# Tagged Questions

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

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Is there a way to put the following equation of a line into vector form using Mathematica (or a Mathematical package)? $\displaystyle y=\frac{cos(s_n)-cos(s_{n+1})}{sin(s_{n+1})-sin(s_n)}(x-sin(s_n))-... 2answers 267 views ### A question regarding “DiscretizeGraphics” I want to find the volume of a torus torus = RevolutionPlot3D[{2 + Cos[t], Sin[t]}, {t, 0, 2 Pi}] ... 3answers 250 views ### Speed of ConvexHullMesh Pick$N$random points on the surface of the sphere, then use ConvexHullMesh[] to compute their convex hull. Empirically, this takes time quadratic time in$N,$... 1answer 138 views ### How could I make visible the convex hull of 3 point inside this region? Small version of the question How can I control the color and the Thickness of this graph?? ... 1answer 180 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: ... 1answer 535 views ### How to draw quantum circuit with mathematica? How to draw quantum circuit as the following one with mathematica? I only find the quantum package which is designed for MMA 7.0 as the author said. But the version of my Mathematica is 9.0 and when ... 6answers 2k views ### Finding length of intersection of two surfaces I would like to know how we find the length of the intersection of two surfaces. For instance, in the following example,a surface intersects with a plane: How do we find the length of intersection ... 5answers 857 views ### Site - Cell Correspondence in Voronoi Diagram obtained via VoronoiMesh Consider the following: ... 2answers 616 views ### Object separation from a 2.5D surface I'm trying to identify the shape and the boundaries of objects. The data was generated with a laser scanner and represent the surface of an area in which many boulders lay on the ground and making up ... 5answers 930 views ### Ordering the Boundary points of a Polygon I feel like this should be simple, but I keep running into walls. Say someone gives you the coordinates of the vertices of a pentagon and the center point of the hexagon. Is there any way to get an "... 2answers 385 views ### How can I only draw outer common tangent to two circles? I have code worked for drawing common tangent lines to two circles(http://en.wikipedia.org/wiki/Tangent_lines_to_circles), now I want to delete the inner common tangent lines, how? ... 1answer 434 views ### Smooth convex hull of a large data set of 3D points I recently needed to deal with a large data set of 600.000 points in three dimensions. My task was to find a convex hull for this data. I have Mathematica 10, so I could use the function ... 3answers 541 views ### Torus triangulation I'd like to plot something similar to this but with a triangle instead of a pentagon. Also, I'd like to triangulate the faces, that is, to insert the diagonals for each face of the 3 prisms used. In ... 1answer 228 views ### RegionPlot3D run forever when plotting 3D ParametricRegion when working with 2D, RegionPlot works fine with ParametricRegion as can be seen in this example: ... 1answer 254 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, ... 2answers 303 views ### How can I decide whether a closed surface is intersected by a triangle? A closed surface consisted of Polygons or GraphicsComplex and a triangle made by 3 points are in a 3D space. How can I decide ... 1answer 180 views ### Problem with clipping of tick labels Please look at Show[DiscretizeGraphics[Graphics3D[{Cone[]}]], Axes -> True, Boxed -> True] Well, there are some Ticks,... 1answer 163 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 ... 1answer 345 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 ... 2answers 308 views ### Possible Bug in DiscretizeRegion with Option MaxCellMeasure Bug introduced in 10.0.0 and fixed in 10.0.2 Consider the following ImplicitRegion: ... 1answer 175 views ### User-defined DistanceFunction for RegionNearest In the function Nearest , I can define my custom function using the DistanceFunction option. e.g: ... 1answer 354 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.: ... 2answers 243 views ### Probable Bug in HighlightMesh with 2D Convex Hulls created via ConvexHullMesh Bug introduced in 10.0 and fixed in 10.2 One nice way to view the new and exciting Mesh objects introduced in Version 10 is by utilizing the function ... 0answers 107 views ### How to make equidistant or split ListPoint [duplicate] How to split the curve with more equidistant points? ... 3answers 630 views ### How to measure cross sectional area of Tube I have modified my question to a simple version. I have vertex clusters, polygons and a list of center points. Attached pts and polygons of 3d tube are: ... 1answer 290 views ### How to draw a 3D convex hull of a set of points with styling IÂ´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 ... 2answers 463 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 ... 1answer 107 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 = ... 1answer 283 views ### Can't plot rotated region I was experimenting with the code from this question when I ran into another problem with regions. ... 0answers 191 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 ... 1answer 226 views ### What kind of object results from RegionIntersection function? I'm trying to use RegionIntersection in a couple of Polygons. The polygons are the following: ... 2answers 283 views ### “The function DiscretizeGraphics is not implemented for GraphicsComplex” confusion Why does DiscretizeGraphics seems to work on one GraphicsComplex and not the other? Here is an example that works: ... 0answers 354 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: ... 1answer 254 views ### Finding corresponding vertex from 3d to 2d I have this simple 3d data points: ... 2answers 946 views ### Difference (or intersection) of two convex polyhedra I have two convex polyhedra stored in the following form: a set of vertices vertices = {{x1,y1,z1},...}, a set of faces, where each face is a convex polygon ... 1answer 553 views ### Find area of polygon on a sphere from a set of latitude-longitude points Given a list of latitude and longitudes say ... 1answer 146 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 ... 2answers 824 views ### How to get UV mapping of 3D tube Here is cylinder data: file We can mesh the surface, thanks to lalmei, Belisarius and Simon (link) How to achieve uv mapping from a 3d straight and curved tube? Working code: ... 1answer 396 views ### How to map vertex points from the surface of a straight pipe onto 2D plane How to map vertex points from the surface of a straight pipe onto 2D plane. The 3D surface points of the straight pipe can be found here: data Working code: ... 1answer 1k 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 ... 2answers 462 views ### Convert DelaunayTriangulation-> Graph->AdjacencyMatrix Is there a way to convert a Delaunay Triangulation into a Graph structure so that one can generate an AdjacenyMatrix of the Delaunay? 1answer 177 views ### How to create bounded diagram plot? I have set of points: ... 0answers 54 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 ... 0answers 126 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$maps three distinct points p, q, r to three distinct points p', q', r'. ... 1answer 128 views ### Problem with PlanarGraphPlot And ConvexHull I'm getting a lot of strange errors when using PlanarGraphPlot with a simple list of 11 points. This is using Mma 9.0.1 64-bit Mac OS X. ... 2answers 772 views ### Image processing: extracting ordered contour Continuing the question How to extract the edge from a set of points and its answer by Simon Woods, I would like to ask if there is a way to extract the boundary of obtained as ... 1answer 510 views ### Area of a convex polygon with a set of points [duplicate] I have a set of points Pts[a_,b_,c_]:={{a, b}, {b, a}, {c, a}, {a, c}, {b, c}, {c, b}} which define a convex polygon and I would like to find its area. There is ... 7answers 1k views ### Choosing$n\$ equidistant points on a circle with given radius and center

I would like to have a function circle which takes two inputs: a tuple {x,y} and a real number ...