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

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34
votes
7answers
4k views

Intersecting graphics

Does the Mathematica graphics system have any concept of intersecting graphics? I've not found much in the documents so far. For example, if I want to show the intersection of two shapes: ...
31
votes
5answers
2k views

Generating evenly spaced points on a curve

In the KnotData package a simple command such as points = Table[KnotData[{3, 1}, "SpaceCurve"][t], {t, 0, 2 Pi, 0.1}]; will ...
23
votes
5answers
944 views

How to plot ternary density plots?

How can I get a ternary density plot just like the plots from OriginLab? ContourPlot and DensityPlot seemingly can solve the ...
22
votes
5answers
1k views

2D random walk within a bounded area

I want to simulate a random walk on two dimension in a bounded area such as a square or circle. I am thinking of using If statement to define a boundary. Is there a ...
21
votes
2answers
907 views

How can I pack circles of different sizes into a spiral?

Given a list of circles of different areas, I need to arrange them tangentially in order of increasing area and spiraling outward. An example of the type of packing I'm attempting is shown by the ...
18
votes
4answers
2k views

How do I calculate the area of a polygon given its coordinates?

I have a polygon: Polygon[{{0, 200 }, {200, 100}, {500, 300}, {100, 700}}] How can I figure out its area? The docs page does not have any example. So far I've ...
17
votes
3answers
523 views

Creating sculptural forms using graphics primitives

This is a question based on this answer by halirutan. Some amazing images can be created with this code, and I was wondering whether it was possible to extend the principle to different shapes. I ...
17
votes
0answers
401 views

Proving the hairy ball theorem using xAct

I would like to formally prove the hairy ball theorem in Mathematica, initially just for $S^2$, and then see about generalizing. An approach I thought about to use the xAct package to define $S^2$ ...
16
votes
4answers
5k views

How to calculate scalar curvature Ricci tensor and Christoffel symbols in Mathematica?

I am seeking a convenient and effective way to calculate such geometric quantities. I've used packages like TensoriaCalc, but they don't work at all time. ...
15
votes
5answers
2k views

How do I draw a triangle given the lengths of the sides?

I know, of course, how to draw a triangle in the plane given the vertices: Graphics[Polygon[{{1, 0}, {0, Sqrt[3]}, {-1, 0}}]] But I'm not sure how to simply draw ...
15
votes
7answers
2k views

Distance between point and line segments

How would you determine the shortest distance between a point and one or more segments? For example, what is the shortest distance between the point and the two segments below? Clearly the point is ...
14
votes
3answers
702 views

Approximating an ornamental curve

How do I go about approximating this ornamental curve? Note that the curve has somewhat variable thickness as typical in calligraphy, which I would also like to replicate. The excellent reference ...
13
votes
4answers
2k views

How to draw a great circle on a sphere?

I apologize for the text description, but new users are not allowed to post images. I want to draw a circle that cuts through the center of a sphere and has an inclination of 15 degrees with the ...
12
votes
4answers
5k views

Finding unit tangent, normal, and binormal vectors for a given r(t)

For my Calc III class, I need to find $T(t), N(t)$, and $B(t)$ for $t=1, 2$, and $-1$, given $r(t)=\{t,t^2,t^3\}$. I've got Mathematica, but I've never used it before and I'm not sure how to coerce ...
12
votes
2answers
932 views

How do I split up a curve into segments of equal length?

I have a curve that is defined as f[x] and what I'm attempting to do is to divide the curve into equal straight lengths for a number of segments of my choosing that I've defined as nSeg. I've created ...
11
votes
6answers
1k views

How to find lattice points on a line segment?

How do I find points on the line segment joining {-4, 11} and {16, -1} whose coordinates are positive integers?
11
votes
2answers
589 views

Rebuild a polygon so it doesn't self intersect

If you consider the following Polygon: ...
11
votes
1answer
539 views

Solving Killing equations

Is it possible to solve Killing equations in Mathematica for a general vector? I am looking for a way to create Killing equations and then find what the vectors are, but I have a problem with this. ...
11
votes
2answers
604 views

How to plot a barycentric line

I want to plot a barycentric function on an equilateral triangle (ternary plot). For example f1 = {Abs[Sin[x]], Mod[x, 2], Abs[Cos[x]]}; At the moment I evaluate ...
10
votes
5answers
602 views

How to plot rectangles aligned by their center?

Supose I have a rectangle which area is $x^2$. In some cases I may not know what is the size of each side, for $x=12,$ we have several possibilites: ...
10
votes
2answers
431 views

Is there a triangle like this?

I want to find the numbers $a$, $b$, $c$, $d$ of the function $y = \dfrac{a x + b}{c x + d}$ so that the triangle $ABC$ with three points $A$, $B$, $C$ have integer coordinates and lies on the graph ...
9
votes
6answers
8k views

How to determine the center and radius of a circle given three points in 3D?

I was wondering if anyone could give me a hand with this problem I have. I have six points on a plane, and I am trying to determine if they form a circle or not. I know that any three points in 2D ...
9
votes
4answers
669 views

To inscribe a circle in a given triangle

I am trying to to inscribe a circle in a given triangle but it isn't working. I've used GeoGebra with this construction and worked but as I'm new to Mathematica I am missing something. It can't be so ...
9
votes
5answers
472 views

How to choose three points on the circle so that the triangle is not a right triangle?

I want to choose three points $A$, $B$, $C$ has integer coordinates on the circle $$(x+2)^2 + (y+1)^2 = 25$$ so that the triangle is not a right triangle. But I can not. I tried ...
9
votes
1answer
462 views

Uniformly distributed n-dimensional probability vectors

What's the right way to generate a random probability vector $p={p_1,\ldots,p_n} \in {(0,1)}^n$ where $\sum_i p_i=1$, uniformly distributed over the $(n-1)$-dimensional simplex? What I have is ...
8
votes
2answers
588 views

How can I plot a loxodrome?

Can someone show me how to plot a rhumb line (loxodrome) in Mathematica via the ParametricPlot function? Here is what I got so far: ...
8
votes
2answers
250 views

Counting and extracting hit circles/triangles for randomly chosen points

Below, you see a triangle in which the incircle was inscribed. As we know, the center of this circle is the intersection of the angle bisectors. At this point, one could go further and find the ...
8
votes
1answer
248 views

How to compile Heike's winding number function?

Heike gave the following function for winding number: ...
7
votes
4answers
594 views

Plotting an epicycloid

I am fairly new to Mathematica and I cannot figure out how to plot an epicycloid. I have plotted some neat looking things in my attempts, but can't make one. I am not looking to make an animation, ...
7
votes
4answers
474 views

How can I shorten this code to rotate a line segment around its center?

I have a list of line segments stored in the form: { {{x11,y11},{x12,y12}} , {{x21,y21},{x22,y22}} , ... , {{xn1,yn1},{xn2,yn2}} } Now I want to rotate all of ...
7
votes
1answer
791 views

How does one draw a parallelepiped in Mathematica?

I'm a bit new to the application, and I'm not sure how to draw a parallelepiped in Mathematica.
6
votes
2answers
603 views

Distribution of 10 points within a unit square

Related to some packing problems, following problem arose: Distribute 10 points within a square of sides 1, so that minimal distance between them is maximized. With the help of random simulation, or ...
6
votes
2answers
325 views

How to punch a hole in some 3D distribution of points

Suppose we have a long list of 3D Cartesian coordinates, defining a distribution of random points in 3D space. How could we remove all the points inside a sphere of radius ...
6
votes
1answer
291 views

Imposing a Periodic Boundary Condition in Nearest Neighbour Search

I am trying to find first nearest neighbour distributions of randomly dispersed point-like objects in an infinite system. To do this I make a finite sized box unit cell with a chosen concentration of ...
6
votes
1answer
142 views

Why is FindInstance failing when I relax a set of constraints?

I'm attempting to use FindInstance to generate coordinate sets for plausible triangles with edge length distance constraints. E.g.: ...
6
votes
2answers
824 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 ...
5
votes
7answers
278 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 ...
5
votes
1answer
494 views

How can I draw a polygon from a set of angles?

In recreational mathematics, polytans are polygons formed by edge-connecting isosceles right triangles. Order-n polytans are those constructed from n such triangles. My question is this: Given a ...
5
votes
1answer
210 views

Generate regularly spaced points from the surface of simplexes

I need to generate regularly spaced samples (points) from the surface of unit simplexes with 2 or greater vertices or end points. I can generate random samples pretty straightforwardly: ...
4
votes
1answer
166 views

How to generate nonperiodic tilings?

I need to generate nonperiodic tilings which are similar to the attached figure (kite-domino tiling). I was thinking the code is similar to the code for the Penrose tiling. However, that code is too ...
4
votes
2answers
151 views

Assumptions for RotationMatrix

I'm making C++ program, and in my program I need a rotation matrix around any vector. I wanted to extract RotationMatrix[fi,{x,y,z}] output and put it in my ...
4
votes
1answer
188 views

Plot a cone in spherical co-ordinates

As we all know in spherical coordinates a function phi = π/3 gives us a cone. The cone makes an angle of π/3 with the imagined ...
4
votes
4answers
496 views

Identifying and counting closely spaced particles

Following in the footsteps of this blog post: http://blog.wolfram.com/2011/09/09/building-a-microscopy-application-in-mathematica/, I took a microscope picture of some particles on a surface, and ...
4
votes
1answer
165 views

Is there a fast way to trilaterate a point?

I have a point in 2D or 3D space at an unknown coordinate, $p_0$, and I'd like to determine its position using distances from known coordinates $(p_1, p_2, p_3)$. Beyond using ...
4
votes
1answer
131 views

Construct a function that can generate a geometry by extruding a section

Toady I want to construct a geometry shown as below: I know the Mathematica has the functions like Cylinder, Sphere and so ...
4
votes
0answers
184 views

Unexpected behavior of GeometricTransformation

I have the following mapping on the complex plane: $$ z \mapsto \tau \mu z-1, $$ where $\mu$ is complex, $\tau$ is real number. I want to draw the image of left unit semidisk and play with $\tau$. ...
3
votes
2answers
327 views

Create polygon using edge lengths and area

Four-sided convex land plots are usually denoted with edge lengths and area. How do I create a Polygon Object with these parameters in Mathematica ?
3
votes
2answers
364 views

Triangle mapped on a sphere in $\mathbb R^3$?

How can I map a triangle on an sphere? I want to visualize (plot or animate) it for my student in my Non Euclidean geometry. I have no restrictions on the triangle's kind or on the sphere in $\mathbb ...
3
votes
2answers
283 views

Intersection of surface with parallel planes

Consider the code (adapted from here) ...
3
votes
2answers
499 views

How to determine the remaining sides given the three angles and one side of a triangle?

The measure of the interior angles of a triangle are $15^\circ$, $30^\circ$, $135^\circ$ and the length of one edge is 3. In order to determine the length of the remaining two edges, I've tried ...