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

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8
votes
2answers
518 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: ...
0
votes
1answer
261 views

Using LatticeData to fill a space with spheres in a face-centered cubic (fcc) lattice packing arrangement

I have a large sphere of radius $R_1$ which I would like to pack with $N$ smaller radius of radius $r_2<R_1$ arranged in a face-centered cubic (fcc) packing arrangement (i.e. Kepler's optimal ...
5
votes
1answer
472 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 ...
7
votes
4answers
465 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 ...
0
votes
0answers
48 views

How to judge if a point is in the interior of a closed curve or not? [duplicate]

For example: pts = {{0, 1}, {-(Sqrt[3]/2), -(1/2)}, {Sqrt[3]/2, -(1/2)}}; trig=JoinedCurve[Line[pts], CurveClosed -> True]; Then ...
6
votes
1answer
141 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.: ...
4
votes
1answer
164 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 ...
3
votes
2answers
351 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 ...
0
votes
3answers
207 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
323 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
70 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
784 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 ...
0
votes
1answer
155 views

Wolfram Alpha's Mysterious Trig Abilities [closed]

This is a very straight-forward question: I'm trying to simplify [sin(2pi*t +pi/4) + sin(2pi*t -pi/4)], and failing at it: ...
14
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
404 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
109 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? ...
9
votes
3answers
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 ...
3
votes
1answer
281 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 ...
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?
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 ...
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 ...
3
votes
2answers
495 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
770 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
771 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.
14
votes
3answers
686 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 ...
10
votes
5answers
597 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
1k 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
182 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
900 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 ...
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. ...
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 ...
3
votes
1answer
115 views

Center of quadrangular

Having 4 points A (ax, ay), B (bx, by), C (cx, cy) and D ...
21
votes
2answers
889 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
591 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 ...
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 ...
34
votes
7answers
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: ...