# Questions tagged [geometric-computation]

The tag has no usage guidance.

33 questions
Filter by
Sorted by
Tagged with
186 views

### Getting cell edges from a picture

I would like to write a program that, given a picture of an epithelium (2D cell array), for example automatically detects the cell edges and returns the corresponding lattice. Illustratively, ...
608 views

### Probable Bug in ConvexHullMesh

Bug introduced in 10.0 and persisting through 10.2 or later Consider points taken from the following parametric plot. See this question ...
95 views

### RegionDifference not working properly for a region from a printable STL file

Some time ago I created a printable STL-file with a certain software of my own and now I want to modify it with Mathematica programmatically, mainly by subtracting certain geometric objects (e.g. ...
176 views

### Cutting a section from a sphere by planes

I want to plot and find out the section of a sphere remaining after putting constraints in terms of cartesian planes. How it can be done? For example, if I have a sphere of $r = 1$, and I put the ...
60 views

### Symbolic formula from GeometricScene?

I'm trying to solve the following problem with GeometricScene What is the shortest circular arc of which the altitude above its chord is one? I have the following code: ...
111 views

### Construct a section (or slice) through 3D Regions

I would like to draw a section through some 3D regions. I start by making some simple 3D regions as a minimum working example. ...
99 views

### RegionUnion for 3D Regions

I make two regions and then find I can't combine them using RegionUnion. Here are the two regions. ...
131 views

### Is there any way to improve the result of DiscretizeRegion on this 3D ImplicitRegion?

Consider two definitions of a cubic region, ...
73 views

### How to output the level of the contour plot based on the desired area enclosed in the contour level?

I am a beginner using Mathematica. I am doing a physics experiment that involves this 3D surface; the function $f(x, y)$. I need a program that can give me the contour level in the $z$-axis which ...
308 views

### How do I verify a vector identity using Mathematica?

I am trying to verify well known Frenet–Serret formulas in general setting using Mathematica. I need to consider a general space curve $r(s)=(x(s),y(s),z(s))$ in $\mathbb{R}^3$ and define its unit ...
57 views

### Simplify behavior: assumption as Interval versus assumption as bounds

I am using MMA V11.2 under Linux I am surprised by this: ...
40 views

### Plot variations in geometric sum within prescribed range

I have a simple geometric sum: Sum[a^(j + 1), {j, 1, k}] which evaluates to (a^2*(-1 + a^k))/(-1 + a) ...
480 views

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

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

### ReflectionTransform gives different colors

Consider this example of the cow cow = ExampleData[{"Geometry3D", "Cow"}, "GraphicsComplex"]; p = {0, 0, -0.25} Compare the rotation and reflection ...
72 views

### Better discretization for intersections of algebraic surfaces

I am looking for better, preferably analytical approaches to discretize intersections of algebraic surfaces. When surfaces are not identical, these solutions are either curves or points. An extremely ...
248 views

### integral over a region boundary

I want to integrate a complex function over a boundary of a region: $$-\frac{i}{v}\oint_\Gamma \exp(-2\pi i(ux+vy))\,dx,$$ where $\Gamma$ is the closed boundary of a region and $y = f(x)$. I know ...
86 views

### Unexpected behaviour of MomentOfInertia

The problem I expected Mathematica to solve rather easily is that of the calculus of a moment of inertia of a "c" section defined by the following Polygon: ...
26 views

### ImplicitRegion RegionPlot fails for circle in 10.4.1 [duplicate]

This must have worked at some point, because the documentation for ImplicitRegion has the right picture. But when I evaluate ...
81 views

### Find best convex approximation of an “almost convex” function

I've got values of a function of two variables at integer points inside a rectangle, that is, a rectangular table $f(i,j)$, $1\leqslant i\leqslant m$, $1\leqslant j\leqslant n$. The function is very ...
253 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 ...
156 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 ...
701 views

### How to mesh a region using adaptive cubic elements

Assume a list of {x,y,z} coordinates. The coordinates are arranged in a regular fashion through a fixed raster size (called ...
81 views

### Minimization with constraint define over a region

I would like to perform a 2D electrostatic minimization between two charged ellipsoids, provided that they should not penetrate each other; they can touch but they are hard ellipsoids. Here is what I ...
435 views

### Alternative to the DiscretizeRegion?

I have a polygon: pgn = Polygon[{{0, 0}, {0, 0.018}, {0.155, 0.018}, {0.155 + 0.015, 0.008}, {0.222, 0.008}, {0.222, 0}, {0, 0}}]; here: ...
94 views

### Convexity Coefficient Calculation

I would like to probabiistically estimate the convexity coefficient of a MeshRegion, described as - Given a region $\mathscr{K}$, calculate the probability that ...
528 views

### How to plot and find the volume of a solid enclosed by surfaces? [closed]

I'm a beginner with both Mathematica and multi-variable calculus. I want to plot and find the volume of the solid enclosed by the surfaces defined by \begin{eqnarray} x^2+y^2 = & 4 \cr x-y+2z ...
406 views

### Possible Bug in DiscretizeRegion with Option MaxCellMeasure

Bug introduced in 10.0.0 and fixed in 10.0.2 Consider the following ImplicitRegion: ...
957 views

### Package for symbolic computation of christoffel symbols and parallel transports in Riemannian geometry, given the metric

I've no knowledge in mathematica (but I do in matlab), but I'd really appreciate if someone could mention what is/are the best and easy to learn mathematica package(s) for symbolic and numerical (both,...
185 views

### Numerical Functions Compatible with Regions Fail with MeshRegions and BoundaryMeshRegions

Bug introduced in 10.0.0 and fixed in 10.0.2 Given a MeshRegion: region = DelaunayMesh[RandomReal[1, {50, 3}]] We can ...
527 views

### How do I get a MeshRegion from an obj file, or from Geometry3D

How do I read in an obj file as a MeshRegion so I can e.g. compute its area? If I just import the object and try Area[O] it ...
2k views

### Faster way to compute the distance from a point to a surface in 3D

I am trying to compute the shortest distance between a point and a triangle in 3D ...