Questions tagged [geometric-computation]

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1answer
80 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. ...
3
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0answers
53 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: ...
3
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3answers
167 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 ...
5
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1answer
100 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. ...
3
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1answer
88 views

RegionUnion for 3D Regions

I make two regions and then find I can't combine them using RegionUnion. Here are the two regions. ...
2
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2answers
72 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 ...
6
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2answers
302 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 ...
5
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1answer
56 views

Simplify behavior: assumption as Interval versus assumption as bounds

I am using MMA V11.2 under Linux I am surprised by this: ...
3
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1answer
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) ...
5
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0answers
72 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 ...
3
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0answers
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 ...
1
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1answer
232 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 ...
1
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1answer
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: ...
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0answers
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 ...
1
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0answers
80 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 ...
12
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1answer
249 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 ...
13
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2answers
677 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 ...
0
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0answers
79 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 ...
6
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1answer
127 views

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

Consider two definitions of a cubic region, ...
7
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1answer
431 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: ...
3
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0answers
91 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 ...
1
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1answer
509 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 ...
7
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2answers
436 views

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

I am interested in the following implicit curve with parametric equation: $$ \left\{\quad \begin{array}{rl} x=& 9 \sin 2 t+5 \sin 3 t \\ y=& 9 \cos 2 t-5 \cos 3 t \\ \end{array} \right. $$ ...
1
vote
1answer
923 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,...
3
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0answers
155 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 ...
6
votes
1answer
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 ...
7
votes
1answer
518 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 ...
12
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2answers
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: ...
8
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1answer
230 views

User-defined DistanceFunction for RegionNearest

In the function Nearest , I can define my custom function using the DistanceFunction option. e.g: ...
6
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1answer
693 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.: ...
11
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2answers
578 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 ...
20
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1answer
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 ...