Questions tagged [geometric-computation]

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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 ...