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

learn more… | top users | synonyms

33
votes
6answers
3k 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: ...
9
votes
3answers
4k 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 ...
14
votes
4answers
4k 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. ...
26
votes
4answers
1k 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 ...
22
votes
5answers
673 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 ...
9
votes
6answers
7k 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 ...
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?
2
votes
1answer
749 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 ...
20
votes
2answers
809 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 ...
15
votes
3answers
1k 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
2answers
796 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 ...
14
votes
6answers
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 ...
4
votes
4answers
151 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 ...
8
votes
2answers
478 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
0answers
171 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
144 views
2
votes
1answer
220 views
13
votes
3answers
652 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 ...
15
votes
4answers
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 ...
8
votes
1answer
357 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 ...
6
votes
2answers
310 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 ...
3
votes
2answers
323 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 ...
1
vote
1answer
139 views

Rotating a a set of points in a square boxed region by $90$ degree increments [closed]

I have a set of two-dimensional points $P$ in a box with dimensions $(d_1,d_2)$. The coordinate for the lower-left-hand corner of the box is $(0,0)$ and the coordinate for the upper-right-hand corner ...
10
votes
5answers
573 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: ...
9
votes
5answers
450 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
1answer
136 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.: ...
5
votes
1answer
177 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: ...