# Tagged Questions

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

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### intersecting cylinders

I try to replicate the two figures of two intersecting cylinders from here. I tried ...
92 views

### Intersection of two volumes [closed]

I would like to know the volume of the intersection of a cone and a cuboid : ...
111 views

### Tell if a point is inside a FilledCurve

Convert a letter into a FilledCurve: ...
113 views

### How do I tell if two sets of dots are in some way similar?

I have two sets of dots (x,y coordinates) and I'd like to figure out if there's a way to find out if the second set of dots is (more or less) "close" to the first one. I may plot these two sets in ...
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 ...
125 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 ...
101 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 ...
176 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: ...
425 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 ...
127 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 ...
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### 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 ...
117 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 ...
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
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Code: ...
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### 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 ...
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: ...
196 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 ...
102 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 ...
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Why does this work: Graphics[{Circle[{0, 0}, -Pi/4]}] But this doesn't? Graphics[{Circle[{0, 0}, N[-Pi/4]]}] Telling me: ...
378 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 ...
404 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 ...
331 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 ...
340 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 ...
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### 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: ...
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### 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 ...
234 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 ...
461 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 ...
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### 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. ...
72 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 ...
230 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 ...
238 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: ...
108 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: ...
127 views

### Create region from polygons and tangential line segments

I have two circles and tangential line segments that I want to define a region: ...
631 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 ...
81 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 ...
216 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 ...
150 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 ...
192 views

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

The desired curve is defined as curve02 below : ...
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### 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 ...
145 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 ...
170 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: ...
114 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.
151 views

### Calculate area from RegionPlot directly

I have a region plot, and I would like to calculate the area: ...
576 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 ...
318 views

### How to solve for the intersection points of two ellipses?

I have a parametric equation of two ellipses as follow $\begin{cases} x=a_1 \text{sin$\theta $}+b_1 \text{cos$\theta $}+c_1 \\ y=d_1 \text{sin$\theta $}+e_1 \text{cos$\theta \$}+f_1 \\ \end{cases}...
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### How to change a point to circle in a Graphics expresion [closed]

Given the following line of code, ...
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: ...
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### 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: ...