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

1
vote
2answers
122 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 $...
2
votes
1answer
112 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 ...
4
votes
1answer
116 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
65 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
353 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
70 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...
16
votes
3answers
523 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
962 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
119 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
516 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
2answers
141 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
208 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
250 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 ...
1
vote
1answer
51 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
910 views

Determine whether points lie within a cow

I would like to determine whether randomly-generated points ...
3
votes
2answers
126 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
138 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
452 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
234 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
287 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
73 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
136 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
706 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
238 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
348 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
148 views
18
votes
5answers
474 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
221 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
117 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
137 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 ...
16
votes
1answer
223 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
197 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
135 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
81 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
89 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 ...
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: ...
7
votes
1answer
70 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}]] ...
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. ...
12
votes
0answers
90 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
150 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
161 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
126 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
524 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
63 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.: ...