Questions on constructing graphical objects using relatively complex computations relating to the mathematical structures defining those objects. Examples include convex hulls, Voronoi diagrams, Delaunay triangulations, mathematical constructions, symmetries, genuses of curves and graphs and ...

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17
votes
3answers
480 views

How to compute the boundary of a group of ellipse efficiently?

Update1 I discovered that the bountary of a series of ellipses consists of the following three parts Part (I): the first ellipse's effective black-segment; Part (II): the effective ...
2
votes
0answers
49 views

Are the triangles in DelaunayMesh oriented ccw?

MeshCells[R, 2] returns the triangles from R=DelaunayMesh[pts], where pts is a list of 2D ...
0
votes
0answers
3 views

Query about hyperplane in SVM [migrated]

I am a beginner in Machine Learning. I was reading through basics of SVM and read this definition: The goal of a support vector machine is to find the optimal separating hyperplane which ...
6
votes
2answers
132 views

Voronoi diagram using RegionPlot, using the hyperbolic metric

I want to compute the Voronoi diagram on the unit disk, using the hyperbolic metric. So, I want to input a list of points and obtain a plot of the cells associated with each of the points. I defined ...
6
votes
6answers
694 views

How to find the vertices of a regular tetrahedron? a dodecahedron?

My question is: how to find the coordinates of the vertices of regular tetrahedron and dodecahedron? I tried to find the coordinates of the vertices of a regular tetrahedron as the solutions of a ...
2
votes
1answer
129 views

How could I make visible the convex hull of 3 point inside this region?

Small version of the question How can I control the color and the Thickness of this graph?? ...
10
votes
3answers
227 views

How to describe the convex hull of a set of points as an implicit region for optimization?

Last edit: 2016-05-03 A.G.'s answer was the one helped me the most, see explanation at the end of this question. Original question In Mathematica you can create out of a set of points in 2D and 3D ...
15
votes
3answers
339 views

Find duplicates in list of InfiniteLine

MMA 10 introduced a new function, which can be very convenient: InfiniteLine. Of course, two infinite lines can be described by different arguments: for example ...
3
votes
3answers
138 views
5
votes
0answers
50 views

How to find the concave points of a point-set?

To solve the boundary of a set of planar geometry, I sampled $6$ graphs, then using RunnyKine's approach. ...
6
votes
2answers
107 views

How to generate higher dimensional convex hull?

I like the function ConvexHullMesh very much, since I often need to take a look at the convex hull of points in 2D and 3D, which as an example can be generated and ...
18
votes
5answers
466 views

Is there a numerical method/built-in to calculate the boundary of a set of graphs?

Recently, I encounted a geometry problem in my work. For a curve-family that owns the following parametric equation: $$E(t,\theta)= \begin{pmatrix} x_E(t,\theta) \\ y_E(t,\theta) \end{pmatrix}$$ ...
6
votes
4answers
217 views

Getting ordered coordinates out of ConvexHullRegion

I'm trying to get the ordered coordinates of a convex hull using MeshCoordnates[ConvexHullMesh[data]], but the coordinates are uselessly out of order: ...
9
votes
2answers
115 views

The theory/algorithm knowledge behind the built-in Discretize* and Boundary*

The ComputationalGeometry package was built-in in V10 distribution. In classical computational geometry field, the following questions were investigated. Convex ...
8
votes
2answers
131 views

How to assign Element marker at boundary edges

How to assign marker at the boundary edges as 1, 2, 3, 4 respectively and set all of the inside elements of region as 0? for example: Code: ...
35
votes
3answers
1k views

Can Mathematica solve Plateau's problem (finding a minimal surface with specified boundary)?

Given a closed curve $\mathcal C$ in three dimensions, is it possible to use Mathematica's built-in functionality to compute a minimal surface whose boundary is $\mathcal C$? For simplicity, let us ...
16
votes
1answer
220 views

Possible Bug in ArrayMesh

Bug introduced in V10.4 and fixed in 10.4.1 Suppose we have the following array from which we intend to create an ArrayMesh: ...
21
votes
0answers
194 views

Regression /Bug in DelaunayMesh from 10.3.1 to 10.4

Bug introduced in V10.4 and persists through 10.4.1 In answering this question, I realized the OP and I were obtaining different results from the alphaShapes2D ...
10
votes
0answers
133 views

Interesting Progression of ParametricRegion: Bug?

Bug persisting through 10.4.1 Consider the following ParametricRegion from an answer to this question: ...
8
votes
0answers
79 views

Defining a MeshRegion from a list of points and Polygons with duplicate points does not work in 10.4

Bug introduced in 10.4 and persists through 10.4.1 This code produces a MeshRegion in versions 10.0 through 10.3.1, ...
9
votes
1answer
88 views

MeshCoordinates from a RegionBoundary no longer in proper order in version 10.4

Bug introduced in V10.4 and persists through 10.4.1 Given that I have the following data set ...
8
votes
0answers
97 views

Is this a bug in DiscretizeRegion in 10.4?

Bug introduced in 10.4 and persists through 10.4.1 Consider the following implicit region: ...
7
votes
1answer
64 views

DiscretizeRegion fails for a triangular region

I define an implicit region like R = ImplicitRegion[ 0 < Sin[u]/Cos[v] < 1 && 0 < Sin[v]/Cos[u] < 1, {{u, 0, 2}, {v, 0, 2}}] But when I ...
3
votes
1answer
55 views

Confused about the behavior of the properties of Regions

Actually we can get some information in here.But I'm confuse this phenomenon still: test = ConvexHullMesh[RandomReal[1, {7, 2}]] ...
0
votes
1answer
51 views

Simulating a Boolean model in a uniform square

I am looking to simulate a Boolean model with specified Poisson point process. ...
12
votes
0answers
79 views

What is a robust way to determine if two polygons overlap? Possible bug in RegionIntersection or Area

When trying to determine if two polygon objects overlap, I think the intuitive way to do this would be to use the RegionIntersection function to find the ...
7
votes
1answer
136 views

How to convert a graph to a mesh region

As we know,the region is very convenient in Mathematica.And we can convert a MeshRegion into graph like this ...
12
votes
1answer
158 views

RegionNearest and neighborhoods

In this previous question we see that RegionNearest isn't quite as 'capable' as Nearest for some things. Similarly, I need to ...
3
votes
0answers
125 views

Differential Geometry on a MeshRegion [closed]

NB- see this question for a more formal request. For many many years (honestly, since 1987) I've had my own MMa computational geometry code for dealing with 3D meshes. I principally (there's a joke ...
21
votes
4answers
510 views

Find the volume of Phobos and Deimos

How can we calculate the volume of a 3D object using the new-in-10 computational geometry functions? For simple objects this works: ...
2
votes
1answer
59 views

Partition a line around intersections

I've got a bunch of lines (ideally in a single Region) as well as a single new line, e.g.: ...
8
votes
1answer
176 views

Why RegionDifference cannot work normally?

Bug introduced in 10.0 and fixed in 10.4 Given that two polygons regions as below: ...
7
votes
3answers
386 views

Finding the two points on a heart-shaped curve which have maximal distance between them

The question originates from Max & min distance between two moving points. I think it can be solved easily because of the function is a parametic function. My heat-shaped curve is given by ...
7
votes
0answers
81 views

RegionIntersection: Point or Line?

This may be a minor point, but I'm wondering why RegionIntersectionof the two rectangles below gives 3 Lines rather than 2 Lines and 1 Point. ...
17
votes
6answers
931 views

Is there a simple strategy to determine whether a point is inside a boundary?

For a ellipse $E(\theta)$, which owns the parametric equation as follows: $\begin{cases} x = a \sin\theta + b \cos\theta + c \\ y = d \sin\theta + e \cos\theta + f \\ \end{cases}$ Now, I have a ...
4
votes
2answers
117 views

Arc length parameterization of a list of points?

Suppose I have a curve represented by a list of points in the form $\{\{x_0, y_0\}, \{x_1, y_1\}, ...\}$. How to generate a list of numbers $\{s_0, s_1, ...\}$ where $s_i$ is the distance of ith point ...
1
vote
1answer
56 views

Angles inside of Voronoi mesh cells

How can I determine the angles belonging to the vertices of each interior Voronoi mesh cell? ...
3
votes
2answers
137 views

Connecting the points surrounding the adjacent polygons

I'm trying to connect the points surrounding the adjacent polygons. I know how to find the adjacent polygons on a Voronoi mesh. However, I'm unable to adjacent of the adjacent polygons. What I'm ...
6
votes
1answer
182 views

How to draw Kobon triangles

I would like to know if Mathematica is capable of constructing Kobon triangles; that is, a figure consisting of the largest number of non-overlapping triangles that can be constructed using $n$ lines, ...
5
votes
3answers
300 views

Removing cells from Voronoi mesh if they exceed a certain area or circumference

I start with the example in Finding the perimeter, area and number of sides of a Voronoi cell with RunnyKine's answer: ...
11
votes
1answer
140 views

How to make a two letter monogram in 3d like the one on www.mymo.is? [duplicate]

I want to achieve the same effect like the project on http://www.mymo.is/. By taking two letters and combine them in 3d, you can get a complex shape that looks like one letter on the one side and the ...
4
votes
2answers
125 views

Color code Voronoi cell areas depending on number of vertices

The following question is similar to Colouring points in a Delaunay Mesh by the number of nearest neighbours ... but I do not know how adapt this answer to my problem. I have the following image: ...
8
votes
2answers
292 views

DelaunayMesh in a specified closed region - creating a concave hull from a set of points

I have a list of discrete points wich I want to use as nodes for creating a 2D mesh. I used DelaunayMesh and it works fine. The problem that I have is that some elements/polygons are outside of the ...
126
votes
4answers
18k views

How to create word clouds?

Word clouds are rather useless fancy and visually appealing plots, where words are plotted with different sizes according to their frequency in a corpus. Many applications exist out there (Wordle, ...
6
votes
0answers
134 views

Possible Bug with Options in DelaunayMesh

Bug introduced in 10.2 and persisting through 10.4 Update: It turns out after some testing, none of the Options work in ...
7
votes
1answer
413 views

Smooth convex hull of a large data set of 3D points

I recently needed to deal with a large data set of 600.000 points in three dimensions. My task was to find a convex hull for this data. I have Mathematica 10, so I could use the function ...
19
votes
6answers
492 views

Find the nearest locations for multiple points

Assume that there are many holes with their locations fixed, and the same number of balls distributed randomly. What is the smallest total distance for the balls fitting into the holes on the ...
5
votes
2answers
214 views

RegionPlot of ImplicitRegion is incorrect

Bug fixed in 10.4. Why does RegionPlot of the ImplicitRegion give an incorrect plot? Also, will how does this affect ...