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

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20
votes
7answers
2k views

Find intersection of pairs of straight lines

I have a list of 24 points, in which two consecutive points (1st and 2nd, 3rd and 4th, …) are supposed to form a line: ...
1
vote
3answers
150 views

Solving my graduation exam geometry problems with Mathematica [on hold]

How capable is Mathematica when it comes to typical school geometry problems? Is there a way to throw constraints at it and get it to spit out a solution? Here are two geometry problems from my ...
1
vote
1answer
70 views

RegionPlot with rank constraint

I am trying to plot the feasible region of a rank constrained semidefinite program shown below: The Mathematica code that I am using is the following: ...
1
vote
1answer
113 views

The new introduced EulerMatrix problem

In the present version of Mathematica, there is a new command EulerMatrix[{α, β, γ}])// MatrixForm I read its document and I still don't understand it. For me, ...
0
votes
1answer
252 views

Is it necessary to introduce ImplicitRegion and ParametricRegion in version 10?

In version 10.0, Mathematica introduced a new function about region plotting: ImplicitRegion. But I'm wondered that haven't this function been already existed in the older version? That is, ...
7
votes
7answers
462 views

how to get $n$ equidistributed points on the unit sphere

We can get $n$ equidistributed points in the unit circle using CirclePoints. But how do you get $n$ equidistributed points on the unit sphere(surface of a ball)? ...
4
votes
1answer
114 views

Getting Area of a region transformed by GeometricTransformation

I tried this: Clear[b1, b2, A, p] b1 = {-1, 1}; b2 = {1, 1}; A = {{2, 1}, {-1, 1}}; p = Parallelogram[{0, 0}, {b1, b2}]; Then drew this: ...
1
vote
2answers
137 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
0answers
15 views

polarized hodge structure [closed]

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
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
354 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
145 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
115 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
72 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
458 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
301 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
votes
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
votes
1answer
84 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
74 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
285 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
votes
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
238 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
vote
2answers
120 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
352 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
45 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
219 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
71 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
75 views
1
vote
2answers
67 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
169 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
475 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
276 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
245 views

The envelope of a set of translated and rotated ellipses

I achieve a dynamic graphics by using Manipulate as follows: ...
5
votes
3answers
244 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
113 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
695 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
122 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
votes
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!