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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10
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0answers
385 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
315 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
105 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
66 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
72 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
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0answers
352 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
85 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
68 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
187 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
75 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
150 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
306 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
869 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
56 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
19 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
41 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
246 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
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0answers
23 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
117 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
30 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
50 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
111 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
22 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
63 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
266 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
71 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
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
128 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
197 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
94 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
134 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
434 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
721 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
14 views

How to compute the best fitting frustum for a set of points?

I am struggling with a problem that I am sure is well known, but I could not find any answer using google or searching on MathOverflow. I have a set of 3D points (x,y,z) and a camera reference frame ...
1
vote
0answers
11 views

Calculate the plane angle from 2D plane

I am analysing a squared plane from a perfect cube. This plane is distorted by the perspective view of a camera. I would like to know ask please, some approaches of how could I get to know the ...
1
vote
0answers
14 views

How do I calculate 3D movement based on yaw, pitch and roll?

I'm creating a 3D game demo and I need to calculate the position of the player in the space (i.e. the player's x, y and z coordinates). I understand that this would be affected based on the camera ...
1
vote
0answers
25 views

Mapping A point from one 3D Coordinate System to Another 3D coordinate System with Euler Angles between the two systems given

Suppose I have a point in the green coordinate system, and I wish to describe it in reference to the orange coordinate system. I know the roll, pitch, and yaw of the green system with respect to the ...
1
vote
0answers
10 views

3D topographic progress compensation by the least squares method.

I'm looking for an explanation of the least squares method used in the case of a correction of 3D point network. We have reference points with known coordinates XYZ, we calculate intermediate points ...
1
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0answers
56 views

Trying to find the volume of a 3D torus shape that I made

After playing around with 3D parametric equations on my calculator (modifying the equations of a standard torus), I came across a shape that I like. The equations are: $$x=(2+\sin t)\cos u$$ ...
1
vote
0answers
39 views

Catenary equation in 3D

I have two points with coordinates A(x1,y1,z1) and B(x2,y2,z2). There is a third point which is lowest point of the catenary curve. I only know z-coordinate of this third point. I need to find ...
1
vote
0answers
49 views

Calculating Normals across a sphere with a wave-like vertex shader

This is a bit of a CS question, but more than not it's a 3D math problem. I've been trying to get the correct normals for a sphere I'm messing with using a vertex shader. The algorithm can be boiled ...
1
vote
0answers
24 views

Sections of cones in higher dimensions

Everybody knows that when a plane intersects a cone at different angles and positions, we get conic sections. But, I wanted to know that if the same was possible in higher dimensions. If we take the 4 ...
1
vote
0answers
41 views

Find 3D concave hull based on original model and convex hull

I want to find the concave hull of a 3d model, with a threshold for the maximum edge size. Googling around let me to the following approach (mainly abstracting from 2d approaches): Determine the ...
1
vote
0answers
104 views

Triple integral, finding the volume between two planes and a surface in 3D

So I have tried to solve this problem, but I'm running into a problem, because the top circle (intersection of the function with z=1) when you project it onto the xy plane is smaller than the circle ...
1
vote
0answers
32 views

unique cube arrangments

i have received this math riddle which i cannot solve, the riddle: given a set of cubes, a unique shape is any shape that was created joining cubes sides together and does not match any previously ...
1
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0answers
57 views

How to determine 3d measurements

I am trying to reproduce an artwork that is both a 2D drawing and 3D paper sculpture by Romanian artist Liviu Stoicoviu done in the 80s, The Triangle: I have tried to trace the 2D artwork which ...
1
vote
0answers
49 views

What function has a 3D graph that will look like a spiral into a singularity?

I am trying to draw text spiraling into a black hole, from a more interesting slightly off-orthogonal viewpoint. I think a function that defines a black hole/singularity surface might look something ...
1
vote
0answers
22 views

Folding a Given Net into a Polyhedron Automatically!

There are some applications to fold predefined nets into the polyhedra, e.g. "Poly" or this applet. Is there any application which automatically folds any net generated by the user, if possible?
1
vote
0answers
277 views

Helix around helix parametric equation?

I know the parametric equation for a 3d helix is: x = R cos t y = R sin t z = h t can somebody explain to me this parametric equation (image and equation from Wolfram) for a "Helix around helix" / ...
1
vote
0answers
106 views

Equation for Circle in 3D Space Given Center, Radius, and Point

I'm looking for how to derive the equation of a circle, in 3D space, given the following information: The Center Point The Radius One point on the circle I understand that this is functionally the ...