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

13
votes
3answers
470 views

Converting a Sierpinski tetrahedron 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 ...
1
vote
0answers
24 views

Having a 2D Parametric Function Wrap Around a Geometric Region

I am trying to study curves on the flat torus (the unit square where opposite edges are identified with each other) and I was wondering if there is a simple way for me to take a parametric curve that ...
7
votes
1answer
95 views

How to efficiently implement k-FN (k-Furthest Neighbors)?

I'd like to pick k points from a set of points in n-dimensions that are approximately "maximally apart" (sum of pairwise distances is almost maxed). What is the simplest efficient way to do this? For ...
3
votes
1answer
94 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): ...
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 ...
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 ...
4
votes
2answers
81 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: ...
16
votes
1answer
259 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: ...
3
votes
1answer
157 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 ...
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
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
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 ...
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, ...
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 $...
4
votes
1answer
119 views

Defining a region from combination of data and geometric region

I would like to define a region in (x,y) by combining the region RegionPlot[ ImplicitRegion[ Sqrt[x^2 + y^2] <= 0.99, {{x, 0.01, 0.99}, {y, 0.01, 0.99}}]] ...
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 ...
14
votes
3answers
366 views

How to convert a surface into a solid

Context I am interested in converting surfaces into solids (so I can make a 3D mesh out of them using ToElementMesh) Say I have the following cool surface ...
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...
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 ...
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 ...
2
votes
1answer
138 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?? ...
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 ...
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 ...
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. ...
6
votes
3answers
216 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 ...
7
votes
3answers
256 views

Lloyd relaxation on VoronoiMesh

How can we apply Lloyd's relaxation algorithm to a VoronoiMesh? Thanks. UPDATE Thanks a lot KennyColnago for your answer. Based on Simon Woods suggestion of ...
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
935 views

Determine whether points lie within a cow

I would like to determine whether randomly-generated points ...
3
votes
2answers
136 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?
6
votes
3answers
168 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 ...
2
votes
2answers
463 views

Convert DelaunayTriangulation-> Graph->AdjacencyMatrix

Is there a way to convert a Delaunay Triangulation into a Graph structure so that one can generate an AdjacenyMatrix of the Delaunay?
1
vote
3answers
242 views

Only show part of a cube below an intersecting plane

I plot a cube and a plane. I just want to show the part below the plane. The code: ...
3
votes
2answers
292 views

Region bounded by Ellipse and Line

I have an ellipse defined either as algebraic or geometric: algebraic: ax^2 + bxy +cy^2 + dx +ey +f = 0 geometric: major Axis, minor Axis, x center, y center, ...
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 ...
6
votes
6answers
710 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 ...
10
votes
3answers
245 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
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
160 views
18
votes
5answers
481 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
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: ...
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
149 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: ...
36
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 ...
21
votes
0answers
206 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 ...
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: ...