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

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0
votes
3answers
227 views

Cover a rectangle with size constrained rectangular regions

I have a big grid (indicated on the image in grey) that is divided in several blocks (each with a maximum width of 3 units). Now I would like to divide a region (indicated on the grid in red) by the ...
6
votes
2answers
374 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 ...
0
votes
0answers
75 views

How to define the tangent gradient operator? [duplicate]

I would like to define a new differential operator that is the tangent gradient for a curve $\Sigma$. This is defined as $$\nabla_\Sigma=\mathbf{P}\nabla$$ where $\mathbf{P}$ is the projection ...
6
votes
2answers
1k 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 ...
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 ...
1
vote
1answer
558 views

Drawing a quadrilateral inscribed within a circle

I would like to draw a quadrilateral inscribed within a circle. How can I construct this figure, taking into account arbitrary (specified) side lengths, while still ensuring that the vertices of the ...
3
votes
0answers
117 views

How can I truncate only a single vertex of a polygon?

One can truncate all the vertices of a polygon at once with Truncate. I want to do exactly that -- but only on a single vertex. Is this possible with Mathematica 9? ...
16
votes
4answers
8k 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 ...
3
votes
1answer
349 views

Turn list of edges into a polygon function

I have a list of coordinates that define the edges of a polygon and I would like to get a function defining the area Inside out if it (The polygon is convex and the points are in order) So that for ...
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?
14
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 ...
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 ...
5
votes
2answers
673 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 ...
2
votes
1answer
821 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 ...
7
votes
1answer
1k 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.
16
votes
3answers
887 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 ...
11
votes
5answers
699 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: ...
1
vote
2answers
2k views

How do I find an equilateral triangle whose vertices have integer coordinates?

In geospace, how do I find coordinates of the vertices of an equilateral triangle whose vertices have integral coordinates? How do I tell Mathematica to do that?
4
votes
0answers
200 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
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 ...
22
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. ...
33
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 ...
3
votes
1answer
123 views

Center of quadrangular

Having 4 points A (ax, ay), B (bx, by), C (cx, cy) and D ...
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 ...
11
votes
2answers
714 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 ...
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 ...
38
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: ...