# Questions tagged [regions]

Questions about functionality that defines or operates on regions (i.e., an open, connected set), including geometric, mesh-based, or data and formula-defined regions.

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### Eccentricity of an ellipse

I would like to calculate the eccentricity of the intersection between a cylinder and a plane when I change their relative orientation. ...
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### How do I properly define and work with region unions?

Suppose I have two regions defined by two hexahedrons (slightly adapted from this question): ...
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### calculate the flux of a vector field through a surface

How to calculate the flux of a vector field through a surface in mathematica? I've this field: F = (x, x^2 * y, y^2 * z) and this surface: ...
127 views

### Region and DiracDelta

The following integral evaluates as expected to 1: Integrate[ DiracDelta[x, y], {x, -1, 1}, {y, -Sqrt[1 - x^2], Sqrt[1 - x^2]}] However, if we use a Region, the ...
118 views

### Checking Membership in Boundary of Conical Hull

I want to check whether a given point is also a member of the edges of a given conical hull. For example, I have: ...
141 views

### Colorize a Region

My searches have lead nowhere on this one. I have a MeshRegion (say, a 2D manifold embedded in 3D) and would like to plot a function on it: such that the color of a ...
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### How to draw this three-dimensional implicit region?

I want to draw the surface of the upper half of the sphere $z = \sqrt {4 x - x^2 - y^2}$ inside the cylinder $(x - 1)^2 + y^2 = 1$ . ...
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### Analytical Solution to Laplace over Irregular Domain using DSolve

I would like to find an analytical solution to a Laplace equation over the following irregular domain using a mix of Dirichlet and Neumann boundary conditions. I've spent a lot of time trying to use ...
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### ContourPlot3D in a Cube region creates just an opaque cube

I tried the following code ContourPlot3D[x^2 + y^2 + z^2 == 1, {x, y, z} \[Element] Cube, RegionBoundaryStyle -> None] And I got only this opaque cube. So I ...
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### Turn a region and points inside that region into a mesh

I have a region defined by a polygon and a few points that are inside that region. I'd like to create a mesh where its boundary is the boundary of the region and the vertices interior to the mesh are ...
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### Why can't I evaluate this bivariate definite integral?

I want to directly use the x function to find the exact value of the following bivariate definite integral: ...
108 views

### Result of Integration over ImplicitPlot not as expected

Edit 1: Issues seem to emerge from within ImplicitRegion as well as Region Plot. Using $Surd[y^{2},{3}]$ or avoiding $y^{2/3}$ ...
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### How to find the shortest distance between two regions?

I need to find the shortest distance between the two regions and the two points of the shortest distance, but the following code cannot achieve this requirement: ...
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### For an enclosed surface region, how to find the furthest point on that surface to another point that is not on that surface?

I have an enclosed 3D surface (a distorted sphere surface region, which is got by finding an enclosed contour of a 3D volumetric data, and apply RegionBoundary[BoundaryDiscretizeGraphics[ ]] to get ...
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### Find the intersection coordinate of a line and a 3D surface defined by a contour plot

I have two points, for instance {1, 1, 1} and {10, 11, 15} that connected to form a line. I also have an enclosed surface region ...
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### RandomPoint fails for any higher dimension

region = ImplicitRegion[x^2 + y^2 + z^2 + p^2 == 1, {x, y, z, p}]; RandomPoint[region] The result is RandomPoint[ImplicitRegion[x^2 + y^2 + z^2 + p^2 == 1, {x, y, z, p}]],and how can I attain two ...
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I want to solve the following problem in Mathematica: Assume that $\lambda_2=-\frac{1}{2}+ r+\frac{1}{1+r}- r^2\log\frac{1+r}{r}$, $v\in[0,1]$ and $\theta\in[0,1]$. For pre-specified values of $k,r>... 0answers 52 views ### RegionIntersection and ListSurfacePlot3D I have a 3D surface and I am trying to find the intersection of this and some line. I have a list of list of three dimensional points (I don't know if the way these are generated is important but we ... 1answer 36 views ### Region measure of a list of points [closed] Regardless of the coordinate values of the points, the output of RegionMeasure is the same, e.g: ... 1answer 31 views ### Why RegionPlot does not show the negative part of a function? I have this function$$f(x)=\frac{1-25 x^2}{\left| 25 x^2-1\right| }\;\frac{2500 x}{\sqrt{\left(25 x^2-1\right)^2 \sinh (\pi x)+9}}+\cosh ^{-1}\left(\frac{1000 x^2+\left(25 x^2-1\right)^2}{\left(25 ... 2answers 101 views ### How to display full 3D region? Answers to an earlier posting, ConvexHullMesh inconsistency, have let me construct a particular 3D region by intersecting a pyramid with a halfspace: ... 1answer 95 views ### ConvexHullMesh inconsistency I am seeing an inconsistency in ConvexHullMesh that I don't understand. Here is Rhull = ConvexHullMesh[pts8] where the$8$... 1answer 120 views ### Furthest point from nearby objects, packing a sphere on a region interior Suppose I have a boundary$\partial\Omega$of a region$\Omega\subset \mathbb{R}^3$and within this are some compact objects$B_i\subset\Omega$. They could be points, lines, polygons, complex 3D ... 2answers 56 views ### How to discretize the boundary of two regions? Problem How to discretize a surface constructed with multiple components? Unsuccessful attempts include combining the objects top and ... 1answer 52 views ### RegionProduct to extrude a 3d volume with thickness variation RegionProduct[] is very useful when one intends to extrude a 2d region into 3d: ... 0answers 43 views ### Computing iterated region integrals A lot of work has been put into region integrals in Mathematica but it is hard to understand from the documentation what is "best practice" in using it. Here is a simple integral that has ... 1answer 111 views ### How to distribute points on a Sphere[] cap from a normal distribution? I was wondering if one could distribute points on a "cap" of a sphere, following a normal distribution of the points instead of a uniform distribution. This normal could be centered at the ... 1answer 45 views ### VoronoiMesh with boundary edges removed I would like to create a Voronoi diagram without the boundary edges highlighted. This code gVD = VoronoiMesh[X, MeshCellStyle -> {{1, All} -> {Thick, Red}}] ... 0answers 47 views ### DiscretizeRegion is not working properly with Graphics3D I have a 3D object and I would like to remove everywhere except a part with a circle shape. Here is the 3D object ... 0answers 28 views ### Extract data from ConvexHullMesh [closed] I have a ConvexHullMesh and want to extract the bounding points. I am familiar with using Cases to extract data from plots but ... 0answers 36 views ### Should behavior of Cube[] and Cubeoid[] be the same in these cases? While attempting to export a symbol with head Region (or Graphics3D) as an OBJ file, I run in to problems using Cube[] that are not readily apparent with ... 1answer 99 views ### Finding lower boundary of a 3D object in list format I have the following point list and would like to find the points located in the lower boundary of the 3D object (It is part of a body torso). https://pastebin.com/L12n0Gfr I am using the following ... 2answers 101 views ### How to get the area of ImplicitRegion 3d object ImplicitRegion[z >= x^2 + y^2 && x^2 + y^2 + z^2 <= 6, {x, y, z}] // RegionBoundary // Area This code returns ... 0answers 18 views ### How to generate a region with a finite width/height on say$ y $-direction, but infinite on$ x \$-direction?

I want to use such a region as an Epilog in other figures. I have tried with HalfPlane, thinking ...
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### How-to extract a region from a ListContourPlot?

Question How could I extract a surface from the ListContourPlot and use it to sample data? Below is the plot, and the code used to generate it. The ...
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### Define a Region where a disequation is satisfied for all values of a variable

I'm having a problem with Mathematica. I have a large and complicate system of 3 inequalities in 3 variables, let's call them x,y,z. Now, I can't use reduce to solve it exactly. There is a way to ...
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### Using RegionPlot with NDSolve

So I have a DE which has no analytical solution and thus solved using NDSolve, involving some parameters like this: ...
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### How to Parallel submit nested do loop

This is the first time I'm trying to parallel compute something on Mathematica. So this question might be silly. I have a nested Do loop of the form: ...
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### Problem with Region Intersection

I have two regions defined as ImplicitRegion[]. ...
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### Problem NIntegrating over 3D Polygon region with 4 points

I am trying to NIntegrate a non-planar polygonal region defined by 4 points, something like this: ...
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### Computing volume of intersection of two regions

I am trying to compute the volume of intersection of the following two regions: ...
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### Hyper Tetrahedron in terms of inequalities

The command Tetrahedron[] seems to work fine for the 3-d case. But how can we get hyper-tetrahedron for 4-d case in terms of inequality? Take for example the points: ...
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### Region bounded by planes in terms of inequalities

Suppose I have 5 planes that intersect to give a bounded region in 4D. For example, the planes are x1==0; x2==0; x3==0; x4==0; x1+x2+x3+x4==1; ...
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### Convert ConvexHull in a array to Inequality

This question is in continuation with the previous post Convert ConvexHull to Inequality There are two problems that I faced. Suppose we have two or more convex hull defined using an array R[i], like ...
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### Convert ConvexHull to Inequality

I have the following convex hull. P0={0,0,0}; P1={1,0,0}; P2={0,1,0}; P3={0,0,1}; ConvexHullMesh[{P0,P1,P2,P3}] Now I want the region algebraically as equality ...
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### RegionResize works improperly with different digital accuracy

The data is copied from the output cell of my original data. ...