Questions on the application of Mathematica to geometric problems. You might also consider adding the [graphics] tag, if appropriate.
28
votes
6answers
2k 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:
...
25
votes
4answers
948 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 ...
8
votes
4answers
2k 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. ...
7
votes
3answers
1k 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 ...
2
votes
1answer
614 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 ...
15
votes
2answers
455 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 ...
7
votes
6answers
2k 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 ...
3
votes
0answers
146 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 $\tau$.
...
12
votes
5answers
783 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 ...
13
votes
4answers
916 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
1k 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 ...
6
votes
2answers
245 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
204 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 ...
10
votes
5answers
484 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:
...
5
votes
1answer
93 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.:
...
