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.
3,853 questions
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Placing $4$ circles of known radii in space such that each pair is tangent to each other
Suppose I give you $4$ circles with radii $r_1, r_2, r_3, r_4$, and I ask you to place the first circle on the $xy$ plane centered at the origin. Then I ask you to place the next three circles in the ...
user948761
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going from 1 3D angle between 2 3D vectors to 2 2D angles?
The 3D angle between two 3D vectors is $$\beta = \arccos\Big(\frac{\textbf{r}\cdot \textbf{r}_0}{|\textbf{r}||\textbf{r}_0|}\Big)$$, is there a way to get the 2D angles between the vector $\textbf{r}-\...
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How to optimize for rotation and translation in 3D for the next equation?
Let us consider we have two known $SE3$ transformations with matrix representations $H_1$ and $H_2$ of the form $H= [R; t]$ where $R$ is a 3x3 rotation matrix and $t$ a 3x1 translation vector. I am ...
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How to have same position and rotation for an object between two coordinate systems.
I have two devices that have different coordinate systems and I want to get the position and rotation of an object from one and display it in the correct position and rotation in the other.
One device ...
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Identifying the 3 Euler angles of rotation from 2 perspective images of a rectangle
I've worked on this problem for 3 days and I've decided to reach out for help. I have 2 images of the same rectangle (see figures). In the first image I have a 2D rectangle, and I know its height and ...
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Torus equation in conformal geometric algebra
How would you define a torus using conformal geometric algebra?
Since CGA has circles as a primitive, It seems to me that we should be able to able to define a torus as a circle C rotated around a ...
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Intersection of multiple great circles on a sphere
There are some online materials on how to get the intersection between two great circles (e.g. link1, link2).
However, I couldn't find any material on how to get the intersection of multiple (more ...
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How to "Clamp" one unit vector between two others?
Assuming a 3D cartesian space, imagine:
I have two unit vectors A and B that are not colinear
I have a third unit vector C that I wish to "clamp" between A and B on the surface of the unit ...
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using vector math to find out pyramid and point intersection.
I'm new to vector math, I've mostly done plane / line intersections.
I'm currently trying to do a very simple stereo vision, and the idea is to use a pyramid (representing a feature being projected ...
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Triangular inequality on the angles of the faces of a trihedron [duplicate]
I just saw this theorem which I'm trying to prove but got stuck.
Given a trihedron like the one below, whose angles between its edges are $\widehat{bc}, \widehat{ac}$ and $\widehat{ab}$, then prove ...
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Is the resemblance in the formula for distance between $2$ parallel planes and foot of perpendicular on a line a coincidence?
I was trying to derive the formula for the foot of the perpendicular of a point $(x_0,y_0,z_0)$ on the line $L_1:\dfrac{x-x_1}{l}=\dfrac{y-y_1}{m}=\dfrac{z-z_1}{n}$, where $\left<l,m,n \right>$ ...
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Determine the inscribed ellipsoid within a cube with given ratios of axes
Given a cube centered at the origin, with side length $2a$, determine the length of the semi-axes of the ellipsoid inscribed in the cube, touching all its $6$ faces, such that the semi-axes lengths ...
user948761
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Determining the Equation of a Parabola in a Three-Dimensional Plane
I have a plane with three points: P1 (x1, y1, z1), P2 (x2, y2, z2) and P3(x3, y3, z3). These points represent a parabola where P3 is the vertex and the other two points are the ends of the parabola. ...
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Range for radius of tangent sphere to three given spheres
You're given three spheres of radii $a, b, c$ where $a \le b \le c $. The three spheres are placed on a table (represented by the $xy$ plane), such that they tangent to each other. I want to find ...
user948761
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How to find the vertices of a 3D Shape Calc III (e.g. hyperboloid of one sheet, elliptical paraboloid, etc..)
I can find out the shape and put it in standard form. I just don't know what to do when it asks about the vertices. Sorry I'm new and it won't let me attach images yet.
Example Question of the ...
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Can any line be rotated such that it touches two arbitrary points?
Using one translation and a rotation this can be done.
From the answers there, I assume that one needs the additional translation. But I can't think of an example where this is obvious.
Edit:
To ...
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How can I adjust the x, y, and z coordinates of inscribed circles on a spinning sphere for different polar angles in an animation?
I am making an animation of a spinning sphere with circles inscribed on it.
I have been successful in rotating it azimuthally. For polar angles, while I can rotate the inscribed circles appropriately, ...
user1129940
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Does this parametrized space curve (or similar) have a name?
My son has a chandelier in his family room that is a space curve with trilateral symmetry, and I'm wondering if this curve has a name (or alternatively, if it belongs to a named class). I won't bother ...
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Converting 3d coplanar points to space of 2d plane then back into 3d
I have the equation of an arbitrary plane of the form $Ax+By+Cz+d= 0$.
I also have a set of points lying on this plane, $\{p_1, p_2, ... , p_i\}$ where each $p_i$ is an $(x,y,z)$ coordinate. I would ...
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Solving vector equations in $ℝ^3$
I've recently been trying to solve the following problems in the unknown vector $\vec{r}$ given non coplanar vectors $\vec{a},\vec{b},\vec{c}$;
(i) $\vec{a} \times[(\vec{r}-\vec{b})\times\vec{a}]+\vec{...
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How deep does a sphere sit in a hole?
Let's say there is a sphere of radius $r$ and a circular hole of radius of $x$. If $x<r$, how deep does the sphere sit inside the hole? I haven't been able to figure this out,
The amount the sphere ...
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Shortest path on the surface of a cylinder between given points $A$ and $B$
Suppose you have the cylinder
$ x^2 + y^2 = R^2 $
And points $A = (R, 0, 0)$ and $ B = (0, R, h) $. Find the parametric equation of the curve of shortest length connecting $A$ and $B$.
My attempt:
If ...
user948761
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3D trigonometry bearing question - finding the bearing of a point to a tower
I'm currently struggling with 3D trigonometry, particularly with drawing a proper diagram and interpreting bearings. The question is below:
The angle of elevation of a tower QR of height 100m at a ...
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Finding the hypervolume within two cylinders and 2 planes where z>0
I was presented with the following exercise: find the hypervolume under f(x,y,z)=z over the solid within the cylinders x^2 +z^2=1 and x^2 +z^2 =16, the planes x-y+z=-1 and x-y+z=-4 where z>0. I ...
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How to find the volume of a tetrahedron that isn't aligned with flat planes with triple integrals
Hi I'm having a lot of trouble solving this math problem, I have been working on it for about 3 hours (please help). I'm learning about triple integrals and I have no idea how to solve the volume of a ...
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