Questions tagged [geometric-computation]
The geometric-computation tag has no usage guidance.
47
questions
2
votes
3answers
111 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 ...
1
vote
4answers
140 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 ...
1
vote
0answers
35 views
Normal of Translate works in 3d but not 2d [duplicate]
Edit: in light of these links, I suppose I'm beating a dead horse here. Normal is inconsistent, that's not technically a bug, just slightly disappointing
Why doesn&...
1
vote
0answers
44 views
RandomInstance of GeometricScene producing unexpected result
Consider the following scene as an example:
...
0
votes
0answers
93 views
1
vote
0answers
44 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 ...
1
vote
2answers
60 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 ...
5
votes
1answer
188 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
...
0
votes
0answers
91 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 ...
7
votes
4answers
646 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 ...
4
votes
2answers
339 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 ...
2
votes
2answers
73 views
How to speed up finding region centroid and plot3d
I have the following code to make 3D of 9 regions.
...
2
votes
1answer
162 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 ...
0
votes
0answers
43 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 ...
-1
votes
1answer
91 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 ...
7
votes
1answer
336 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,
...
1
vote
1answer
204 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. ...
4
votes
3answers
313 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
249 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
173 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
97 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
380 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 ...
6
votes
1answer
89 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
48 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
82 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
81 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
391 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
92 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
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
...
1
vote
0answers
101 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
282 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 ...
16
votes
2answers
818 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
87 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 ...
5
votes
1answer
142 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
471 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
114 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
744 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
738 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
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,...
3
votes
0answers
167 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
196 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
583 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 ...
13
votes
2answers
437 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
251 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
797 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.:
...
14
votes
2answers
631 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
...
