# Tagged Questions

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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### Rotating prism in 3 dimensional space

Say you have a rectangular prism, whose sides can be expressed as specific domains and ranges of 3 dimensional planes. I'm trying to calculate the new position of the prism after a series of rotations....
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### triangulation of a surface, adapted to curvature

This is about my printed models of mathematical objects. All of the designs that I've published so far consist of grids of bent ‘rods’, and in most of them the spacing of vertices depends on the rod'...
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### Cone in three dimension

According to me the following statements are true Statement 1: The guiding curve of a right circular cone is always a circle. Statement 2: If the guiding curve is a circle then the cone may or may ...
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### Cube divided into subcubes: Find out index of the side of subcube $c$ that faces subcube $n$

I'm trying to figure out a general formula to find out the side for every cube that faces a specific cube inside the following structure: Given index n and the subcube index c find out the ...
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### An equation to figure out where on the other side of earth you are looking

I'm trying to derive out an equation that will take variables for the longitude and latitude of your current position on earth, and the pitch and heading that you are looking downwards towards the ...
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### Solve for Rotation Angle About Arbitrary Axis

I'm working on an embedded system which has been tasked with an interesting problem. It knows the initial location of three points on a sphere. After the sphere rotates, it knows the distance by which ...
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### 3d equivalent geometric shape of a 2d tiled space

In case anyone remembers the old game Comets, it was about this: You had a spaceship which you could move around the screen and various meteors appeared and you had to shoot them up. When you moved ...
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### Inverse of Perspective Matrix

I am trying to calculate Image to World model for my thesis dealing with road lanes. As a disclaimer I have to say that linear algebra is not my strong suite. The idea is - given that I know yield, ...
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### Surface of a polynomial

How can I find the surface represented by the polynomial $$x^2-y^2-2xz=0$$ any clue please?? I have tried to plot it using Maple
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### Ellipsoid but not quite

I have an ellipsoid centered at the origin. https://en.wikipedia.org/wiki/Ellipsoid Assume $a,b,c$ are expressed in $mm$. Say I want to cover it with a uniform coat/layer which is $d$ mm thick ...
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### How can I get the angle between two 2-component 3d angles?

If I have two 3d angles like [120 degrees, 40 degrees] and [70 degrees, 90 degrees], how would I calculate the scaler angle ...
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### minimize tip-tilt in surface data via simple matrix transformation

I have an $M \times N$ array $(A_{M\times N})$ of regularly-spaced elevation points which thus define a surface, although each $z(x,y)$ datum corresponds to a unique $(x,y)$ pair -- so-called 2.5D ...
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### difference between 2 quaternions

I'm trying to calculate quaternions relative to a given orientation. It is easiest for me to explain my intentions by means of an example: Suppose you have a vector $v1=[0,0,1]$ and I want to rotate ...
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### Dot Product of Position and Directiom Vectors

Assume that we have one normalised 3D vector (D) representing direction and another 3D vector representing a position (P). How can we calculate the dot product of D and P? If it was the dot product ...
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### Retrieve Cubes that Share a Vertex [closed]

Suppose that we have a world with an infinite number of cubes, each of which are 1x1x1 in size and have integral coordinates, e.g. (1, 2, 3) Given that C is a cube at (XC, YC, ZC) and that P is a ...
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### Matlab 3D plots

I am currently in high school and is writing a maths research paper on a calculus problem. In the conclusion, I would like to include a 3D plot of a function I found. It goes something like this: a, ...
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### Find a vector from the origin that is a known length and is orthogonal to the plane defined by its endpoint and two other known points?

I have a mechanism that pivot on one point, which I'll call the origin, and is moved by pushing on two other points. These other points are not fixed on the mechanism, but I can compute where they ...
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### How do projections in 3D with homogeneous coordinates work?

Affine 3D transformations can be expressed in homogeneous coordinates by a matrix $M \in \mathbb{R}^{4 \times 4}$. This means we have 16 parameters to calculate. The first thing I asked myself is how ...
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### How do I compute the angles of a pyramid from the angle between its sides?

I have been given the following problem to solve: In a right pyramid whose base is an equilateral triangle, the angle between 2 side-faces is 70 degrees. Compute the base angle of a side-face. I ...
Find the equation of the plane which contains the line of intersection of the planes $x+2y+3z-4=0$ and $2x+y-z+5=0$ and which is perpendicular to the plane $5x+3y-6z+8=0$ By setting $z=0$ I found a ...