The (3d) tag is for things related to 3-dimensions. For geometry of 3-dimensional solids, please use instead (solid-geometry). For geometry that is not on a plane, but otherwise agnostic of dimensions, perhaps (euclidean-geometry) or (analytic-geometry) should also be considered.

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11
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0answers
435 views

Visualizing a Calabi Yau

I would like to understand how I can visualize the quintic threefold $$ z_1^5 + z_2^5 + z_3^5 + z_4^5 +z_5^5 - 5\psi z_1z_2z_3z_4z_5 = 0$$ For a similar problem, Hanson proposes the following: ...
6
votes
0answers
564 views

Random 3D points uniformly distributed on an ellipse shaped window of a sphere

How can I generate random points uniformly distributed on the surface of a sphere such that a line that originates at the center of the sphere, and passes through one of the points, will intersect a ...
6
votes
0answers
107 views

Analytic caustics for 3D objects

Is it possible to efficiently calculate caustics for a given 3D object, like a torus, or a cube? To be more precise: let's assume that we have a 3d torus, resting on a 2d plane and a single light ...
5
votes
0answers
59 views

Visualising 3rd degree equations

I know that general second degree curve, i.e. $ax^2 + by^2 + 2hxy + 2gx + 2fy + c=0$ gives us the equation of different cross sections of a cone. Similarly, what does a third degree* curve actually ...
5
votes
0answers
29 views

Does a point quadrilateral form a rect in 3D space?

I have 4 points with x and y coordinate and would like to find out a way to check if given quadrilateral would be a rectangle in 3D space. I tried a bunch of conditions, but there was always and edge ...
5
votes
0answers
93 views

From Icosahedron to Pentagonal hexecontahedron (Floret Tessellation)

Inspired by this post: Floret Tessellation of a Sphere I tried to transform myself an icosahedron into its simplest Floret tessellation. But I am having trouble when applying the 'method' given in the ...
5
votes
0answers
85 views

Generating a 3d ribbon from a series of points

I am attempting to generate a 3d ribbon from a set of 3d points. The idea is to generate a realistic ribbon which follows those points. In its current state, one example looks like this: In this ...
5
votes
0answers
383 views

How can I solve the Poisson PDE efficiently and fast in cylindrical coordinates?

I am trying to numerically solve the Possion PDE in cylindrical coordinate system. $$\Delta f = {1 \over \rho} {\partial \over \partial \rho} \left(\rho {\partial f \over \partial \rho} \right) + {1 ...
3
votes
0answers
80 views

Is it 3-D Catalan numbers?

I am studying Catalan numbers recently but I think that how about 3-D Catalan? So that I imagine following situation ; A man travel through the path-way parallel to $ x, y, z $ axis from O ...
3
votes
0answers
132 views

Is this a legit way to visualize complex functions?

I am doing laplace transform in a class and I hate how there seems to be no graphical support when things are transformed to laplace domain i.e. nobody cares what they look like in laplace domain But ...
3
votes
0answers
115 views

Is it possible to create a volumetric object which has a circle, a square and an equilateral triangle as orthogonal profiles?

This question was posed to me by a friend (formulated as creating a peg to fit perfectly into holes of these shapes), and after an experiment in OpenSCAD it seems it is not possible - either one ...
3
votes
0answers
219 views

Maximum length of pencil in a pencil case

What is the maximum length of an unsharpened, cylindrical pencil inside an empty rectangular pencil box? Or, in a rectangular cuboid of dimensions $x \times y \times z$, what is the maximum possible ...
3
votes
0answers
78 views

How to solve a distance problem inside of a picture?

sorry for my bad english. I have the following problem: In the picture you can see 4 different positions. Every position is known to me (longitude, latitude with screen-x and screen-y). Now i want ...
3
votes
0answers
152 views

Visualizing and manipulating 4-dimensional data with 3D technology

It is possible to visualize 3 dimensional data (like a scatter plot) by projecting it on a 2 dimensional screen in a way that allows to interact with it in an intuitive way. Is it possible to ...
3
votes
0answers
339 views

Convolution theorem in 3D

Suppose to have a 3-dimensional discrete grid. I would like to convolve it with a 3-dimensional tensor (a 3x3x3 "cube"), applying the convolution theorem. Hence, I should apply a Fourier transform to ...
3
votes
0answers
881 views

Three-dimensional vectors and force systems

Full disclosure: this is a homework problem. However, I find myself stuck in the middle. The problem is below As shown, a system of cables suspends a crate weighing W = 350 . (Part C 1 figure) ...
3
votes
0answers
58 views

Scale-agnostic, differentiable, co-planarity measure

I am looking for an (almost everywhere) differentiable function $f(p_1,p_2,p_3,p_4)$ that given four points will give me a scale-agnostic measure for co-planarity. It is zero if the four points lie on ...
2
votes
0answers
53 views

3D Shape with only coplanar faces?

I just thought of this problem, and it's bugging me that I can't find any sort of shape that fits it. Are there any 3D shapes with only faces that have coplanar matches with other faces in the shape? ...
2
votes
0answers
21 views

can't figure out multilateration with xyz positions of each post and difference in time

I'm having some real issues figuring out multilateration. I'll start by saying I'm not a math whiz, but I am usually able to figure most things out, but this one has been throwing me through a loop ...
2
votes
0answers
11 views

How can i reflect position and direction vectors from a plane

I'm now working on a project that has mirrors. I'd like to reflect a virtual camera and the way which i can do this is to reflect two vectors - position and normalized direction vectors of the camera. ...
2
votes
0answers
23 views

Cartesian/Parametric 3d equation of a cheese twist?

Hi I'm looking for the equation of a cheese twist in 3d (either parametric or cartesian)... Can be multiple planes but was wondering if anyone had any idea to execute something like this? Thanks e.g. ...
2
votes
0answers
15 views

Finding intersections of tori/toruses

I am looking for intersections of three tori. Is this possible? If so, how? To put things in perspective: I am looking for the coordinates of point P in space, and I have a triangle on the 'ground'. ...
2
votes
0answers
62 views

Calculating object position in 3D space

I'm looking for an algorithm to calculate the position of point P in space using a triangular(/rectangular) plane on the 'ground'. The position between the points ABC of the triangle on the ground are ...
2
votes
0answers
28 views

Taylor expansion need help understanding.

I am at the moment reading a paper (SURF) and trying to understand what is happening here and how the things works as it does.... a non maximum supression is performed on the scale space ...
2
votes
0answers
15 views

Dinamically generate Goldberg polyhedra G(m,n)

In these pages the autor provided a lot of info about some Goldberg polyhedra (http://en.wikipedia.org/wiki/Goldberg_polyhedron): http://dmccooey.com/polyhedra/DualGeodesicIcosahedra.html ...
2
votes
0answers
33 views

Compute volume of the tetrahedron from circumsphere test

I'm working on a computational geometry algorithm. In every iteration I solve the matrix below, where (a,b,c,d) are the vertices of a tetrahedron, and e is an arbitrary point. Solving the determinant ...
2
votes
0answers
22 views

Calculate vector of an object aligned to another object in a 3D envorionment

I have an object (100x100x5) with given coordinates and angles. Now I want to place another object aligned to the left/right side of the "original" object. On the X-Axis I need to substract/add 100, ...
2
votes
0answers
79 views

Rotate a 3D Vector onto Another 3D Vector

I am trying to transform one triangle onto another triangle in 3D space (Right Triangles). My thought was I align the forward and left vectors, then translate the center of one to the other. ...
2
votes
0answers
352 views

Rotating a cube about an axis through opposite vertices

I have a cube made using CSS transforms that I'm trying to animate rotating about an axis going through 2 opposite vertices. What I have: Initial cube: ...
2
votes
0answers
25 views

rotating vector based on plane normal

This is probably very basic, but here is a drawing of what I'm trying to achieve : Explanation : Those are 3D normalized vectors and I'm trying to change v1 to v1' based on vn. As shown in the ...
2
votes
0answers
121 views

Best closed convex surface fitting N points in 3D

First. It's easier to understand the problem by describing the application where it arises from. We have a convex body $B$ in $\mathbb{R}^{3}$ and measure points on its surface. The measurements are ...
2
votes
0answers
66 views

How many edges is sufficient to check to prove polyhedron convexity?

Consider the set $\{u_{1}, u_{2}, \ldots, u_{n}\}$ of points on the spere in $\mathbb{R}^{3}$ (i. e. $||u_{i}|| = 1$) and their convex hull C = $Hull(u_{1}, \ldots, u_{n})$. It's obvious that each ...
2
votes
0answers
31 views

Taking into account Camera Direction in 3d models using Trig

I have been working on a 3d rendering project as code. I am a bit stumped on the math though. I know how to render points using arctangent on an HTML canvas using JavaScript, like this: ...
2
votes
0answers
57 views

What should happen to an impossible cube at a vertex?

I have automated the process of impossible-cube renders in Blender3D as an exercise. However, while the automator works fine as long as the intersection of the 'impossible' edge and the nearer edge is ...
2
votes
0answers
116 views

What is the Area formed when a line is traced between two 3D curves?

This question is quite related to intersection of cylinders, Hyperbolic paraboloid and modelling. I am welding a trunnion to a pipe (both are hollow cylinders in different geometry). They intersect ...
2
votes
0answers
23 views

The exact type of my 3d model

I have reconstructed vertical features (hole like objects lie on a vertical face) lie on two connected faces. To understand the situation, I say I have 2 walls with many windows and doors on ...
2
votes
0answers
70 views

Finding point of contact of a sphere in an image

I have an image, in which there is a table, and on this table, a sphere. I would like to find the point of contact between the sphere and the table. This point can be the center of the sphere, for ...
2
votes
0answers
313 views

how to calculate the volume of irregular shape by the Cartesian coordinates of its corners?

I've 4 points in a plane "A" and another 4 in another plane "B". is there a way to automatically calculate the volume contained into this irregular box? The automation is important as this set of 8 ...
2
votes
0answers
74 views

Find an SO(3) matrix which satisfies some linear constraints

I have the following optimization problem: $\displaystyle \min_R \sum_{i=1}^n (X_i^T R Y_i)^2$ where $R \in \text{SO}(3)$, i.e. is a 3x3 rotation matrix, and $X_i,Y_i \in \mathbb{R}^3$. If $n \le ...
2
votes
0answers
58 views

Are there algorithms related to cloud shapes?

This is going to be applied in programming, but I thought the question would be best answered here, since I'm just looking for algorithms at the moment. I'm generating clouds on the fly, but I'm not ...
2
votes
0answers
57 views

Finding a simple template within a 3D point cloud

I want to find a template - defined by 5 coplanar, non-collinear points - within a point cloud of say 100 3D points, in the most efficient way possible. I know there is the ICP (Iterative Closest ...
2
votes
0answers
145 views

RANSAC line fitting (3d) by line segments (3d)

I am having many 3d line segments. some of them are nearly parallel and some are oriented in to different direction. I want to avoid outliers and to get the best line 3d to represent the given ...
2
votes
0answers
227 views

Big data: 3D clustering with over 40 groups

I am a computational neuroscientist and I struggling over a problem; I have around one hundred 3D matrices (I am working on MATLAB at the moment), each of them is 121x145x121. Any 'cell' stores a ...
2
votes
0answers
74 views

Are there 3D tilings of a 3D projective hyperplane or 3-sphere?

I noticed that pentagons tile the projective plane (a spherical dodecahedron). Something they do not do on a flat euclidean plane. Is there analogous 3D tilings (honeycombs) of a 3D projective ...
2
votes
0answers
106 views

How do you call a 3d convex shape made of 8 arbitrary points?

Is there a name for a 3d convex shape made of 8 arbitrary points ? That would be like a cube or a box, except that the distances would not necessarily be equals, neither the angles necessarily be ...
2
votes
0answers
136 views

Transform 3D vectors between planes using a matrix

I've got 6 points in 3D space: $A,B,C,D,E,F$, that represent 4 vectors. $AB$ is perpendicular to $AC$ and $DE$ is perpendicular to $DF$. I need to find a transformation matrix M, that transforms $AB$ ...
2
votes
0answers
508 views

points of intersection on a randomly situated plane and ellipsoid (spherical) in 3d space

if i have an ellipsoid and a plane oriented in any way in a 3 dimensional coordinate system, and they intersect; is there a way to find an equation that describes (or at least approximates) all points ...
2
votes
0answers
763 views

Is there a formula for the solid angle at each vertex of tetrahedron?

A tetrahedron has four vertices as much as a triangle has three vertices. A tetrahedron therefore can have four solid angles as much as a triangle can have three angles. I am wondering: Is there a ...
1
vote
0answers
24 views

Given a single point in 3d space, and 3 points that make up a triangle, find the closest point in/on the triangle to the point.

Given point $(p,q,r)$ and 3 points which make up a triangle, find the closest point in the triangle to the point in space. From the triangle, we can find the equation of the plane $Ax+By+Cz+d=0.$ ...
1
vote
0answers
21 views

What is the total volume of wood used for the model?

A person makes a model of a house in construction class. The block of wood for the base measures 6 inches by 4 inches, and is 4 inches tall. He used a triangular prism for the roof, whose ...