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

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0
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0answers
15 views

polarized hodge structure [on hold]

With the notations in the picture blew, we define the classifying space D for the polarized hodge structures is the set of all collections of subspaces of H, how to deduce the conjugation relation?
0
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0answers
76 views

Distance between rectangle and parametric curve

Given a 2D parametric curve $(x(s), y(s))$ and a rectangle where each of the four vertices is parameterized $(x_i(t), y_i(t))$, $i \in \{1,2,3,4\}$, how can Mathematica compute the distance function $...
0
votes
2answers
266 views

How to construct new geometrical shapes in Mathematica?

In this question of mine I asked for how to implement a 2D random walk within a bounded area. In the provided solution one can use Rectangle[{-10, -10}, {10, 10}] ...
14
votes
3answers
353 views

How to convert a surface into a solid

Context I am interested in converting surfaces into solids (so I can make a 3D mesh out of them using ToElementMesh) Say I have the following cool surface ...
1
vote
2answers
143 views

Displaying Dandelin spheres touching hyperbola boundary patches in cone

Can we show the Dandelin spheres scenario (shown by Hrhm for case of ellipse) for a hyperbola as well? I'm not happy with what we get to see of this on the net. The double nappe/sheet of a cone is ...
4
votes
1answer
113 views

VertexNormals depends on Polygon's orientation - an expected behaviour?

I'm studying VertexNormals (on Mathematica 10.0.2 for Mac) and have set up the following to represent three points and a normal vector: ...
1
vote
1answer
71 views

How can I reflect a graphic across a line? [closed]

I would like to make an animation that shows where a graphic (square, circle etc) would be after it is reflected over a line. Thanks
5
votes
1answer
454 views

How to combine solid objects using logical expressions?

How can one define and render in 3D a single solid object using logical operations on component solid objects? For instance, I would like to define a solid object that consists of a ...
11
votes
6answers
300 views

Probability of a random point inside the intersection of two triangles

I hope I can explain this problem clearly. It has been bothering me for sometime and I do not know how to solve it even with Mathematica's help. I finally stumbled upon an idea, see my answer below. ...
0
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0answers
11 views

How many sphere on the boundary of a big sphere? [migrated]

I don't know exactly how to ask this in a comprehensible way. I am trying to find a solution to my problem which is to find how many sphere of radius r are lying on the boundary (which means that in ...
0
votes
0answers
17 views

Lines tangent to two circles [migrated]

I'm trying to find the lines tangent to two circles. I've seen several examples but with poorlyy explained methods. Given the circle $(x-x_{0})^2+(y-y_{0})^2=r_{1}^2$ and the the line equation $y=...
1
vote
1answer
169 views

Finding distance between a point and a plane

I was tasked with finding a distance between a plane of the form $ax+by+cz +d=0$ and a point say $(a,b)$. Now I know a way to show a plane in Mathematica is with ...
0
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1answer
82 views

Intersection of two circles

I have two circles that intersect at point A, as shown in the image: The first figure shows the circle center greater (${125,0}$) in its initial position. The second figure shows the circle center ...
1
vote
1answer
73 views

Issue formulating RegionPlot3D to visualize RegionIntersection

Description I am looking to visualize gas cloud growth within custom modules. For demonstration purpose, it is assumed gas cloud takes a spherical shape whilst module is defined using a ...
2
votes
1answer
284 views

Extract coefficients of differential form in package RGTC

I am using the Package RGTC to do some calculations in Supergravity. It allows to define differential forms after specifying a co-frame. I am working in with the 10d coordinates $\{t,x,y,z,r,\phi_1,\...
11
votes
4answers
3k views

Axis/Angle from rotation matrix

With r=RotationMatrix[a,{x,y,z}] I can compute a 3D rotation matrix from axis/angle representation. Given a 3D rotation matrix r...
-3
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0answers
61 views

How to find equation of a sphere [migrated]

i'm having difficulty to find equation of a sphere in Mathematica. I already found the radius and center. ...
0
votes
1answer
46 views

Scale size PolyhedronData

How can I plot a truncated cube with size (sqrt(2)-1)? The code I am using is simply PolyhedronData["TruncatedCube"]
-5
votes
1answer
43 views

Calculating the top left corner in a 2d field [closed]

Given I have a field with several rectangles like shown in the picture. A point with its x and y coordinates are given. The height(h) and the width(w) are also given. How can I calculate the top left ...
1
vote
3answers
233 views

Only show part of a cube below an intersecting plane

I plot a cube and a plane. I just want to show the part below the plane. The code: ...
1
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2answers
115 views

How can I plot two concentric circles with a polygon inscribed in one and circumscribed about the other

So I am new to Mathematica still learning basic codes.. However I need help to become quicker in my research. Can anyone help me with the simplicit code to plot 2 concentric circles and a polygon of ...
2
votes
2answers
345 views

Draw a circle through 4 points on parabola [closed]

I have two dynamic perpendicular parabolas: $y=ax^2+c, x=by^2+d$, which intersect in four points (the coefficients are chosen that way). There is a fact that we can construct a circle through these ...
0
votes
0answers
44 views

How can I plot 2 concentric fixed circles with a polygon inscribed in one and circumscribed about the 2nd

Can anyone help me with the simplicit code to plot 2 concentric circles and a polygon of sides n (that I can manipulate) inscribed in one circle and circumscribed about the other. However I want the ...
7
votes
1answer
218 views

Rigid Rotation of a Point Cloud

If I have a group of points that are aligned along some vector. For example: ...
2
votes
1answer
70 views

Plotting a manifold within an existing surface

I have a dynamical system $\textbf{x}'=\textbf{f(x)}$ where $x\in \mathbb{R}^4$. However, $x_1 +x_2 +x_3 + x_4 =1$ and $0\leq x_i \leq 1$ for $i = 1,2,3,4$, meaning the system lives on the Tetrahedron....
1
vote
1answer
74 views
1
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2answers
66 views

Selecting points in list that are inside a contour [duplicate]

I have a list of points which form a closed (connected) contour or path in two dimensions. I would like to get all points from a second list which satisfy the requirement that they are inside the ...
2
votes
3answers
166 views

Distance from point to line [duplicate]

I'm a newbie with Mathematica and I managed to draw a line and a point in 3D on a graph ...
0
votes
0answers
46 views

Check if interpolated function passes through a specified region

Is there an efficient way to check if a curve that was obtained as an Interpolating Function (from solving differential equations numerically) passes through a given region? I am solving for two ...
18
votes
5answers
474 views

Is there a numerical method/built-in to calculate the boundary of a set of graphs?

Recently, I encounted a geometry problem in my work. For a curve-family that owns the following parametric equation: $$E(t,\theta)= \begin{pmatrix} x_E(t,\theta) \\ y_E(t,\theta) \end{pmatrix}$$ ...
6
votes
1answer
273 views

Generating cylindrical geometry via extruding a section

Toady I want to build geometry as shown below: I know the Mathematica owns the built-in like Cylinder[], Sphere[] and so on, ...
36
votes
3answers
1k 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 ...
16
votes
0answers
174 views

Bug in RegionMember?

Bug persisting through 10.4.1 RegionMember (new in V10) appears to have a bug. For some polygons it finds points that are clearly outside to be "members" of the ...
10
votes
3answers
244 views

The envelope of a set of translated and rotated ellipses

I achieve a dynamic graphics by using Manipulate as follows: ...
5
votes
3answers
243 views

Assumptions for RotationMatrix

I'm making C++ program, and in my program I need a rotation matrix around any vector. I wanted to extract RotationMatrix[fi,{x,y,z}] output and put it in my program....
1
vote
1answer
89 views

Plot a line passing through two given points in 3D space

How can I plot straight line passing through two given points in 3D coordinates? For example, given the points M1: (2, -2, 0) and M2: (1, -3, -5) ...
2
votes
0answers
111 views

Plotting Seifert surfaces

Is it possible to make a Seifert surface in Mathematica, such as a Seifert surface for a trefoil knot? I was thinking of taking the parametrization equations for a trefoil knot and then somehow ...
7
votes
6answers
692 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 the Wolfram Language? Edit: The result should still be ...
13
votes
5answers
1k views

To inscribe a circle in a given triangle

I am trying to to inscribe a circle in a given triangle but it isn't working. I've used GeoGebra with this construction and worked but as I'm new to Mathematica I am missing something. It can't be so ...
5
votes
4answers
1k views

An easier way to find the properties of an ellipse from its equation?

In this Q&A about fitting an ellipse to a set of points, there are multiple answers that generated general equations of the ellipse, like this one by @ubpdqn: However, the steps to find out the ...
4
votes
2answers
121 views

Arc length parameterization of a list of points?

Suppose I have a curve represented by a list of points in the form $\{\{x_0, y_0\}, \{x_1, y_1\}, ...\}$. How to generate a list of numbers $\{s_0, s_1, ...\}$ where $s_i$ is the distance of ith point ...
0
votes
1answer
76 views

Geodesic circle on a pseudosphere

I am trying to 3D print a portion of the pseudosphere, whose edge is geodesic circle. To do so, I plotted a region of the pseudosphere with the geodesics emanating from a point and I got this: The ...
-2
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3answers
121 views

Constructing an Equilateral Triangle Inscribed Inside a Circle

How to plot something like this? I need only the triangle and the 3 circles green. Thank you!
0
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3answers
39 views

A shift of a trapezoid and a connect to the original

I have: Graphics[{ Line[{{0, 0}, {30, 0}, {55, 50}, {-25, 50}, {0, 0}}] }] Now, I'd like to keep it in place, then shift a copy up and to the right, then ...
11
votes
1answer
149 views

How to make a two letter monogram in 3d like the one on www.mymo.is? [duplicate]

I want to achieve the same effect like the project on http://www.mymo.is/. By taking two letters and combine them in 3d, you can get a complex shape that looks like one letter on the one side and the ...
11
votes
4answers
2k 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, ...
9
votes
1answer
778 views

Max & min distance between two moving points

I am trying to find the minimal and maximum distance between two moving points with Mathematica in an interval. For example, ...
4
votes
1answer
207 views

geodesics' on torus

Is it possible to draw geodesics between the points in a path on a torus - toroidal surface? geodesics: generalization of the notion of a "straight line" to "curved spaces" ...
0
votes
0answers
44 views

How to apply a shear matrix?

I have curves that I made to create a design using graphics[], and I wanted to apply a shear to this. I know/think that a shear comes in the {1,lambda}{0,1} form, and that I'm supposed to my multiply ...