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 ...

learn more… | top users | synonyms

10
votes
2answers
125 views

Converting Graphics geometry to a Graph

I need a representation of a 3D Sierpinski Gasket in a form of a graph to perform some simulations on. The 2D version is included in Graphdata[] but the 3D one is nowhere to be found, so I was ...
4
votes
1answer
54 views

Does mathematica have a k-furthest neighbors?

I'd like to pick k points from a set of points in n-dimensions that are maximally apart. What is the simplest way to do this? Example: ...
3
votes
1answer
86 views

Why does RegionUnion fail for these Regions?

Bug introduced in V10.0 and persisting through 10.4.1. Introduction Lately, I asked for a solution to inflate and unite a List of BoundaryMeshRegions: Inflate ...
6
votes
3answers
109 views

Inflate and unite a list of 0D to 2D regions

I've got a List of BoundaryMeshRegions, created via ConvexHullMesh: ...
3
votes
1answer
117 views

Find biggest Circle having all points close to a List of Polygons

Setting Imagine a List of polygons polys (type: BoundaryMeshRegion, polygons may also overlap): ...
3
votes
3answers
180 views

Remove inner points from collinear List

Imagine a List of Points that is collinear: {{-1,-1},{1,1},{0,0},{-2,-2},{1,1}} How can I at first check, if such a List is collinear and if so, reduce it to ...
1
vote
0answers
48 views

ConvexHullMesh fails for collinear points

I've got a List of PointLists, of which some contain only collinear points. I now want to obtain all ConvexHullMeshes of my PointLists. For more than two ...
4
votes
2answers
79 views

Union of a List of ConvexHullMesh

How can I create a Union of a List of several ConvexHullMesh? My List is of variable length and the containing BoundaryMeshRegions may overlap. I want to create ...
3
votes
1answer
64 views

ConvexHullMesh fails with small numbers

When I try to get the ConvexHullMesh of a List of points that are "small scale", I get errors: ...
1
vote
0answers
51 views

Line-crossing Algorithm Implementation (pt. 2) [closed]

This is a continuation of the problem I posted earlier with the line-crossing algorithm that I tried to implement in Mathematica. I took Kuba's suggestion, removing the underscore on everything ...
1
vote
1answer
67 views

Deleting circular regions from a larger Circle

I am trying to determine how the Dirichlet eigenvalues of the Laplacian of a circular region change. I would calculate the principal eigenvaluen of this image, and gradually decrease the radius of the ...
1
vote
1answer
71 views

Defined a function but it doesn't seem to work

I'm trying to implement the line-crossing algorithm on Mathematica and I seem to be having trouble getting it to work. More specifically, I would like to know what is causing the function to not ...
4
votes
1answer
83 views

How to calculate the area of all the subareas in a mesh?

I have used Voronoi mesh to generate a mesh of a group of random numbers, pts = RandomReal[{-1, 1}, {8, 2}]; mesh = VoronoiMesh[pts] So, it will generate a graph ...
1
vote
2answers
149 views

Distance between rectangle and parametric curve

Given a 2D parametric curve $(x(s), y(s))$ and a rectangle where each of the four vertices is parameterized $(x_i(t), y_i(t))$, $i \in \{1,2,3,4\}$, how can Mathematica compute the distance function $...
5
votes
0answers
73 views

How-to derive conical region in an arbitrary geometry?

Description I have been working with derived geometric regions and ran into a problem when deriving RegionIntersection of a Cone...
3
votes
1answer
155 views

Finding area of intersection regions

I want to be able to find the area of the intersection between a hexagon and a slice. I have tried RegionMeasure or Area but I ...
17
votes
3answers
552 views

How to speed up estimation of Mean and Gaussian curvatures on triangular meshes?

I am trying to estimate curvatures on a triangulated surface/manifold using the algorithm of : Meyer, M., Desbrun, M., Schröder, P., & Barr, A. H. (2003). Discrete differential-geometry operators ...
3
votes
1answer
120 views

The unexpected behavior of region calculate

In my this answer,I get some overlapped disk like this placed with red arrow point out But actually that function of diskMake is designed to produce ...
6
votes
3answers
215 views

Can one use MeshRefinementFunction to obtain a nonobtuse triangulation?

I have a planar convex polygonal region Rc. I would like to triangulate it such that every triangle is nonobtuse. I was hoping that the ...
8
votes
2answers
142 views

Inscribed square problem

There is a well-known unsolved problem in geometry: $\textbf{Toeplitz' conjecture}:$ Every continuous simple closed curve in the plane contains four points that are the vertices of a square. ...
2
votes
1answer
58 views

How to get coordinates from GeometricTransform?

I'm trying to get the exact coordinates of the resulting points from my transform: ...
19
votes
2answers
932 views

Determine whether points lie within a cow

I would like to determine whether randomly-generated points ...
3
votes
2answers
135 views

Visibility Graph of Polygon

Could anyone provide a function that takes a polygon as input and outputs its visibility graph ? Visibility Graph If not, is there a function that checks whether a line segment lies inside a polygon?
5
votes
1answer
76 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 ...
6
votes
2answers
139 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 ...
15
votes
3answers
351 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
159 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: ...
10
votes
3answers
244 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 ...
6
votes
3answers
167 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
225 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: ...
7
votes
1answer
73 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
58 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}]] ...
1
vote
1answer
53 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
118 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
148 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: ...
12
votes
0answers
95 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
164 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 ...
17
votes
3answers
518 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 ...
9
votes
0answers
107 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: ...
8
votes
0answers
82 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
165 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 ...
9
votes
1answer
90 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
258 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
65 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
109 views
8
votes
1answer
188 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
85 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
967 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 ...
11
votes
0answers
138 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
124 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 ...