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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13
votes
3answers
242 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
120 views

How to obtain the coordinates of the intersection line of two surfaces?

I can plot the intersection line of two surfaces $f$, $g$ by using: ...
-2
votes
0answers
28 views

how to know two aircraft getting far away each other? [on hold]

Dataset: my algorithm is: calculate velocity vector each aircraft ...
5
votes
0answers
41 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. ...
7
votes
3answers
134 views
+200

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

In Mathematica you can create out of a set of points in 2D and 3D the convex hull and use it as a region for optimization problem, e.g., ...
6
votes
2answers
96 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 ...
6
votes
4answers
213 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: ...
6
votes
1answer
62 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
53 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
50 views

Simulating a Boolean model in a uniform square

I am looking to simulate a Boolean model with specified Poisson point process. ...
9
votes
2answers
108 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
118 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: ...
11
votes
0answers
74 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 ...
12
votes
1answer
151 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 ...
12
votes
1answer
164 views

How to solve the boundary of a group of curve-segments via the simple rule?

Update The problem that I encountered is how to trim the un-effective curve automatically. An ellipse $E_0$ was generated at monment $t_0$, which was splitted by two critical point $\theta_0^1$ ...
7
votes
0answers
91 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
0answers
78 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, ...
7
votes
1answer
126 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 ...
8
votes
1answer
81 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 ...
16
votes
1answer
215 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: ...
2
votes
1answer
57 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.: ...
3
votes
1answer
89 views
7
votes
1answer
173 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
0answers
79 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
922 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 ...
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: ...
4
votes
2answers
113 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
51 views

Angles inside of Voronoi mesh cells

How can I determine the angles belonging to the vertices of each interior Voronoi mesh cell? ...
21
votes
0answers
191 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 ...
3
votes
2answers
129 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 ...
18
votes
5answers
448 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: $$E(t,\theta)= \begin{pmatrix} x_E(t,\theta) \\ y_E(t,\theta) \end{pmatrix}$$ ...
5
votes
3answers
296 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
128 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
115 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: ...
7
votes
3answers
376 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 ...
2
votes
1answer
126 views

MeshRegion: How to take out a subregion

I have this application at hand: I need to find the Voronoi Regions of a finite set of point and then i have to find the center of mass of each of these Voronoi regions for a given mass distribution. ...
5
votes
2answers
110 views

MeshRefinementFunction missing points

I'm doing some FEM on a rectangular region with a spherical cavity: ...
3
votes
1answer
195 views

How to calculate a Delaunay mesh nerve?

How to calculate a Delaunay mesh nerve? A Delaunay mesh nerve is a collection of triangles that surround a single triangle called the nerve nucleus. The triangles in a Delaunay mesh nerve either have ...
14
votes
1answer
302 views

GeoGraphics : path within a country

I am using GeoGraphics to visualize electricity distribution networks in certain countries. I have susbtation location data, as well as network incidence matrices ...
4
votes
0answers
73 views

ParallelTable slow down, Region functions

I am experiencing speed issues with ParallelTable. There are a few related problems on SX posted here and here, but no resolution. The various respondents to those ...
3
votes
3answers
235 views

Help with finding the point(s) inside a closed shape with the highest average ray length?

I am trying to find the point(s) with the highest average ray length of any implicit relation that is closed shape (ex. $x^2+y^2+\sin(4x)+\sin(4y)=4$). I have some idea of how to mathematically ...
12
votes
3answers
453 views

How to find the outline of a country given the imperfect outlines of its administrative subdivisions?

I have a larger outline divided into several regions. While my data represents something else, let us think of this as the provinces/counties of a country, for the sake of simplicity. This is, for ...
5
votes
2answers
189 views

Separate boundaries of multiply connected region

I have a multiply connection two-dimensional region such as the following: br = BoundaryDiscretizeGraphics@Graphics[Disk[#, 8/9] & /@ CirclePoints[9]] I am ...
5
votes
2answers
205 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 ...
14
votes
2answers
237 views

Why is DiscretizeGraphics missing points on my curve?

I have a graphics expression which renders nicely as a closed curve when put in Graphics, I don't understand why I can't get the lines from DiscretizeGraphics or ...
5
votes
1answer
107 views

Minimal perimeter of all possible polygons

We had a fun problem for a student activity today: Let $P(z) = z^8 + \left(4\sqrt{3} + 6\right)z^4 - \left(4\sqrt{3} + 7\right)$. What is the minimum perimeter among all the $8$-sided polygons in the ...
13
votes
2answers
359 views

How to determine whether a point is within a polygon in Mathematica 10

In Mathematica 9, I was able to use the function Graphics`Mesh`InPolygonQ to determine whether a given point was within a polygon. How do I do this in Mathematica ...
3
votes
3answers
371 views

intersection between polygon. Algorithm to check it [closed]

I'm working on an algorithm which should check if two polygons, described by their vertex coordinates, are: one inside the other, are intersecting or are separated image below describe this three ...
6
votes
1answer
93 views

Expensive MeshRefinementFunction

I want to discretize a region using DiscretizeRegion. Now, I want the mesh to be more refined, when the curvature of a certain function ...
6
votes
1answer
181 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, ...