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
216 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: ...
5
votes
0answers
38 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
264 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
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0answers
133 views

3D Rotation Decomposition?

I have a 3D local xyz coordinate system placed in a world ENU (East-North-Up) coordinate system. The current relationship ...
3
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0answers
111 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
71 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
134 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
240 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
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68 views
+50

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 ...
3
votes
0answers
638 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
49 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
86 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
14 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
55 views

Pipe-fitting problem 3D

I have a 3D pipe-fitting problem for which I was able to write the following equations: $$ y = \tan (a)\sqrt{x^2 + z^2}\\ z = \tan (b)\sqrt{x^2 + y^2}\\ y = \sin (a)\sqrt{x^2 + y^2 + z^2}\\ z = \sin ...
2
votes
0answers
85 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
21 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
34 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
117 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
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0answers
50 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
55 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
67 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
82 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
66 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
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0answers
119 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
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0answers
520 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
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0answers
34 views

Counting the number of cubes in an isometric view

I had seen questions in a sample aptitude test, where an isometric view of an object made up of cubes was given, with some of the cubes removed. We were supposed to count the number of cubes present ...
1
vote
0answers
15 views

Find the volume between a hyperboloid and a cylinder

I'm trying to find the volume bounded by the graphs of $z = 0$ and $z = h$, outside of the cylinder $x^2 + y^2 = 1$, and inside the hyperboloid $x^2+y^2-z^2 = 1.$ I have tried to use cylindrical ...
1
vote
0answers
9 views

Why is tree traversal the fastest ray-box method?

I'm learning ray tracing (the problem of intersecting a ray, aka a vector, against a 3D box defined by a max and a min point) and I'm wondering: why is a tree traversal (e.g. bounding volume ...
1
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0answers
50 views

Find the linear (vertical) acceleration using a three axis accelerometer.

I genuinely apologise for what may be a poorly worded question. I'm extremely tired but have a ridiculous huge and important project due in on Monday for my degree. Thank you in advance for any help ...
1
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0answers
37 views

Best way to plot a 4 dimensional meshgrid

I have $4$ variables $X$, $Y$, $Z$ and $C$, and I want to plot these on a graph. Usually I would just plot the surface $X$, $Y$, $Z$ and then use color to represent the $4$th dimension, as shown ...
1
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0answers
35 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 ...
1
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0answers
24 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 ...
1
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0answers
37 views

3D Animation of object flying straight towards a surface

Lets say we have the following the orthogonal(?) 4x4 matrix, which represents a world space transformation in a right-handed coordinate system. ...
1
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0answers
96 views

3D Game: Pitch Yaw Roll of a point

I have a flat elliptical plane and I'm trying to figure out how to represent it based on its direction. So I basically need to calculate its pitch, yaw, and roll. I have a camera at $C$, and a point ...
1
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0answers
40 views

3d transformation in html5

I am trying to understand 3d-transformation in html5 and when it's rotation, scaling and moving - it is simple. But adding perspective confuses me. For example we have a rectangle: [400, 200], origin ...
1
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0answers
64 views

How to calculate center coordinates of two reverse arcs in 3D space

Given 3D points P1(200,60,140), P2(300,120,110), P3(3,0,-1), P4(-100,0,-1) and the radius of arc C1MP3 is equal to radius of arc C2MP1. How do I calculate coordinates x, y, z of points C1 and C2? ...
1
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0answers
44 views

Noob Question about a discrete surface

I am looking for a nudge in the right direction as to how to solve this problem. I have data which defines a solid cylinder. The data is composed of a 3d internal radius and a thickness at each point ...
1
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0answers
45 views

Finding area of intersection between 2 circles projected on a 3D mesh

disclaimer: I'm using terms from the 3D modeling world, so a "mesh" is just a finite set of 3D vertices, edges and polygonal faces; and with "topology" I mean the way the given mesh appears to the ...
1
vote
0answers
64 views

Least Squares Conformal Map Algorithm for UV coordinates

Can someone explain Least Squares Conformal Map in terms using Vertices(Vx,Vy,Vz) and UV coordinates or ST coordinate? I have read the lscm paper but I need it in XYZ value to understand it. ...
1
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0answers
43 views

determine the position of axis in 3d space

I added a picture here for the challenge of the day! I have a coordinate system (Xg, Yg, Zg) marked in blue color, and I want to determine their positions in the space (Xf, Yf, Zf). Those are unit ...
1
vote
0answers
34 views

Equation of ellipsoid given foci and two semi-axes

How does one find the equation of an ellipsoid given two foci, $(a,b,c)$ and $(d,e,f)$, and one semi-axis $l$? $c$ may not be equal to $f$.
1
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0answers
28 views

sweeping edges till they get a given elevation on an oblique plane

I am constructing wireframe model of 3d objects (prisms,..etc.). from a triangular mesh, I have obtained boundary points and fit striaght lines in order to get polygon edges refering to prism ...
1
vote
0answers
45 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 ...
1
vote
0answers
58 views

Determining pose of an object in 3d space

Given a 3D model of an object centred at the origin, if I place a camera at position (x,y,z) and make it face the origin, from the image rendered the object appears ...
1
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0answers
98 views

Change of coordinates in 3D

It's been a while since my last geometry class and I need some help in solving a very simple problem I have. I need to implement a zoom function in 3D in a piece of software I am writing. My system ...
1
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0answers
21 views

Higher-dimensional analogue of a cone point

If you look at the intrinsic geometry of a cone, there's a defect on the point of the cone known as a cone point. The only higher dimensional analogue I've heard of is what you get if you take the ...
1
vote
0answers
73 views

Mapping an object's projected 3D path to a pre-defined top-down 2D path.

The title of the question may be misleading and the context simpler. Please suggest more appropriate tags for this question. Consider looking at a plane from two different perspectives. Perspective ...
1
vote
0answers
70 views

Mathematical Basis for Dimetric Projection

For a school project, I need to make a program that can plot $y = f(x,z)$ using a form of dimetric projection. I was given the projection formulae $$\begin{align*} x' &= x + sz\cos(\theta)\\ y' ...
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0answers
72 views

3d Implicit Trigonometry help?

I'm trying to understand implicit 3D trigonometry, specifically with this equation: $$\sin(y)+\cos(z)=\cos(x)$$ Can someone please explain to me what is going on with this equation? I really can't ...
1
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0answers
82 views

Vector Tangent to Curve of Intersection

I am having problems solving this. Find a vector tangent to the curve of intersection of $z = 4x^2 + y^2$ and $z=(27-x^2-y^2)^{1/2}$ at the point $(1,1,5)$. I'm able to do this kind of thing using ...