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

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17
votes
4answers
9k 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 ...
39
votes
7answers
5k 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: ...
23
votes
4answers
8k 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. ...
36
votes
6answers
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 ...
32
votes
6answers
2k 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 accept the ...
12
votes
6answers
11k 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 ...
13
votes
6answers
2k views

Find intersection of pairs of straight lines

I have a list of 24 points, in which two consecutive points (1st and 2nd, 3rd and 4th, …) are supposed to form a line: ...
12
votes
2answers
1k 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 ...
13
votes
2answers
950 views

Rebuild a polygon so it doesn't self intersect [duplicate]

If you consider the following Polygon: ...
21
votes
4answers
3k 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 ...
12
votes
6answers
2k 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?
30
votes
6answers
1k 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 ...
2
votes
1answer
828 views

Using triangulation

I have been presented with 3 known points and the power densities at those points. I need to use those points to find the location of the actual antenna which is generating the signals. Power ...
23
votes
2answers
1k 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 ...
27
votes
3answers
703 views

Can Mathematica solve Plateau's problem (finding a minimal surface with specified boundary)?

Given a closed curve $\mathcal C$ in three dimensions, is it possible to use Mathematica's built-in functionality to compute a minimal surface whose boundary is $\mathcal C$? For simplicity, let us ...
15
votes
5answers
3k 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 ...
9
votes
1answer
663 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 ...
4
votes
2answers
603 views

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

How can I map a triangle on a sphere? I want to visualize (plot or animate) it for my student in Non-Euclidean geometry. I have no restrictions on the triangle's kind or on the sphere in $\mathbb ...
3
votes
1answer
304 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: ...
35
votes
2answers
760 views

Numerically solving Helmholtz equation in 3D for arbitrary shapes

Context While studying manifold Learning I got interested in finding the eigenvectors of the Laplacian. (also in connection to this problem of solving the heat equation) Following this and that ...
26
votes
5answers
2k 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 ...
20
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
1k views

Fitting ellipse to 5 given points on the plane

Five points are required to define a unique ellipse. An ellipse has five degrees of freedom: the $x$ and $y$ coordinates of each focus, and the sum of the distance from each focus to a point on the ...
6
votes
6answers
616 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 ...
4
votes
3answers
586 views

Computing Gaussian curvature

Can Gaussian curvature $K$ be computed from WolframAlpha or any other available Mathematica program? Please indicate the program or its reference. If input ...
8
votes
2answers
797 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: ...
4
votes
3answers
253 views

How to find a length of a curve constructed using Spline?

By fitting the data using spline, I have created a curve. sp = SplineFit[data1, Cubic] I am trying to divide this curve into small segments of equal length. To ...
4
votes
0answers
202 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 $\tau$. ...
1
vote
1answer
230 views
11
votes
5answers
708 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: ...
3
votes
2answers
831 views

Intersection of surface with parallel planes

Consider the code (adapted from here) ...
2
votes
1answer
155 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: ...
2
votes
1answer
469 views
17
votes
5answers
495 views

Plot a partition of the sphere given vertices of polygons

I saw in this question that Mathematica can draw spherical triangles. I guess something similar can be done to plot a spherical polygon. I am interested in something similar: I have a set of ...
16
votes
3answers
902 views

Approximating an ornamental curve

How do I go about approximating this ornamental curve? Note variable thickness typical in calligraphy. Handbook and Atlas of Curves by E.V. Shikin (1995) contains many directions, including curve ...
10
votes
1answer
210 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. ...
7
votes
1answer
308 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 ...
18
votes
5answers
3k 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 ...
11
votes
2answers
729 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
4answers
1k 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, ...
8
votes
1answer
284 views

How to compile Heike's winding number function?

Heike gave the following function for winding number: ...
7
votes
2answers
384 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 ...
5
votes
3answers
381 views

Finding volume of a segment

I'm still pretty new to Mathematica, so I would like to seek advice regarding a geometrical problem. I am currently trying to define that as an extra condition in the Mathematica code below. ...
5
votes
1answer
178 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 ...
24
votes
2answers
321 views

Bug in ArcLength?

fixed in 10.1 (windows) With Mathematica 10.0.2: ArcLength[Line[{{0, 0}, {1, 0}, {2, 0}}]] ArcLength[Line[{{0}, {1}, {2}}]] (* 2 *) (* 2 *) However, ...
10
votes
5answers
529 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 ...
6
votes
5answers
379 views

How to draw a dodecahedron with each face modified to a pentagram?

I'd like to draw a dodecahedron with each face carved on the sides so it becomes a pentagram. I wonder how to start to do this kind of task in Wolfram language? Edit: The result should still be a ...
6
votes
1answer
783 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
4answers
609 views

Distance between two line segments in 3-space

I need to compute the distance between two line segments in a project. After googling, I found this algorithm and used it to implement a Mathematica version: ...
4
votes
2answers
111 views

ToElementMesh problem on Ball defined by ImplicitRegion?

Could any one please confirm the following bug in mathematica 10.0.2 ? If I define this ball Ω = ImplicitRegion[0 <= x^2 + y^2 + z^2 <= 1, {x, y, z}]; and ...