# Tagged Questions

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

54 views

### Mirror image of a point about a line [migrated]

How can I calculate the mirrored position for a point in 2D space? I know the xy-coordinates of the two points which define the vector. I also know the coordinates for the yellow point which I want to ...
29 views

### how to know two aircraft getting far away each other? [closed]

Dataset: my algorithm is: calculate velocity vector each aircraft ...
449 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: $$E(t,\theta)= \begin{pmatrix} x_E(t,\theta) \\ y_E(t,\theta) \end{pmatrix}$$ ...
68 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 ...
255 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, ...
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 ...
165 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 ...
241 views

### The envelope of a set of translated and rotated ellipses

I achieve a dynamic graphics by using Manipulate as follows: ...
240 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 ...
80 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) ...
90 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 ...
649 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 ...
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 ...
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 ...
113 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 ...
65 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 ...
108 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!
37 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 ...
130 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 ...
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, ...
749 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, ...
183 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. Right isosceles triangle E (the large red triangle) ...
189 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" ...
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 ...
1k views

### Numerically solving Helmholtz equation in 3D for arbitrary shapes

Context While studying manifold Learning I got interested in finding the eigenvectors of the Laplacian. (also in connection to this problem of solving the heat equation) Following this and that ...
79 views

### Angle between two vectors in spherical coordinates [closed]

I have two vectors: H = {1, 0, π/4}; EA = {1, 0, 0}; Which I want to be in {r, Phi, Theta} - which would should give an angle between the two vectors as ...
114 views

### Draw Vectors in Spherical Shell and then Animate

I want to draw three vectors inside a spherical shell. One of the vectors will be moving, the others will be stationary. However, the animation is the next step. For now, I would like to get the ...
145 views

### HIghlight intersection of two disks [duplicate]

I tried this: reg1 = Disk[{0, 0}, 1]; reg2 = Disk[{1, 0}, 1]; reg3 = RegionIntersection[reg1, reg2]; Then this: ...
86 views

### Intersection of two volumes

I would like to know the volume of the intersection of a cone and a cuboid : ...
330 views

### How to export textures?

Is there any object geometry format for which Mathematica supports the exporting of textures for external (non-Mathematica) use ? If not does anyone know of work arounds? All the texture primitives ...
105 views

### hippocrates moons for any shape

Can someone help me create code for a hippocrates moons on random shape with given amount of edges? I want to make something like this: when you press button, it asks you for the amount of ...
77 views

### Intersecting ellipsoids

First of all I know that findng whether two ellispoids intersect is complicated and there are specific algorithms created for this purpose (see, for instance, [1]. Actually, I am trying to follow this ...
3k views

### Drawing a square root spiral

Here is a start. I'm looking for a nice way to draw it. ...
85 views

### Wolfram alpha algorithm for geometric packing in 2D [closed]

Is there any way to gain access to the algorithm that wolfram alpha uses? More specifically, I want to pack small circles in hex and square patters in a larger cicle ...
259 views

### Unexpected behavior of GeometricTransformation

Bug introduced in 8.0 or earlier and persisting through 10.3 or later I have the following mapping on the complex plane: $$z \mapsto \tau \mu z-1,$$ where $\mu$ is complex, $\tau$ is real ...
184 views

### intersecting cylinders

I try to replicate the two figures of two intersecting cylinders from here. I tried ...
143 views

### Surface Plot 3D of a strongly concave shape

I have a list of {x,y,z} points that all lie on the surface of an object (model output from COMSOL). I would like to generate a graphics object that reproduces the surface. Ideally, I would like ...
423 views

### How to use Undocumented Functions Prism, Tetrahedron and Hexahedron

Taking a look at this question and this one, I checked to see if Mathematica really does not have a Prism primitive. To my surprise the function ...
107 views

### Tell if a point is inside a FilledCurve

Convert a letter into a FilledCurve: ...
108 views

### How do I tell if two sets of dots are in some way similar?

I have two sets of dots (x,y coordinates) and I'd like to figure out if there's a way to find out if the second set of dots is (more or less) "close" to the first one. I may plot these two sets in ...
78 views

### Easy way to get the boundary of a geometric object [closed]

I am trying to define von Neumann boundary conditions for a prism. To do so I need the boundary of the geometric object. I can't seem to find an easy way to do this. I have tried to hard code a ...
515 views

### How to manipulate a circle in GeoGebra style?

I want to emulate the GeoGebra app. I want to get an effect like this in Mathematica. I don't know how to move whole circle without changing the radius of the circle. My sample code： ...
58 views

### Find volume of a translated and rotated ellipsoid below xy (horizontal) plane

I am trying to find the volume of the lower part (above horizontal plane) of an ellipsoid that is clipped by the horizontal (or x-y) plane. This ellipsoid is also translated (i.e. origin is not at ...
107 views

### Minimal perimeter of all possible polygons

We had a fun problem for a student activity today: Let $P(z) = z^8 + \left(4\sqrt{3} + 6\right)z^4 - \left(4\sqrt{3} + 7\right)$. What is the minimum perimeter among all the $8$-sided polygons in the ...
167 views

### Simple triangular meshes of primitive shapes

I'd like to generate triangular meshes or a cylinder and sphere primitives as part of a lattice meshing program I am writing to experiment with Mathematica. Consider the following snippet: ...
91 views

### How do I create a function to rotate a rectangle about its origin? [closed]

I am new to Mathematica and was trying some new things. I wanted to rotate a rectangle using a rotation matrix by any angle theta from say o to 2pi. I could do it using predefined Mathematica ...
373 views

### intersection between polygon. Algorithm to check it [closed]

I'm working on an algorithm which should check if two polygons, described by their vertex coordinates, are: one inside the other, are intersecting or are separated image below describe this three ...
124 views

### Animate FromQuarternionTo3DRotation nb file with 4 quarternion values

I have a csv file. Inside the csv file, there are few rows of 4 quartenion values. I would like to animate the quarternion nb in http://demonstrations.wolfram.com/FromQuaternionTo3DRotation/ I ...