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

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14
votes
5answers
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 I still can't make one. I am not looking to make an ...
2
votes
5answers
162 views

Intersection coordinates of two spheres

I am trying to obtain a list of coordinates at which two spheres intersect. Take for example the spheres: sp1=Sphere[{0, 0, 0}, 1] and ...
6
votes
3answers
106 views

Inflate and unite a list of 0D to 2D regions

I've got a List of BoundaryMeshRegions, created via ConvexHullMesh: ...
11
votes
1answer
318 views

How to solve for the intersection points of two ellipses?

I have a parametric equation of two ellipses as follow $\begin{cases} x=a_1 \text{sin$\theta $}+b_1 \text{cos$\theta $}+c_1 \\ y=d_1 \text{sin$\theta $}+e_1 \text{cos$\theta $}+f_1 \\ \end{cases}...
3
votes
1answer
117 views

Find biggest Circle having all points close to a List of Polygons

Setting Imagine a List of polygons polys (type: BoundaryMeshRegion, polygons may also overlap): ...
1
vote
0answers
48 views

ConvexHullMesh fails for collinear points

I've got a List of PointLists, of which some contain only collinear points. I now want to obtain all ConvexHullMeshes of my PointLists. For more than two ...
1
vote
1answer
130 views

How to calculate the probability exactly

I random chioce three points from unit disk.I want to calculate the probability exactly that they circumcircle is contained within the unit disk still.Of curse,we can use the Monte Carlo to estimate ...
4
votes
2answers
79 views

Union of a List of ConvexHullMesh

How can I create a Union of a List of several ConvexHullMesh? My List is of variable length and the containing BoundaryMeshRegions may overlap. I want to create ...
3
votes
1answer
149 views

Projecting a Graphics3D object onto a plane

I would like to project a 3-dimensional cone onto a plane and mark the intersection (which is an ellipse) with a line. I find cone2 by performing a transformation ...
1
vote
1answer
80 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 ...
0
votes
2answers
66 views

Obtaining arc from a DXF file

I have a DXF file that contains an arc. I did the procedure to import a DXF file and generate a Graphics3D as below: ...
2
votes
1answer
296 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,\...
10
votes
7answers
562 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)? ...
0
votes
1answer
635 views

Code to give center of circle given three points in 2D? [duplicate]

does anyone know how to make a function C(p1,p2,p3)=center of circle that goes through p1, p2, and p3? This is in 2D Sorry this is poorly written but I ...
8
votes
1answer
252 views

Law of Cosines to determine angle change along spiral

The Spiral I'm trying to place circles along the outside of an Archimedean spiral. Shown below: ...
-1
votes
2answers
164 views

Selecting points inside a closed curve

Let's create a rather dense grid of initial conditions ...
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
163 views

Solving my graduation exam geometry problems with Mathematica [closed]

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
80 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
120 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
254 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, ...
4
votes
1answer
122 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
149 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
271 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
362 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
149 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
76 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
470 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
303 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. ...
1
vote
1answer
171 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 ...
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...
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
241 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
131 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
357 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 ...
7
votes
1answer
224 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
74 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
78 views
1
vote
2answers
68 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
173 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
481 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
277 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
176 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
246 views

The envelope of a set of translated and rotated ellipses

I achieve a dynamic graphics by using Manipulate as follows: ...
5
votes
3answers
247 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....