Tagged Questions

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.

0answers
34 views

Returning a non-degenerate list of triangles that (strictly) define the outer mesh of a 3-polytope using PolyhedronData?

I'm looking for a simple method of returning a list of triangles that strictly define the outer surface of a 3-polytope using PolyhedronData? For example: ...
2answers
135 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 ...
6answers
286 views

How do I draw a hemisphere?

I want to draw a solid or partially transparent hemisphere above a partially transparent cuboid object in Graphics3D. However, I do not know how to do this s.t. only half the sphere is drawn. Here's ...
0answers
78 views

Does anyone have any suggestions how to determine equal size Voronoi cells in a Bounded Voronoi diagram? [closed]

Does anyone have any suggestions how to determine equal size Voronoi cells in a Bounded Voronoi diagram? [The answer for Finding the perimeter, area and number of sides of a Voronoi cell was ...
2answers
305 views

Graphics3D: Finding intersection of 3d objects and lines

I found these two nice links 1) intersecting graphics 2) Implementation of Balaban's Line intersection algorithm in Mathematica which works for 2d. However, I need to find whether a ray(line) ...
0answers
77 views

Determining if a point is inside or outside a 3DS (.3ds) or 3DS MAX (.max) object?

Imagine I import some 3DS (i.e. 3D studio) file (http://reference.wolfram.com/mathematica/ref/format/3DS.html) or a 3DS MAX file. How could I place this model (say, the 747.3ds file in the ...
1answer
214 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?
2answers
155 views

Create a planar graph from a set of random points

A planar graph is a graph embedded in the plane in such a way that the edges intersect at vertices. This is an example of a planar graph: g = GridGraph[{3, 3}] ...
3answers
144 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 ...
3answers
644 views

Creating a 2D meshing algorithm in Mathematica

As what is proving to be a difficult, but entertaining task, I am attempting to adapt a 2D meshing algorithm created for MATLAB and port it to Mathematica. I understand meshing functions already exist ...
2answers
277 views

Create triangular mesh from random list of points

I have a list of points. I would like to take these points and create a mesh of triangles from them, making sure triangles don't overlap. So here's a list of points: ...
2answers
202 views

Equidistant points on a polyline

Set of 2D-points connected by a polyline B-spline function: ...
2answers
252 views

Convex hull of a 3D object?

I am trying to find a convex hull command for a Graphics3D object. Does it exist in Mathematica? ...
0answers
147 views

How to make 3D object smooth?

This thread considers mathematical methods here to make the 3D object smooth but this question consider how to achieve the goal of smoothing a 3D object in Mathematica. I want to get smoother ...
0answers
90 views

Computing Ehrhart's polynomial for a convex polytope

Is there a Mathematica implementation for computing the Ehrhart polynomial of a convex polytope which is specified either by its vertices or by a set of inequalities? I am interested in knowing this ...
1answer
72 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 ...
2answers
245 views

Calculating a minimum bounding box for a set of 3-space coordinates / spheres

I have a set of 3-space coordinates for the atoms of a molecule (I could also transform them into spheres with radii corresponding to the atoms they represent). I would like to place this molecule ...
5answers
588 views

Voronoi diagrams for generators other than points

Any suggestions how to determine Voronoi diagram for sites other than points, as e.g. in the picture below? Input is a raster image.
1answer
188 views

Finding the perimeter, area and number of sides of a Voronoi cell

Does anyone have any suggestions how to determine the perimeter, area and number of sides of each Voronoi cell in Voronoi diagram?
1answer
170 views

A GraphicsMeshConvexHull[] peculiarity

I have been unable to explain the behavior of GraphicsMeshConvexHull[] on the following (highly simplified) example: ...
3answers
419 views

Efficiently determining if 3D points are within a surface composed of polygons

This is the 2nd part of a previous question which I edited to make into 2 separate questions: Extracting polygons from 3D contour plot surface As an extension of my earlier question involving simple ...
1answer
278 views

Extracting polygons from 3D contour plot surface

Edit: This question turned out to be two parts so I am going to make this question about only the first part a kguler provided an excellent answer. Here is a better representation. My actual data ...
0answers
100 views

Has anyone implemented cohomology for complex manifolds?

I'm investigating the cohomology of complex manifolds, and need to construct chain complexes, Mayer-Vietoris sequences etc. I use Mathematica for numerically tracing manifolds with geodesics, but ...
5answers
446 views

How can I define a 3D version of the built-in VoronoiDiagram function?

Can anybody point me in a direction that will guide me to extend the VoronoiDiagram function in Mathematica to handle 3D (three dimensional) situations (i.e. points in 3D)? Any help will be greatly ...
2answers
407 views

Movable text on a curve

Having an arbitrary curve defined as InterpolatingFunction, what is the best way to place a text on this curve? The text generally has two rows, for example: ...
2answers
328 views

Checking if a point is in a convex 3D polyhedron

Extending from these questions How to check if a 3D point is in a planar polygon? and How to check if a 2D point is in a polygon?. I'm trying to do this to render specific shapes made up of spheres. ...
1answer
263 views

How can Mathematica be used to detect an area surrounded by the most lines?

I have an array of lines that produce random shapes. These lines define edge boundaries from an array that I would like to use to reconstruct the main feature of the array. Can Mathematica find the ...
3answers
220 views

How to find all graph isomorphisms in FindGraphIsomorphism

I found the second definition of the function FindGraphIsomorphism not working. Here's the definition Mathematica 8 gives: ...
2answers
419 views

Generating convex polyhedron from face planes?

Suppose I have lists of normals and points for planes. There's a convex polyhedron whose faces lie on these planes and are bounded by plane intersections. What would be the easiest way to produce an ...
1answer
369 views

Implementation of Balaban's Line intersection algorithm in Mathematica

I'm trying to implement a Brillouin Zone algorithm within Mathematica, including the generation of Brillouin zones of higher order in 2D and 3D. There is a nice implementation of generating these ...
3answers
576 views

How to speed up the function DelaunayTriangulation?

First define a function meshGrid to generate some points: ...
2answers
167 views

Vectors in a spherical shell

I have written code that randomly generates a 3D vector of random magnitude. I now want to create a histogram of how many vectors lie in the concentric spherical shells (n*delta r, (n+1)delta r) ...
3answers
675 views

Randomly packing spheres of fixed radius within a cube

How can I have Mathematica randomly place spheres in a cube so they won't overlap? The cube is $20 \times 20 \times 20$, and the spheres have a radius of $0.7$.
1answer
598 views

Delaunay Triangulation for 3D Surface Data

I want to do a Delaunay triangulation on scattered 3D surface data. Mathematica itself does it only for 2D through the command DelaunayTriangulation[], which gives ...
1answer
195 views

Perimeter and area are positive integers

In Geometry 3D, How can I create a triangle whose perimeter and area are positive integers with Mathematica? I found three triangles. For example $A(-6,1,2)$, $B(-9,1,2)$, $C(-9,1,6)$ or ...
2answers
436 views

How to check if a 3D point is in a planar polygon?

Following up on ndroock1's question, I naively tried to apply the solutions to a 3D point and polygon and they didn't work. For example, functions involving ArcTan ...
3answers
275 views

How to ensure that Polygon[list] plots a simple polygon?

Consider the following code which plots a triangle. p = {{0, 0}, {.2, 0}, {0, .2}}; {Cyan, Polygon[Dynamic[p]]} // Graphics Then adding (for example) ...
8answers
3k views

How to check if a 2D point is in a polygon?

Background: I use code from An Efficient Test For A Point To Be In A Convex Polygon Wolfram Demonstration to check if a point ( mouse pointer ) is in a ( convex ) polygon. Clearly this code fails for ...
1answer
200 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 ...
2answers
336 views

Finding concave hull for separated small clusters

Data : data3D = Import[file, "VertexData"]; Graphics3D[Point[data3D]] How to find concave polygon for separated small clusters.
2answers
596 views

Finding a Concave Hull

I have a 3d clustered data: Is there any other way to get concavehull of 3D data points?
3answers
455 views

Build a refined grid based on intersecting line

I honestly have no idea where to begin with this problem. In summary, I have a 2D coarse grid with an intersecting line. For an easy example, let's assume it's a 4x4 grid. I wish to pass through ...
3answers
1k views

Mathematica function intersection points with 3D grid

I need to produce a 3-dimensional equispaced grid over a given function in a way, that I can calculate intersection points of the function with the grids edges. So my first question is how to produce ...
6answers
2k views

Circuit drawing in Mathematica

This past semester I taught an introductory electromagnetism course and had quite a nice time using Mathematica to draw all sorts of figures and diagrams (mostly for problems and etc.). However, I was ...
2answers
670 views

How to process .vtk file

I want to extract the cluster of points inside 3D box, is there any way one can do this in Mathematica?
1answer
173 views

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1answer
447 views

Construct a simple mesh or tetrahedral mesh from 3D image surface

I have a 3D Y-Shape hollow tube, not so good surface. Import["http://dl.dropbox.com/u/68983831/tube02.vtk", "Graphics3D"] I tried to use following vertex data ...
3answers
342 views

Generating a non-convex polyhedron from a list of vertex coordinates

I want to include a figure in a paper I am writing on Combinatorial Geometry which features a non-convex polyhedron given by the following vertices, EDIT: I was unaware that Mathematica could convert ...
2answers
906 views

How to calculate volume of convex hull and volume of a 3D object

I have a random 3D data points. How to calculate volume of the convex hull and volume of the object.
2answers
4k views

How can I calculate a jigsaw puzzle cut path?

I want to generate a path to cut an arbitrary shape into a set of jigsaw puzzle pieces. All pieces must be unique to preclude placing a piece in the wrong spot. Pieces must be interlocking such that ...
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