# Tagged Questions

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 ...

256 views

### 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 ...
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: ...
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 ...
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: ...
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.
270 views

### Finding an optimal overlay of two point clouds

Imagine I have two sets of points: ...
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. ...
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 ...
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 ...
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 ...
128 views

### MeshRefinementFunction missing points

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

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

I am interested in the following implicit curve with parametric equation: $$\left\{\quad \begin{array}{rl} x=& 9 \sin 2 t+5 \sin 3 t \\ y=& 9 \cos 2 t-5 \cos 3 t \\ \end{array} \right.$$ ...
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 ...
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 ...
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### Are the triangles in DelaunayMesh oriented ccw?

MeshCells[R, 2] returns the triangles from R=DelaunayMesh[pts], where pts is a list of 2D ...
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.: ...
177 views

### How to create bounded diagram plot?

I have set of points: ...
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 ...
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...
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 ...
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: ...
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) ...
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 "...
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 ...
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?
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: ...
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 ...
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 ...
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 ...
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: ...
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}}]] ...
178 views

### Problem with clipping of tick labels

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

### A GraphicsMeshConvexHull[] peculiarity

I have been unable to explain the behavior of GraphicsMeshConvexHull[] on the following (highly simplified) example: ...
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 ...
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 ...
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 ...
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: ...
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 ...
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 ...
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, ...
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 ...
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?
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 ...