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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Find the equations of the lines of greatest slope and least slope

Find the equations of the lines of greatest slope and least slope on the plane $3x-4y+5z-5=0$ drawn through the point $(1,2,2)$ given that the plane $4x-5y+6z-6=0$ is horizontal. I do not need the ...
2
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1answer
27 views

3D calculate new location of point after rotation around origin

I've tried to boil down my problem as much as possible. I've got two questions, but really I'd be satisfied enough just knowing how to accomplish the first one. I'm looking to do this programatically, ...
0
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0answers
26 views

Finding a x-y-z equation based on data

I have a large number of x, y, z point values. I am wanting to know the equation that represents these values I have in hand. This equation I am looking for should be a fit that will represent these ...
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0answers
61 views

Trajectory on a sphere

I've asked a question before concerning a parallel problem, and I read a wikipedia page on spherical caps (Nominal Animal), which gave me an idea to do the following: I have the Cartesian coordinates ...
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1answer
17 views

Set of transformations to get a point on the X-Axis.

I have a two points in the 3D coordinate space. Now, I want to send one of the points to the origin and make it (the line joining the two points) align with the X-axis and get the transformation ...
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1answer
16 views

Position of point between 2 points in 3D space

I need to find the position v3 between the given points v1, and v2 and a given distance d in 3D space. I came across this post: Position of point between 2 points which is basically what I need but ...
2
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1answer
43 views

How to find the closest point to three vector lines?

So this is the question here I know the angles $A$ and $B$ for each individual, and their positions in longitude and latitude (assuming height of person $z =0$), am I correct in thinking that for any ...
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2answers
46 views

Ray intersecting a quad mesh

I am trying to solve the math behind rendering a quad-mesh surface. MatLab for instance can take a regularly spaced (x,y) grid with arbitrary third-dimension (z) values, treat each four neighbouring ...
2
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1answer
35 views

figure-8 knot complement

The figure-8 knot seen as a 2-bridge knot with two maxima and two minima of the height function, has a complement in $S^3$ with one 0-handle,two 1-handles, two 2-handles and a 3-handle which cancels ...
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1answer
106 views

Cartesian equation cylinder along a line

What is the cartesian equation for a cylinder along a line in a 3d space? Imagine two points in a 3d space, (Xc,Yc,Zc) and (Xp,Yp,Zp). The equation for the line connecting these points is: (x-Xc)/(...
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1answer
18 views

Why and how two skew vectors' cross product gives normal vector of plane containing one of those vectors

I got a question which says : Given $$\vec{v} = <1,0,-1> $$ and line $$L_1 : (1-2t)\vec{i}+(4+3t)\vec{j}+(9-4t)\vec{k}$$ Find an equation of plane $P$ which is parallel to the vector $\vec{v}...
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0answers
17 views

Converting homogeneous projection matrix

I have a 4x4 homogeneous projection matrix which converts 3D world space coordinates into 2D image coordinates + a depth value. It is of the form $\mathbf{H} = \begin{bmatrix} m_{1,1} & m_{1,...
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0answers
16 views

properties of a Varignon parallelogram from a skew quadrilateral,

I was editing https://en.wikipedia.org/wiki/Varignon's_theorem and that made me wonder. At the moment https://en.wikipedia.org/w/index.php?title=Varignon%27s_theorem&oldid=713877982 the ...
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1answer
16 views

Need help understanding what the curve made by two or three intersecting surfaces looks like

I have trouble visualizing what curves are traced out by the intersection of multiple surfaces in $R^3$. for example take the parametric equations $ <cos(t),sin(t),sin(t)$ > Clearly this would ...
2
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1answer
61 views

Compute weight of a point on a 3D triangle

Let's say I have a 3D triangle $ABC$ with $x$, a random point on it, I know the coordinates of each one of the points. Each of $A$, $B$ and $C$ have a "weight" which is a decimal value between 0 and 1 ...
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1answer
44 views

Is there a good program to download or online for plotting certain functions in 3d?

I am interested in a program that can plot me, without too much trouble shapes in 3d, when I type in the function. For example a elliptical paraboloid and an ellipse of the same time, so I can analyze ...
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0answers
24 views

Triangle verticies given 2 points, all angles and sides (3D)

--Visual Image for the problem-- Alright, I hope that you are able to view the visualization of the problem in the link above. If not, I'll give a quick run-down of the information I have as well as ...
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1answer
35 views

Helix along vector in 3D space

Let's say I have a random vector, for example <1, 3, 5>. What would the function be for a helix that spirals around/along this vector with a given radius?
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1answer
46 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
13 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 ...
0
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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
28 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
31 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
18 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
37 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
48 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 matrix,...
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1answer
40 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
45 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 ...
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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 band ...
10
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1answer
250 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
76 views

Geometrical interpretation of solving a $3 \times 3$ 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
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1answer
61 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: https://en.wikipedia.org/wiki/...
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0answers
18 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 ...
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1answer
20 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 ...
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4answers
186 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
31 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 ...
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3answers
41 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
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1answer
24 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 rotations....
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0answers
12 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 rod'...
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1answer
17 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
27 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
17 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
32 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 ...
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1answer
93 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
49 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
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5answers
809 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
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1answer
36 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 ...
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0answers
28 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 ...
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1answer
22 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 $<2,3,...