Questions tagged [geometric-computation]

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GeometricScene doesn't quite work in v13.0.1

I used GeometricScene in v12.x quite a bit in some project and although the feature was experimental it was reliable before. I recently upgraded to v13.0.1 and had ...
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1 vote
1 answer
90 views

Understanding GeometricScene [closed]

I tried to expand a simple geometric scene: RandomInstance[GeometricScene[{a, b, c }, { Triangle[{a, b, c}]}], 1] works fine and shows the triangle. But if ...
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2 votes
1 answer
63 views

Minimize relating a geometric test

I want to find a circle with a center and a radius that includes all given points, like a circumscribed circle for the points. points data: https://www.dropbox.com/s/0unlv1vbngopu38/new_ref.txt?dl=0 ...
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2 votes
3 answers
117 views

Find sum of positive geometric progression numbers

I have a task to get the total number of games played in a soccer tournament. Apart from the group stages, I observed that the number of games played in each round from the knockout round down to the ...
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1 vote
4 answers
208 views

Given three points in space, find center of circle [duplicate]

Given the coordinates of three points in space, {x1,y1,z1}, {x2,y2,z2}, {x3,y3,z3}, how can ...
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1 vote
0 answers
60 views

RandomInstance of GeometricScene producing unexpected result

Consider the following scene as an example: ...
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0 answers
98 views

Why the output is not in numerical form in Mathematica 12.2?

Consider the following code: ...
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2 votes
0 answers
56 views

GeometricScene extremely slow or cannot complete

I would like to find instances of the following dodecahedral wheel generalized to the situation where the red squares become rhombuses. I tried this using RandomInstance[GeometricScene], but ...
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1 vote
2 answers
91 views

Exact symbolic area of an intersection of two regular pentagons with parameters

The question of finding the area of intwrsection of two regions with parameters has been answered here using and RegionIntersection with delimeter ...
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  • 185
5 votes
1 answer
209 views

Exact symbolic area of an intersection of two polygons with parameters

On the one hand, can handle expressions which include parameters, including polygons, for example: Area[Polygon[{{1, 2}, {-1, 1}, {2, 5}, {1, a}}]] returns ...
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  • 185
0 votes
0 answers
116 views

Surface area of a list of points

I would like to know how I can get the area of the following point list. I am using the following script to make a mesh region and then find the area. However, the area is much larger than the value ...
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7 votes
4 answers
827 views

Find smallest distance from a point to a Bézier curve

I wish to find the smallest distance from a point to a curved defined via a Bézier function. I want to do this automatically. For particular cases it is not to difficult. Here is a minimum working ...
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4 votes
2 answers
356 views

Finding shadow area of a 3D object

Given a 3D object, how could one find the area of the shadow? In effect, this is a measure of optical cross section. The ultimate goal would be a table showing latitude, longitude, and, optical cross ...
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2 votes
2 answers
83 views

How to speed up finding region centroid and plot3d

I have the following code to make 3D of 9 regions. ...
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2 votes
1 answer
200 views

Periodic boundaries for a 3D walk in a Bravais lattice?

I'm using a Bravais lattice, 'face-centered', which is implemented in Mathematica in LatticeData[]. I want to simulate a random walk over neighboring points using ...
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  • 1,303
0 votes
0 answers
47 views

Torus Hex Mesh - Need Unique Hex Dimensions

I'm looking to laser cut a bunch of hexagons and assemble them into a torus (using hot glue or tape). How do I get the dimensions of the individual unique hexagons? I've seen Create a torus with a ...
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-1 votes
1 answer
125 views

How to wrap any function/curver around a circle? [closed]

I have a function defined as $y=f(x)$ which i want to wrap around a circle, to get a transformed function $r=f(ϕ)$. It is important that the length of the wrapped curve stay's the same. For two ϕ ...
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7 votes
1 answer
487 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, ...
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1 vote
1 answer
264 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. ...
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4 votes
3 answers
386 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 ...
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  • 973
5 votes
1 answer
325 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. ...
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  • 14.5k
3 votes
1 answer
212 views

RegionUnion for 3D Regions

I make two regions and then find I can't combine them using RegionUnion. Here are the two regions. ...
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  • 14.5k
2 votes
2 answers
111 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 ...
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6 votes
2 answers
418 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 ...
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  • 359
6 votes
1 answer
129 views

Simplify behavior: assumption as Interval versus assumption as bounds

I am using MMA V11.2 under Linux I am surprised by this: ...
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3 votes
1 answer
50 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) ...
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5 votes
0 answers
87 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 ...
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3 votes
0 answers
84 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 ...
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1 vote
1 answer
450 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 ...
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1 vote
1 answer
97 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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  • 2,058
0 votes
0 answers
28 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 ...
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  • 5,559
1 vote
0 answers
107 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 ...
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12 votes
1 answer
317 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 ...
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16 votes
2 answers
864 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 ...
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0 votes
0 answers
94 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 ...
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  • 249
5 votes
1 answer
151 views

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

Consider two definitions of a cubic region, ...
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7 votes
1 answer
490 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: ...
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3 votes
0 answers
125 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 ...
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  • 1,760
1 vote
1 answer
863 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 ...
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  • 11
7 votes
2 answers
861 views

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

I am interested in the following implicit curve with parametric equation: $$ \left\{\quad \begin{array}{rl} x=& 9 \sin 2 t+5 \sin 3 t \\ y=& 9 \cos 2 t-5 \cos 3 t \\ \end{array} \right. $$ ...
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1 vote
1 answer
1k 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,...
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  • 111
3 votes
0 answers
174 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 ...
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  • 1,760
6 votes
1 answer
203 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 ...
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  • 32.5k
7 votes
1 answer
604 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 ...
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  • 73
13 votes
2 answers
460 views

Possible Bug in DiscretizeRegion with Option MaxCellMeasure

Bug introduced in 10.0.0 and fixed in 10.0.2 Consider the following ImplicitRegion: ...
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  • 32.5k
8 votes
1 answer
257 views

User-defined DistanceFunction for RegionNearest

In the function Nearest , I can define my custom function using the DistanceFunction option. e.g: ...
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  • 83
6 votes
1 answer
837 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.: ...
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  • 32.5k
14 votes
2 answers
650 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 ...
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  • 32.5k
20 votes
1 answer
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 ...
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