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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Point belonging to a Disk in a Cartesian Coordinate System

The image below represents a human subject fixations while observing this abstract pattern for 3 seconds. I would like to know how much time they spent looking at the actual disk. That is a red point ...
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3answers
306 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: ...
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3answers
1k views

How to create a planar graph from a set of random points

Question Given a set of points in the plane, how can you create a planar graph in the standard graph representation of Mathematica (version 9 or higher), from these points? Background A planar ...
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votes
3answers
618 views

How to measure cross sectional area of Tube

I have modified my question to a simple version. I have vertex clusters, polygons and a list of center points. Attached pts and polygons of 3d tube are: ...
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1answer
386 views

Areas of Voronoi cells from image file

I have an binary image with non-point objects. Does anyone have any suggestions how to determine area of each Voronoi cell in Voronoi diagram (goal is area distribution)? Thank you in advance.
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1answer
270 views

Finding an optimal overlay of two point clouds

Imagine I have two sets of points: ...
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2answers
591 views

How to use a ConvexHull as RegionFunction?

I have a set of data supported over a region in 2D. I want to use RegionPlot and ContourPlot on interpolations of my data, but want to restrict the Plots to the region over which my data is supported. ...
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2answers
197 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 ...
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3answers
171 views

Find Unconnected Subregions

If I have a region, how can I identify sub regions that may be disconnected, if any exist? region defines a rectangular region given two diagonally opposed ...
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3answers
717 views

Triangulated Mesh from Voronoi Diagram

I want to generate a mesh (using Mathematica 10) in the following manner: Generate a Voronoi diagram, like so: and then triangulate each individual Voronoi grain, were an edge is formed by ...
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2answers
128 views

MeshRefinementFunction missing points

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

ListPlot3D of a set of points in a non-convex region

I would like to plot a set of points in the same style as ListPlot3D does, but only in a non-convex region that I can specify (e.g. using a ...
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2answers
222 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 ...
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1answer
173 views

How to fill the closed region by ParametricPlot with solid color?

I am interested in the following implicit curve with parametric equation: $$ \left\{\quad \begin{array}{rl} x=& 9 \sin 2 t+5 \sin 3 t \\ y=& 9 \cos 2 t-5 \cos 3 t \\ \end{array} \right. $$ ...
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2answers
250 views

Extracting ragged array from an image

I have a list of points, which represent positions of peaks in an image. The nature of the image itself shouldn't matter, as I already have the peak positions. As a simple example, consider the ...
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1answer
117 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 ...
5
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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 ...
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1answer
346 views

How can one compute a 3D Periodic Delaunay Triangulation using DelaunayMesh?

Given a non-periodic point set, one can easily tetrahedralize it using the new (in V10) DelaunayMesh function. e.g.: ...
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1answer
177 views

How to create bounded diagram plot?

I have set of points: ...
5
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1answer
159 views

Intersecting cones for weighted Voronoi diagram - DiscretizeRegion was unable to discretize the region

I want to make a diagram (and also a Graph of the vertex + edge config) of the orthogonal projection of the intersections of a set of conical surfaces in order to ...
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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...
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0answers
336 views

Computing Ehrhart's polynomial for a convex polytope

Is there a Mathematica implementation for computing the Ehrhart polynomial of a convex polytope which is specified either by its vertices or by a set of inequalities? I am interested in knowing this ...
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2answers
143 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: ...
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2answers
282 views

Vectors in a spherical shell

I have written code that randomly generates a 3D vector of random magnitude. I now want to create a histogram of how many vectors lie in the concentric spherical shells (n*delta r, (n+1)delta r) ...
4
votes
5answers
910 views

Ordering the Boundary points of a Polygon

I feel like this should be simple, but I keep running into walls. Say someone gives you the coordinates of the vertices of a pentagon and the center point of the hexagon. Is there any way to get an "...
4
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2answers
121 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 ...
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2answers
1k views

How to process .vtk file

I want to extract the cluster of points inside 3D box, is there any way one can do this in Mathematica?
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2answers
153 views

How to take something from DelaunayMesh and similar family of functions

I was looking at this question here and I tried the suggested idea by Anton Antonov to use DelaunayMesh It will look like this: ...
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3answers
313 views

Cut a polygon by a line

I have a polygon, says, Polygon[{0,0},{10,0},{10,10}{0,10}]. I would like to cut it by a line (through two points) and take one half of it. Could you please suggest ...
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1answer
63 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 ...
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2answers
761 views

Image processing: extracting ordered contour

Continuing the question How to extract the edge from a set of points and its answer by Simon Woods, I would like to ask if there is a way to extract the boundary of obtained as ...
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1answer
1k views

How to split compound polygons into convex polygons?

Is it possible to split non-convex polygons into convex plygons with Mathematica 9? For example: ...
4
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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}}]] ...
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1answer
178 views

Problem with clipping of tick labels

Please look at Show[DiscretizeGraphics[Graphics3D[{Cone[]}]], Axes -> True, Boxed -> True] Well, there are some Ticks,...
4
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1answer
223 views

What kind of object results from RegionIntersection function?

I'm trying to use RegionIntersection in a couple of Polygons. The polygons are the following: ...
4
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1answer
128 views

ConvexHullMesh sometimes excludes valid points from convex hull

I have a sequence of polytopes that I am trying to visualize, and I find that ConvexHullMesh sometimes excludes points from the convex hull, and it does so inconsistently. In particular, notice these ...
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1answer
405 views

A Graphics`Mesh`ConvexHull[] peculiarity

I have been unable to explain the behavior of Graphics`Mesh`ConvexHull[] on the following (highly simplified) example: ...
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0answers
84 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 ...
4
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0answers
257 views

Region Intersection for MeshRegion objects embedded in 3D

How can I create a logical intersection of MeshRegion objects that are three-dimensional? The RegionIntersection function will ...
3
votes
3answers
401 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 ...
3
votes
3answers
148 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: ...
3
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1answer
205 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 ...
3
votes
2answers
453 views

Finding if a point is in a region bounded by a curve and the axes (curve made of discrete points)

Here's a small example this is not the real curve but a simple example I made for this question. Here's the plot of a list with a point A of known coordinates. Now I need to find if the point A ...
3
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2answers
286 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, ...
3
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3answers
1k views

How to integrate a function over a 3D planar polygon?

I am trying to integrate a function over a planar polygon in 3D. In 2D, this is fairly straightforward, using either answer from this question (I use the second answer). If we use an equilateral ...
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?
3
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2answers
345 views

Selecting for 2D points that are within a threshold distance of an upper- and lower-bound number of points

I have a very large set of 2D points: numberOf2DPoints = 10^6; pointList = RandomReal[{0, 1000}, {numberOf2DPoints, 2}]; I'd like to find a way to quickly ...
3
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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 ...
3
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2answers
146 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 ...