Questions tagged [3d]
For things related to 3 dimensions. For geometry of 3-dimensional solids, please use instead (solid-geometry). For non-planar geometry, but otherwise agnostic of dimensions, perhaps (euclidean-geometry) or (analytic-geometry) should also be considered.
3,855 questions
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Is this a known theorem?
Reference image ^^^
Edit: a person has answered this and I have rediscovered Euclid's Elements, Book 13, Proposition 15.
Ok so I think I might have found a new theorem or maybe rediscovered an old one....
- 103
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1
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Rotating a unit vector to another vector using two consecutive axes
Given a unit vector $u$ and another unit vector $v$, I want to rotate $u$ into $v$ in two stages. In the first stage, I rotate $u$ about a given axis $a_1$ (by an unknown angle) to produce a vector $...
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Cutting a Möbius strip in thirds. Why are the resulting strips interlinked?
It is well known that cutting a Möbius strip "in half" down the middle results in a band with two twists, homeomorphic to a cylinder. See this question for example.
If instead, one begins ...
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4
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How to rotate a 3d object drawn along the z axis so that it lies along some other arbitrary axis
There are several very similar questions to this one, and I have read them all, but they are all a generalized version of the problem, and full of Math language. I don't speak Math, so the answers to ...
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Bearing angle of great circular arc between Ottawa Canada, and Sarajevo, Bosnia
I have this problem that I have been working on today. I want to calculate the local direction of the great circle connecting Ottawa, Canada, and Sarajevo, Bosnia. I assume Earth is perfectly ...
user1709783
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Finding the minimum distance path on the surface of an ellipsoid [duplicate]
Suppose I have the ellipsoid
$$ \dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} + \dfrac{z^2}{c^2} = 1 $$
And I have two points on this surface, $P_1 = (x_1, y_1, z_1)$, and $P_2= (x_2, y_2, z_2) $.
I am ...
user1709783
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1
answer
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Minimal possible area of a given union of polygons.
Consider $P$ to be the union of polygons inside a $3\rm{D}$ space. Find the minimal possible area of $P$ provided that the projection of $P$ onto the axis planes is a unit square.
This is a question ...
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Rotating a line in space to align it with another line
In my previous problem, I asked about rotating a plane into another plane.
In this question, I am given two lines in 3D space: $P_1(t) = r_1 + t v_1$ , $P_2(s) = r_2 + s v_2$. I am interested in ...
user1480757
2
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3
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Rotating a plane into another plane
I am given two planes $n_1 \cdot (r - r_1) = 0 $ and $n_2 \cdot ( r - r_2 ) = 0 $ where $ r = (x, y, z), r_1 = (x_1, y_1, z_1) $ is a point on the first plane, and $r_2 = (x_2, y_2, z_2) $ is a point ...
user1480757
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Volume of the cylinder surface
Problem
In three-dimensional $xyz$-space, consider the cylindrical surface given by $x^2+y^2=1$, and let $S$ be its portion with $0\le z\le 2$.
A sheet of paper of negligible thickness is wrapped ...
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A formula for the diagonal of a skew quadrilateral
Let $i,j,k,m\in\mathbb R^3$. Write $\ell_{ab}=\|a-b\|$ for edge lengths, $A_{ijk}$ for the area of $\triangle ijk$, and let $\theta$ be the dihedral angle along edge $ij$ between the oriented ...
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$6$th Angle Between $4$ vectors [closed]
If I am given $4$ unit vectors in $3D$ space, there are $6$ angles between them. If I have $5$ angles out of them, I think I should be able to find the $6$th angle(intuitively it sounds like that)(...
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Condition for two tetrahedra to be related by inversion
Given two labeled tetrahedra
$$
V_0V_1V_2V_3 \quad\text{and}\quad V_0'V_1'V_2'V_3',
$$
define their opposite-edge pairs
$$
(01,23),\quad (02,13),\quad (03,12).
$$
Let
$$
m_{ij}=\frac{|V_i'V_j'|}{|...
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Volume of polytope spanned by vertex pairs $(A_i,A_i')$ is invariant under translation of diagonals $A_iA_i'$
2D case
Let a convex quadrilateral $Q= \operatorname{conv}\{A_1,A_1',A_2,A_2'\}$ have vertex pairs
$$(A_1,A_1'),\quad (A_2,A_2'),$$
and define the “diagonal vectors”
$$d_i = \overrightarrow{A_iA_i'} = ...
- 695
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2
answers
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Finding the curvilinear length of quadratic Bézier curves in 3D
A quadratic Bézier curve is defined by three points in 3D, $P_0$, $P_1$, and $P_2$. The equation for the Bézier curve is defined through the parameterization of $t$, which has the range $0\leq t\leq 1$...
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