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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1answer
39 views

How to convert 2D coordinates to 3D coordinates?

I am writing some software for image processing where a user can just draw something (e.g. a cube) in paint and the software will give you the 3d coordinates of the corners on that drawing. What would ...
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0answers
12 views

Distance between a point and a 3D figure

If I have some basic 3D shapes like rectangular prisms, cylinders and spheres (whose positions, orientations and dimensions are fully known), what is the simplest way of finding the shortest distance ...
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1answer
21 views

Find third vector with opposite deviation

Say there are two unit vectors a and b. I want to find unit vector c such that the deviation between c and a is the opposite to the deviation between a and b. The angles between c and a, and a and b ...
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1answer
26 views

Concatenating two Rotation-Matrices

I have two $2\mathrm{D}$-planes in $3\mathrm{D}$-space with orientation parameters expressed as rotation $R_1$ and translation $T_1$ and rotation $R_2$ and translation $T_2$ with respect to some ...
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1answer
21 views

How to find the amount of degrees to rotate a vector to be 90 degrees another vector?

I have a vector V that rotates around an axis K and a vector N all in 3D space. I need to find how much to rotate the vector V around S so that it lies 90 degrees to N. So far I have been doing it ...
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1answer
15 views

How can the angle between any two azimuth dip pairs be found?

The order of rotation is azimuth then dip. I've tried pythagoras style answers but testing showed it was the wrong approach. How can I find the angle between any two pairs?
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1answer
36 views

Write the equation $4x^{2}+4z^{2}=5$ in spherical coordinates.

Write the equation $4x^{2}+4z^{2}=5$ in spherical coordinates. I used the facts that $$ \begin{align} x&=ρ\sin\theta\cos\phi\;,\\ z&=ρ\cos\phi\;, \end{align} $$ And ended up with: $ 4 (ρ^2 ...
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1answer
44 views

Variance of $3$-dimensional vectors

I am currently optimizing some code and thus, I want to replace an inefficient OpenCV function, which calculates a covariance matrix. The thing is, that I only need the trace of this covariance ...
-2
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1answer
35 views

Give a geometrical interpretation of the intersection of the planes with equations [closed]

Give a geometrical interpretation of the intersection of the planes with equations \begin{align} &x + y − 3 = 0\\ &y + z + 5 = 0\\ &x + z + 2 = 0 \end{align} what is a geometrical ...
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0answers
25 views

Finding angle between y axis in two rotated coordinate systems

I basically have two coordinate systems that have the same origin, and can measure the coordinates of a vector (but only one) in respect to both of them. I need to calculate the angle between the y ...
1
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2answers
35 views

Given a band of $m$ opaque squares arranged in a circle, can we find a viewpoint from which we see exactly $m/2-1$ squares?

Given a band of $m\ge 3$ opaque squares arranged in a circle, can we find a viewpoint (i.e. a point on a sphere centered at the midpoint of the circle with a radius large enough to see the whole ...
10
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1answer
239 views

How many spheres can fit in this box?

HASELBAUER - DICKHEISER TEST #15: What is the maximum number of one inch-diameter spheres that can be packed into a box ten inches square and five inches deep? My attempt to solve this: If i ...
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2answers
54 views

Geometrical interpretation of solving a 3x3 system of equations

Solve the following system of equations and give a geometrical interpretation of the result. \begin{align*} x + y + z &= 6\\ 2x + y − 3z &= -5\\ 4x − 5y + z &= −3 \end{align*} I know that ...
2
votes
1answer
31 views

find 3 angles to rotate vector to align with second vector

First I would like to say that I have seen posts such as that found here: Calculate Rotation Matrix to align Vector A to Vector B in 3d? As well as formulas such as: ...
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0answers
17 views

Visible faces of a polyhedron $P$ on a path of viewpoints on the unit sphere looking at the center of $P$

Let $P$ be an opaque polyhedron. Assuming parallel projection, let's define a viewpoint to be a point on the unit sphere around the center of $P$. Let's say that two viewpoints $v_1$ and $v_2$ are ...
0
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1answer
17 views

3D Denjoy–Riesz theorem

The Denjoy–Riesz theorem states that every totally disconnected subset of $\Bbb R^2$ is the subset of a Jordan arc. Is this true in $\Bbb R^3$? Originally I thought Antoine's necklace would be a ...
8
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4answers
182 views

Show that every rotation in $\mathbb{R^3}$ can be written as the product of two rotations of order 2.

Show that every rotation in $\mathbb{R^3}$ can be written as the product of two rotations of order 2. Here's my attempt at a solution: We know that any rotation in $\mathbb{R^3}$ can be ...
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0answers
16 views

Relation between focus and camera intrinsic parameters

Does a focus tuning affect the camera intrinsic parameters? More precisely, if the focus of a camera is changed, does the camera intrinsic parameters matrix remain unchanged? Apparently, since this ...
1
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3answers
40 views

Conclusion that can be drawn from 4 points in space whose angles are $90^{\circ}$

Four points A, B, C and D are in space such that angles $A\hat BC, B\hat CD, C\hat DA$ and $D\hat AB$ are all right angles, then A, B, C, D cannot be coplanar A, B, C, D are necessarily coplanar. A, ...
0
votes
1answer
22 views

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 ...
0
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0answers
11 views

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 ...
0
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1answer
15 views

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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0answers
22 views

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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0answers
13 views

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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0answers
16 views

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 ...
3
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1answer
27 views

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 ...
1
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1answer
62 views

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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1answer
47 views

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
11
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5answers
804 views

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 ...
0
votes
1answer
31 views

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 ...
0
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0answers
24 views

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 ...
0
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1answer
21 views

Equation of plane passing through intersection of line and plane

Find the equation of the plane passing through the intersection of line $$\frac{x-2}{3}=\frac{y+1}{4}=\frac{z-2}{2}$$ and the plane $$x-y+z=5$$ and parallel to a vector with direction ratios ...
5
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3answers
90 views

One-sided submanifolds in Hempel's 3-Manifolds

Early on in Hempel's book 3-Manifolds, he discusses two-sided submanifolds: if $N$ is a manifold of dimension $n$, and $M$ is a submanifold of dimension $(n-1)$, then $M$ is two-sided if there is an ...
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3answers
49 views

Equations of the line which intersects the lines $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ and $\frac{x+2}{1}=\frac{y-3}{2}=\frac{z+1}{4}$

Find the equations of the line which intersects the lines $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ and $\frac{x+2}{1}=\frac{y-3}{2}=\frac{z+1}{4}$ and passes through the point $(1,1,1)$. First I ...
0
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1answer
47 views

Get 4 points of a rectangle inside a plane

There is a plane defined by 3 points in 3D space. I need to get the 4 edges points of a rectangle that: Lies on the plane. Has Width and high of w and h. Centered at the Z axis. One of it side is ...
1
vote
1answer
47 views

Find the equation of the plane through a given point, with given normal vector [duplicate]

I need to find the equation of the plane through the point $(−1,.5, 3)$ with normal vector $𝐢 + 4𝐣 + 𝐤$. I know that the equation will look something like this: $1 (x + 1) + 4 (y - .5) + 1 (z - 3) ...
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2answers
25 views

Solving vector equations of planes

Find the line of intersection of two planes denoted by: $r=\overrightarrow{b}+\lambda(\overrightarrow{b}-\overrightarrow{a})+\nu(\overrightarrow{a}+\overrightarrow{c})$ ...
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3answers
21 views

Vector equation to line equation

I've not read vectors in math yet but I'm done with those in physics. I want to find out a line equation from a vector equation. Say I've 2 points in 3D space: Point A with coordinate $(a, b, c)$ and ...
0
votes
1answer
43 views

Why do two different quaternions appear to have the same rotation?

When using a Quaternions I've noticed something I don't quite understand. If I'm rotation $\frac{\pi}{2}$ radians on the Y axis it goes from $[0,0,0,1]$ to $[0,\sqrt{2},0,\sqrt{2}]$. A rotation of ...
2
votes
1answer
44 views

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 ...
0
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0answers
11 views

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 ...
0
votes
1answer
12 views

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 ...
0
votes
2answers
37 views

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, ...
1
vote
1answer
21 views

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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0answers
16 views

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 ...
0
votes
0answers
18 views

Scaling 3D-Points depending on Groundtruth

I generated points of a trajectory of a plane, like: $$ \begin{array}{lcr} \text{x} & \text{y} & \text{z} \\ \hline 0.396950& -0.199959& -0.000336\\ 0.122995& -0.199975& ...
1
vote
1answer
50 views

How to adapt “System of Circles” method to 3D for finding a sphere given 4 points?

I want to analyze (computational complexity & running time) of different approaches to determining a sphere in 3D given 4 points on its surface. To start I have been searching for different ...
0
votes
1answer
26 views

direction cosines to axis confusion

I'm asking for clarification on following question : Find the direction Cosines of AB and hence calculate the angle in degrees ,between AB and each of the positive coordinate axes. AB = = ...
0
votes
1answer
24 views

Cutting a cube into pieces

A cube has four diagonal planes. Let them be $P_1, P_2, P_3, P_4$. $P_1$ and $P_2$ intersect at exactly two corners. The cube is cut by $P_1$ and $P_2$ diagonal planes. What are the volumes of the ...
0
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0answers
32 views

explicit solution examples for Kirchhoff's formula in 3d waves

I have been scouring the internet to find some examples of using Kirchhoff's formula for the 3D wave equation, given initial conditions such as $g(\mathbf{r}) = x^2 \sin y \cos z$ and $h(\mathbf{r}) = ...