# Tagged Questions

Questions on the application of Mathematica to geometric problems. You might also consider adding the [graphics] tag, if appropriate.

0answers
79 views

### Easy way to get the boundary of a geometric object [closed]

I am trying to define von Neumann boundary conditions for a prism. To do so I need the boundary of the geometric object. I can't seem to find an easy way to do this. I have tried to hard code a ...
1answer
117 views

### Minimal perimeter of all possible polygons

We had a fun problem for a student activity today: Let $P(z) = z^8 + \left(4\sqrt{3} + 6\right)z^4 - \left(4\sqrt{3} + 7\right)$. What is the minimum perimeter among all the $8$-sided polygons in the ...
1answer
99 views

### How do I create a function to rotate a rectangle about its origin? [closed]

I am new to Mathematica and was trying some new things. I wanted to rotate a rectangle using a rotation matrix by any angle theta from say o to 2pi. I could do it using predefined Mathematica ...
3answers
171 views

### Simple triangular meshes of primitive shapes

I'd like to generate triangular meshes or a cylinder and sphere primitives as part of a lattice meshing program I am writing to experiment with Mathematica. Consider the following snippet: ...
3answers
403 views

### intersection between polygon. Algorithm to check it [closed]

I'm working on an algorithm which should check if two polygons, described by their vertex coordinates, are: one inside the other, are intersecting or are separated image below describe this three ...
0answers
125 views

### Animate FromQuarternionTo3DRotation nb file with 4 quarternion values

I have a csv file. Inside the csv file, there are few rows of 4 quartenion values. I would like to animate the quarternion nb in http://demonstrations.wolfram.com/FromQuaternionTo3DRotation/ I ...
0answers
40 views

### Creating a triangle from the difference of two points [closed]

I'm attempting to create a triangular area from the difference of two points. I basically have a straight line that could be the length of 1. I would like to create points on both of the sides of the ...
0answers
105 views

### How to plot several small circles in a bigger circle [closed]

I want to plot several small circles in a bigger one with constraint minimization. The distance between any two small circles must be >= to 2*the radius in order not to enter one another. When I ...
1answer
75 views

### How to determine the value of an angle starting from an image? [duplicate]

I have two lines drawn with Mathematica, how do I calculate the angle between these two lines to have the numeric value of that angle? Thank you
2answers
174 views

Code: ...
0answers
34 views

### How to put n circles on a sphere [duplicate]

I have a piece of code that generates a circle on a sphere, but the problem is, this code creates only one circle. How can I change it in order to create n circles on the same sphere? Do I have to put ...
4answers
335 views

### Picking points in a plane under a curve given by a list

Suppose that I have a set of points in a plane, which range from $x\in [0,20]$ and $y\in[0,10]$, and a curve given by a list of points in the same region: ...
2answers
192 views

### How do I get ConvexHullMesh to return polygons instead of triangle as surface mesh?

I would need to identify the types of regular polygons forming the surface of a convex hull of 3D points. If I e.g. take the following example of a regular polyhedron ...
1answer
100 views

### How can I plot a sector of an ellipse using the central angle and not the Eccentric Anomaly?

It would appear that the Disk function, when asked to produce the sector of an ellipse between two angles treats those angles as Eccentric Anomalies (i.e. arguments ...
0answers
454 views

### Circle with negative radius?

Why does this work: Graphics[{Circle[{0, 0}, -Pi/4]}] But this doesn't? Graphics[{Circle[{0, 0}, N[-Pi/4]]}] Telling me: ...
3answers
370 views

### Rotating a circle about a larger circle

I've got some wonderful answers this morning on Mathematica Stack Exchange. See Diagonals of a regular octagon and Determine the height of a box packed with spheres. I'm just smiling with the amount I ...
2answers
401 views

### Determine height of box packed with spheres

I got such a wonderful answer regarding The Diagonals of a Regular Octagon, so I thought I'd try asking another question we had on our Pizza and Problem quiz activity at College of the Redwoods. The ...
2answers
314 views

### Diagonals of a regular octagon

We had a little activity after school today and one of the questions was: All diagonals are drawn in a regular octagon. At how many distinct points in the interior of the octagon (not on the ...
2answers
335 views

### How to make geometric intersection faster for geographic borders?

I have developed a solution to identify geographic regions bordering a region in this post (94723). Can this functionality be made to execute any faster? Find which entities in a set border other ...
1answer
95 views

### Recursive calculation is very slow

I've got a recursive definition of Arcs that shares equal length and a several other dependencies to each respective predecessor. (Imagine a book being bent.) I formulated all necessary things here: ...
4answers
261 views

### Administrative Divisions bordering a geographic region (e.g. an ocean)

Update 3 I've worked out a solution that is bearable for a small number of subregions in the neighbour and added it as an answer. I'm going to make a post for optimisation help. Update 2 For a ...
2answers
232 views

### How do I rotate a curve?

I have a circular segment defined as: ParametricPlot[5 {Sin[ϕ], 1 - Cos[ϕ]}, {ϕ, -0.2, 0.8}, PlotRange -> All] which I have to rotate around point ...
4answers
460 views

### Minimal overlap area of circles

I have 20 points in the 2D plane with $(x_i,y_i)$ coordinates. I want to use Mathematica to optimally distribute 10 circles with equal radius of a given positive value $R$, i.e. to determine with the ...
1answer
70 views

### Area of a surface spanned by 2 parametric curves

I would like to find the area of a surface spanned by two parametric curves in 3D. I came up with this metric for distance between curves. The illustrations are in 2D for simplicity. ...
0answers
70 views

### Equilateral triangulation of a polyfile-defined surface

I would like to be able to make a (low fidelity) triangulation of a given surface with constant edge lengths (using equilateral triangles). This requirement limits the Gaussian curvature at each ...
1answer
222 views

### Is DiscretizeRegion not yet ready ro discretize 3D-solids?

In the DiscretizeRegion documentation: "The region reg can be anything that is ConstantRegionQ and RegionEmbeddingDimension less than or equal to 3." With DiscretizeRegion there could be an easy way ...
3answers
231 views

### Reflect point over a line in 3D

I'd like to sample points on a triangle randomly. The following code yields points that are uniformly distributed on a quadrilateral: ...
1answer
106 views

### Create region from set of lines and arcs [duplicate]

I have a shape that is a knuckle plate with two holes cut in it, thus: ...
3answers
123 views

### Create region from polygons and tangential line segments

I have two circles and tangential line segments that I want to define a region: ...
9answers
629 views

### Plotting a sequence of isosceles triangles of diminishing size

I try to plot the following graph using Graphics and Table. The graph consists of infinitely many isosceles triangles (without ...
1answer
80 views

### Distance of a point from a line using multiplicative distance [closed]

How can we determine the multiplicative distance (http://link.springer.com/article/10.1007/s10115-014-0813-4#page-1) of a point (x0,y0) from a line (ax+by+c=0)? Let X = (x_1, x_2 ..., x_m) be a ...
3answers
215 views

### How to find points along the inner and outer edge of a ring along a specific direction

I have a set of random numbers distributed on a annular disk. I want to find points on the inner and outer edge along a particular angle. One possibility is to use ...
1answer
144 views

### 4D rotations of 600-cell to make cell centered stereographic projection

I have made a 600-cell wireframe model from Eric Weinsteins' 2/13/14 600-cell notebook (600-cell: a regular polytope, 4D, analogous to the icosahedron, with 600 tetrahedral cells, 120 vertices, 720 ...
2answers
191 views

### How to obtain the area enclosed by such a curve?

The desired curve is defined as curve02 below : ...
0answers
41 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 ...
1answer
144 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 ...
3answers
168 views

### Easy way to bind rect to geometrical 2D line?

I got stuck with the following problem. For some calculation and visualization purposes I need to draw different shapes (like rectangle) with proper slope on custom line. The trivial example: ...
2answers
106 views

### Draw a vector with mathematica [closed]

at the risk of being trivial I would like to draw the vector $\vec{AB}$ where $A$ an d $B$ have the coordinates $(1,1,1)$ and (1,-1,2) respectively.
1answer
146 views

### Calculate area from RegionPlot directly

I have a region plot, and I would like to calculate the area: ...
3answers
565 views

### Solve a trig equation system

Background of the problem In the same plane, P is a fixed point, A,B,C are moving point, PA=a, PB=b, PC=c, find the maximize perimeter of △ABC. let ∠BPC=A, ∠CPA=B, ∠APB=2*Pi-A-B, then the perimeter ...
1answer
99 views

### How to change a point to circle in a Graphics expresion [closed]

Given the following line of code, ...
1answer
185 views

### Confusion with SplineFit (Angle calculation)

This question is continuation to this other one I am creating polymers (where each monomer is of equal length) using this method: ...
1answer
71 views

### Why are these methods giving me different results? (Trying to test SplineFit)

I am creating a polymer(where each monomer is of equal length) using this method: ...
1answer
437 views

### How do I create a triangulated surface from points?

I have a set of points in a nx3 matrix and I would like to convert them into a surface, so that I may calculate its surface area. The function ListSurfacePlot3D creates the surface how I want it. ...
1answer
75 views

### MaxCellMeasure fails in 3D?

Question How come MaxCellMeasure works in 2D but fails in 3D? Indeed if I try ...
1answer
139 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: ...
3answers
354 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 ...
1answer
80 views

### Is there a package that can calculate the Ricci tensor from a numerically given metric?

There are many packages about general relativity or differential geometry, and they can calculate the Ricci tensor from a symbolically given metric, for example, $g_{tt}=-f(r)$, $g_{rr}=h(r)$, etc. ...
2answers
265 views

### ToElementMesh problem on Ball defined by ImplicitRegion?

Bug introduced in 10.0 and fixed in 10.2 Could any one please confirm the following bug in mathematica 10.0.2 ? If I define this ball ...
2answers
178 views

### Implementing AnglePath in Mathematica 10.0

Does anyone have an implementation for AnglePath (see AnglePath Documentation and example usage) in Mathematica 10.0?