diagram"] However, I'm ...
2
votes
2answers
135 views

Finding the area bounded by a logspiral curve and two straight lines

I'm facing some trouble with finding the area of a region which is described by x-y coordinates (or line equations) and a curved line represented by logspiral. I tried my best in coming up with the ...
5
votes
3answers
397 views

Finding volume of a segment

I'm still pretty new to Mathematica, so I would like to seek advice regarding a geometrical problem. I am currently trying to define that as an extra condition in the Mathematica code below. ...
7
votes
1answer
165 views

Getting the coordinates of GeoDisk[] and similar Mathematica 10 GeoObjects

I'm a big fan of the new Mathematica 10 geographic capabilities and functions such as GeoDisk[], GeoCircle[] and others. One limitation of these functions, however, is the transformation of the actual ...
0
votes
1answer
234 views

Order contour points in clockwise

I want to describe shape of an object using contour points descriptor. Given a silhouette (image black white of an object), I extrait the contour points using EdgeDetect[] fonction. After that, I need ...
4
votes
3answers
597 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 ...
3
votes
2answers
232 views

Constructing a list of Cartesian coordinates of the Icosahedron

I’m learning Mathematica and I need the coordinates of the Icosahedron vertices. This is my attempt at writing a program for it. The vertex coordinates are simply all cyclic permutations and ...
2
votes
2answers
137 views

Controlling PointSize in a RegionPlot

I have a "named" point in Mathematica 10 and am plotting it like this using RegionPlot: ...
-1
votes
1answer
101 views

Labeling named point in Mathematica 10 [closed]

I have a "named" point in Mathematica 10 defined like this: point["camp location"] = Point[{latitude, longitude}]; I assume there is some way to make the name of ...
0
votes
1answer
189 views

How to construct new geometrical shapes in Mathematica?

In this question of mine I asked for how to implement a 2D random walk within a bounded area. In the provided solution one can use Rectangle[{-10, -10}, {10, 10}] ...
14
votes
3answers
1k 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 ...
11
votes
3answers
783 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 ...
30
votes
6answers
1k 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 ...
0
votes
0answers
28 views

DelaunayTriangulation in Mathematica V 7.01.0 [duplicate]

I have a list of 2D point coordinates in the form of {...,{xi,yi},...} and want to make a triangular mesh for it. By using DelaunayTriangulate function in Mathematica V7, it gives me something that ...
2
votes
1answer
161 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 > ...
11
votes
4answers
921 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
725 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 $S^2$ ...
27
votes
5answers
2k 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 ...
1
vote
1answer
175 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
285 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 ...
7
votes
1answer
324 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 ...
5
votes
1answer
183 views

Construct a function that can generate a geometry by extruding a section

Toady I want to construct a geometry shown as below: I know the Mathematica has the functions like Cylinder, Sphere and so ...
2
votes
0answers
155 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 ...
2
votes
0answers
213 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: ...
3
votes
1answer
90 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 ...
17
votes
6answers
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
131 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
313 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
270 views

Generate a set of 3D coordinates subject to constraints

Generating a set of random 3D coordinates is ok, e.g. ...
13
votes
2answers
996 views

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

If you consider the following Polygon: ...
3
votes
1answer
253 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 ...
0
votes
1answer
129 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
697 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
645 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: ...
18
votes
3answers
723 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 ...
3
votes
2answers
867 views

Intersection of surface with parallel planes

Consider the code (adapted from here) ...
0
votes
1answer
397 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
6answers
661 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
151 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
341 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
485 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
169 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
389 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
247 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 ...
40
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 ...
1
vote
1answer
558 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 + ...
33
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 ...
2
votes
1answer
244 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 ...
14
votes
2answers
512 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
306 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 ...