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
votes
1answer
69 views

Clean & efficient bounding box non-intersection test

I would like a quick test to tell me that segments $ab$ and $cd$ cannot intersect in the plane. If the maximum $x$-coordinate of $a$ and $b$ is less than the minimum $x$-coordinate of $c$ and $d$, ...
4
votes
1answer
47 views

DelaunayMesh in a specified closed region

I have a list of discrete points wich I want to use as nodes for creating a 2D mesh. I used DelaunayMesh and it works fine. The problem that I have is that some elements/polygons are outside of the ...
5
votes
1answer
120 views

DiscretizeGraphics and BoundaryDiscretizeGraphics Fail on CapsuleShape and SphericalShell

It seems the new Graphics3D primitives have some incomplete features. Earlier, I uncovered a problem with computing their exact surface area see here. Now, I ...
10
votes
2answers
126 views

Possible Bug in Computing Surface Area of Certain Geometric Regions

Mathematica 10.2 introduced some new geometric regions. Two of the new regions include SphericalShell and CapsuleShape. ...
5
votes
0answers
87 views

Possible Bug with Options in DelaunayMesh

Update: It turns out after some testing, none of the Options work in DelaunayMesh when 3D point sets are involved. Original ...
1
vote
1answer
81 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 ...
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 ...
6
votes
1answer
102 views

Why is RegionMeasure so slow when calculating intersection area of a 2D and a 3D object?

If you think this description is too long, you can read the problem directly I know normally when one wants to calculate an region, this guide is useful. However, when it comes to calculating an ...
3
votes
0answers
58 views

Simple ways to implement vector dilation

Suppose we have a singly connected but not necessarily convex polygon. Something like shape = CountryData["Chad", "Coordinates"]. Is there a simple way to ...
0
votes
0answers
37 views

MaxCellMeasure fails in 3D?

Question How come MaxCellMeasure works in 2D but fails in 3D? Indeed if I try ...
2
votes
1answer
91 views

ToElementMesh fails on DodecahedronIcosahedronCompound

Context I would like to compute the eigenmodes of a DodecahedronIcosahedronCompound. Why? Because it is cool! and I wonder how it rings… Starting with: ...
10
votes
2answers
179 views

How to convert a surface into a solid

Context I am interested in converting surfaces into solids (so I can make a 3D mesh out of them using ToElementMesh) Say I have the following cool surface ...
4
votes
2answers
126 views

ToElementMesh problem on Ball defined by ImplicitRegion?

Could any one please confirm the following bug in mathematica 10.0.2 ? If I define this ball Ω = ImplicitRegion[0 <= x^2 + y^2 + z^2 <= 1, {x, y, z}]; and ...
2
votes
0answers
76 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}}]] ...
9
votes
2answers
141 views

VoronoiMesh without edges

How can I remove the edges of a VoronoiMesh? I would like to display only the closed cells not touching the border of the image. This is my binarized source image (imgbw): I am doing this: ...
3
votes
1answer
79 views

ConvexHullMesh sometimes excludes valid points from convex hull

I have a sequence of polytopes that I am trying to visualize, and I find that ConvexHullMesh sometimes excludes points from the convex hull, and it does so inconsistently. In particular, notice these ...
5
votes
1answer
117 views

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

I am interested in the following implicit curve with parametric equation: $$ \left\{\quad \begin{array}{rl} x=& 9 \sin 2 t+5 \sin 3 t \\ y=& 9 \cos 2 t-5 \cos 3 t \\ \end{array} \right. $$ ...
36
votes
2answers
858 views

Numerically solving Helmholtz equation in 3D for arbitrary shapes

Context While studying manifold Learning I got interested in finding the eigenvectors of the Laplacian. (also in connection to this problem of solving the heat equation) Following this and that ...
3
votes
0answers
91 views

Region Intersection for MeshRegion objects embedded in 3D

How can I create a logical intersection of MeshRegion objects that are three-dimensional? The RegionIntersection function will ...
6
votes
1answer
97 views

Need help on the proper use of a formula to produce a cambered airfoil

Following the book on "The Theory of Thin Wing Sections" page #112 describes the method to combine a camber line (i.e Mean Line) and a thickness distribution to form a cambered wing section. Data ...
0
votes
1answer
37 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
0answers
44 views

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

Consider a semialgebraic set; such as reg below: ...
1
vote
0answers
47 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: ...
1
vote
1answer
90 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 ...
-2
votes
1answer
55 views

Solve on parametric equation produces inequal results

I have a parametric (parameter t) equation in two dimensions (vectors). s = Solve[pt[t] == qt[t], {a, b}] Both pt and qt are parametric lines using a and b as ...
0
votes
0answers
72 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 ...
2
votes
1answer
174 views

Region bounded by Ellipse and Line

I have an ellipse defined either as algebraic or geometric: algebraic: ax^2 + bxy +cy^2 + dx +ey +f = 0 geometric: major Axis, minor Axis, x center, y center, ...
3
votes
0answers
87 views

Differential Geometry on a MeshRegion

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 there somewhere) use it to calculate coordinate ...
1
vote
0answers
102 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 ...
2
votes
3answers
252 views

Surface area of a cylinder [closed]

Evaluating expr = {Sin[t], Cos[t], Sin[p]}; ParametricPlot3D[expr, {t, 0, 2 π}, {p, 0, 2 π}] Area[expr, {t, 0, 2 π}, {p, 0, 2 π}] gives an area of ...
2
votes
2answers
266 views

Finding if a point is in a region bounded by a curve and the axes (curve made of discrete points)

Here's a small example this is not the real curve but a simple example I made for this question. Here's the plot of a list with a point A of known coordinates. Now I need to find if the point A ...
1
vote
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 ...
2
votes
0answers
149 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 ...
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 ...
3
votes
1answer
132 views

Meshing of a cube

I want to mesh a cube and what I use is ToElementMesh[Cuboid[ {-1, -1, -1}, {1, 1, 1}]]. This creates a regular grid of the cube. Is there a way to specify that ...
28
votes
3answers
754 views

Can Mathematica solve Plateau's problem (finding a minimal surface with specified boundary)?

Given a closed curve $\mathcal C$ in three dimensions, is it possible to use Mathematica's built-in functionality to compute a minimal surface whose boundary is $\mathcal C$? For simplicity, let us ...
6
votes
2answers
168 views

Discretizing regions with pointy boundaries

I'm trying to discretize a region with "pointy" boundaries to study dielectric breaking on electrodes with pointy surfaces. So far I've tried 3 types of boundaries, but the meshing functions stall ...
2
votes
1answer
174 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 ...
1
vote
0answers
112 views
1
vote
1answer
91 views
5
votes
3answers
151 views

Find Unconnected Subregions

If I have a region, how can I identify sub regions that may be disconnected, if any exist? region defines a rectangular region given two diagonally opposed ...
1
vote
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 ...
5
votes
2answers
210 views

Extracting ragged array from an image

I have a list of points, which represent positions of peaks in an image. The nature of the image itself shouldn't matter, as I already have the peak positions. As a simple example, consider the ...
25
votes
2answers
325 views

Bug in ArcLength?

fixed in 10.1 (windows) With Mathematica 10.0.2: ArcLength[Line[{{0, 0}, {1, 0}, {2, 0}}]] ArcLength[Line[{{0}, {1}, {2}}]] (* 2 *) (* 2 *) However, ...
4
votes
3answers
262 views

Cut a polygon by a line

I have a polygon, says, Polygon[{0,0},{10,0},{10,10}{0,10}]. I would like to cut it by a line (through two points) and take one half of it. Could you please suggest ...
1
vote
2answers
172 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: ...
8
votes
1answer
129 views

Decomposition of a semialgebraic set into connected components

Is there any built-in function for doing decomposition of a semialgebraic set into connected components? The only way I now can think of is to use ...
5
votes
2answers
149 views

Test existence of a path from one side of a graph to another

I'm trying to determine how I can test if a path exists from one side of a graph to another as efficiently as possible. If I have the Lines given by: ...
6
votes
5answers
1k views

How to check if a line segment intersects with a polygon?

The naive method is to bisect the line segment iteratively as asked here, and then check the bisection points using How to check if a 2D point is in a polygon?. Would there be an other way? I'm ...
6
votes
1answer
208 views

Obtain polygons describing all intersections of many polygons

I have 6894 polygons describing zones in a state plane (i.e., cartesian) coordinate system. Most are not very complex, and I believe none have holes. A random example is Polygon[{{351633., ...