Questions tagged [geometric-computation]
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31
questions
3
votes
0answers
50 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
votes
3answers
161 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
votes
1answer
98 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
votes
1answer
87 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
votes
2answers
71 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
votes
2answers
299 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
votes
1answer
54 views
Simplify behavior: assumption as Interval versus assumption as bounds
I am using MMA V11.2 under Linux
I am surprised by this:
...
3
votes
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
votes
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
votes
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
vote
1answer
225 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
vote
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:
...
0
votes
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
vote
0answers
79 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
votes
1answer
248 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
votes
2answers
669 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
votes
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
votes
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
votes
1answer
426 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
votes
0answers
90 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
vote
1answer
500 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
votes
2answers
428 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
904 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
votes
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
517 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
votes
2answers
403 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
votes
1answer
228 views
User-defined DistanceFunction for RegionNearest
In the function Nearest , I can define my custom function using the DistanceFunction option. e.g:
...
6
votes
1answer
686 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
votes
2answers
577 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
votes
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
...
