Questions on constructing graphical objects using relatively complex computations relating to the mathematical structures defining those objects. Examples include convex hulls, mathematical constructions, symmetries, genuses of curves and graphs and programmatic constructions of polyhedra.

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2
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1answer
542 views

Creating hexahedral finite elements in Mathematica

Is it possible to do FEM using hexahedral elements in Mathematica? If it possible, is there any help to do that?
2
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1answer
341 views

Find area of polygon on a sphere from a set of latitude-longitude points

Given a list of latitude and longitudes say ...
2
votes
1answer
131 views

how to find iso-cost contours on a 2d plot efficiently

Consider a 2D plot in which dimension 1 and 2 represent quantity 1 and 2 respectively ranging over 0 to 100. Each point in the space corresponding to (x,y) represent cost of choosing quantity 1 as x ...
2
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2answers
180 views

Are there built-in functions for testing if a point lies within Graphics3D primitives?

I noticed in this question, Behavior of Graphics`Mesh`InPolygonQ with self-intersecting polygons, that Mathematica has some "psuedo-hidden" functionality for allowing one to quickly perform a winding ...
2
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1answer
65 views

RegionUnion issues with many Regions

The new RegionUnion[] function is just what I needed if only I could get it to work. I have many non-overlapping regions that I will need to use as plotting domains ...
2
votes
1answer
170 views

How to draw a 3D convex hull of a set of points with styling

I´m trying to obtain the convex hull (with transparent faces) of a small number of points. I would like the Plot to have the points shown with small spheres numbers 1, 2, 3, ... along the axes ...
2
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1answer
359 views

Calculate scalar potential from electric field

Is it possible for Mathematica to solve an equation like $\nabla f(\mathbf{r}) = - \mathbf{E}(\mathbf{r})$ for $f(\mathbf{r})$? I tried ...
2
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1answer
160 views

RegionPlot3D run forever when plotting 3D ParametricRegion

when working with 2D, RegionPlot works fine with ParametricRegion as can be seen in this example: ...
2
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1answer
96 views

About TetGenTetrahedralize Mesh Size

I have used TetGenTetrahedralize to generated a cubic mesh. I want that the edge size of the triangle to be 0.2, how can realized this? And What does the word "pq1.414a1" mean? inst1 = ...
2
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0answers
74 views

Defining a region from combination of data and geometric region

I would like to define a region in (x,y) by combining the region RegionPlot[ ImplicitRegion[ Sqrt[x^2 + y^2] <= 0.99, {{x, 0.01, 0.99}, {y, 0.01, 0.99}}]] ...
2
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0answers
147 views

Fitting a rotated ellipse to data points [closed]

I have a bunch of x,y scatter data and I am trying to fit an ellipse through them. I understand that this question has been asked before and there are resources for this, e.g.: Fitting ellipse to 5 ...
2
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1answer
171 views

Distinguishing left from right adjacent triangles in triangle mesh [closed]

What I'm trying to do: I'm trying to create a path-drawing function which will produce a path like the one I-P in the diagram below. The way this path was generated requires me to swap between the ...
2
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0answers
210 views

Death of parallel sub-kernels

EDIT : Finally, the new Mathematica 10.0 seems to fix it. I have a little parallelization problem. I wrote a code to generate a quasicrystal by dynamical generation. Here the code: ...
2
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0answers
44 views

Voronoi diagram for line segments in Mathematica [duplicate]

I know that mathematica has built in functions for creating triangulations and Voronoi diagrams. However I haven't found a function that would create a Voronoi diagram for line segments. Is there a ...
2
votes
0answers
335 views

Visualising Special Relativity

Mathematica newbie learning by doing (or not so far, in this case). Problem: Special Relativity - consider two inertial frames $A$ & $A'$ in relative motion. At a time $t0$ as measured in $S$, ...
2
votes
0answers
209 views

4 circular arcs, how plot the minimal surface?

By using Sjoerd de Vries code for circular arcs: ...
1
vote
2answers
195 views

Rotating a plane about an arbitrary axis

I would like to rotate a plane by $k$ degrees about an arbitrary axis. How should I do it using RotationTransform? hmm i realise if I do the following ...
1
vote
2answers
339 views

intersection between function and plane

I try to solve a ODE system of equations and i want to plot the intersection of the 3D solutions with a costant plane. To do this i use the follow code: ...
1
vote
2answers
565 views

Translating a “Point-to-Triangle” distance script from MATLAB to Mathematica

Update - Thanks everyone for your responses! After fixing a problem with vector normalization, the code below now works. I'm a new user, and I was attempting to port some Mathematica code from ...
1
vote
1answer
389 views

Implementing Central Symmetry

I'm interested in implementing symmetry groups. So it would be useful to have central symmetry (isometry transformation). There are built-in functions: ...
1
vote
1answer
266 views

Code to draw geometry doesn't run

I'm new to Mathematica and have no background whatsoever in programming, although I will teach myself soon. I was wondering if one of you programming pros could help me out. I received a code from ...
1
vote
1answer
174 views

Is it necessary to introduce ImplicitRegion and ParametricRegion in version 10?

In version 10.0, Mathematica introduced a new function about region plotting: ImplicitRegion. But I'm wondered that haven't this function been already existed in the older version? That is, ...
1
vote
2answers
171 views

Only show part of a cube below an intersecting plane

I plot a cube and a plane. I just want to show the part below the plane. The code: ...
1
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1answer
185 views

Complex surface: Finding the perimeter of the union of multiple disc intersections

Consider a system of $N$ circles($N>40$) Each of radius $5$ and the center of these circles along a circle at origin of radius $3$ [as given in code]. Code for above description :- ...
1
vote
1answer
87 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 ...
1
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1answer
90 views
1
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1answer
77 views

How to reconstruct a surface given points {x, y, z} and the surface normals {nx, ny, nz} at these points

I have 3D points above a 2D regular grid. At those points I know the normal vector of the surface. I am looking a command or function in Mathematica, like ...
1
vote
1answer
125 views

how to find the vector intersection in a collection of triangulated 3D points?

I'm trying to calculate the 3D point coordinates for the intersection of a vector with a plane. I have been using the following code to do this: ...
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0answers
46 views

How to speed up geometric Resolve query involving $\exists$ and $\forall$?

I would want to test connectedness of semialgebraic sets with naive code like this: ...
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0answers
100 views

Collision detection algorithm (discrete) with sweep and prune algorithm for periodic boundary conditions

EDIT: Question Updated with solution approach, but solution much slower than original implementation. Any ideas to speed up implementation? In the discussion on collision detection (see here) I asked ...
1
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0answers
71 views

Implementation of Lubaehevsky-Stillinger Algorithm to pack hard spheres

To generate a model of a polycrystalline material with specified grain size distribution (e.g coming from a Monte Carlo Grain Growth simulation) the Paper "Effects of grain size distribution and ...
1
vote
0answers
87 views

Von Neumann's method to generate points uniformly distributed on a region of a n-sphere surface

I am trying to generate points uniformly distributed on a region of a single n-sphere surface (all angles in hyperspheric coordinates are between 0 and Pi/2). I decided to use von Neumann's method ...
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0answers
108 views
1
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0answers
76 views

How can I define a metric in xAct?

I'm using "xAct" package and I want to define a my metric, that is a non standard metric. For example, my metric is diagonal ...
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0answers
69 views

projecting a RegionProduct into 3D space

Apparently, RegionProduct should allow you to generate convolution-generated shapes. For instance, take a 1D curve and a sphere, and the region product I would ...
1
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0answers
74 views

Use of Mathematica to put equation into vector form

Is there a way to put the following equation of a line into vector form using Mathematica (or a Mathematical package)? $\displaystyle ...
1
vote
0answers
176 views

How to define two polyhedron intersect or not?

Recently I have used Mathematica to simulate the concrete structure. The most important point is generate random concrete aggregate. As you know, concrete aggregate can be looked as a polyhedron. We ...
1
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0answers
107 views

Trying to study the three points theorem of the Mobius Transformation

I am trying to study the three points theorem of the Mobius transformation. This theorem says that the Mobius transformation $M$ maps three distinct points p, q, r to three distinct points p', q', r'. ...
0
votes
2answers
322 views

Integrating polynomial functions over polytopes with an add-on package

There is a Mathematica package to evaluate integrals over polytopes: http://library.wolfram.com/infocenter/Books/3652/ In the documentation (Functions.nb file) I ...
0
votes
1answer
35 views

Parse notation recursively

For a special notation I would like to get the help of Mathematica to expand complex expressions through a set of Notation rules. However since this tasks involves applying the notation recursively ...
0
votes
3answers
231 views

Cover a rectangle with size constrained rectangular regions

I have a big grid (indicated on the image in grey) that is divided in several blocks (each with a maximum width of 3 units). Now I would like to divide a region (indicated on the grid in red) by the ...
0
votes
0answers
34 views

Finding intersection of two infinitely long lines using points [duplicate]

EDITED In the Find intersection of pairs of straight lines problem, it is assumed that line are intersected by default and the purpose is to find the intersection points. In the present problem, two ...
0
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0answers
36 views

MaxCellMeasure fails in 3D?

Question How come MaxCellMeasure works in 2D but fails in 3D? Indeed if I try ...
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0answers
43 views

Computing symbolic surface normal of a surface point on a semialgebraic set

Consider a semialgebraic set; such as reg below: ...
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0answers
67 views

Broad Phase Collision Detection with Mathematica and using CUDA

In this and this post, I asked the question about a fast sweep and prune algorithm implementation for broad phase collision detection. To further speed up things a CUDA implementation would be even ...
0
votes
0answers
58 views

How to determine if a point is within a geopositioned RegionMember

I have a KML file which contains an area of interest, I also have a number of lat/long geo positions. I'm trying to filter out the points not within my AOI. So I have my KML file. I convert it to a ...
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0answers
92 views

How to make equidistant or split ListPoint [duplicate]

How to split the curve with more equidistant points? ...
0
votes
1answer
395 views

Area of a convex polygon with a set of points [duplicate]

I have a set of points Pts[a_,b_,c_]:={{a, b}, {b, a}, {c, a}, {a, c}, {b, c}, {c, b}} which define a convex polygon and I would like to find its area. There is ...
0
votes
1answer
212 views