# 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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### How to figure out if coordinate points are Coplanar?

Determine whether the vectors are coplanar. $i, i − 2j, 3j + k.$ My first intuition tells me that one must multiply the given points to find out the answer. So that is $a*b*c$ so that gives you zero....
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### Finding a perpendicular plane

Question Plane $B$ contains the points $(4, 2, 1)$ and $(4, 1, -6)$, and it is perpendicular to the plane $7x+9y+4z=18$ . What is the equation of the plane $B$? What I tried: I know that to find ...
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### Circle-Circle intersection centroid in a 3D space

I am trying to find the centroid of a circle-circle intersection (the shaded region in the image) in a 3D space. The circles are defined by their center points, their radii, and their plane's normal ...
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### Getting the closest upmost vertexes

In order to make it clear on what my question is, I'll firstly illustrate it in 2D, and then move on to the more complex 3D case. In a complex polygon in any shape (see image for example), the idea ...
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### vector 3d rotation of a cube

I have a cube which is rotated by plane you can see it in an example here. What am I trying to achieve is algorithm that tells what is the top, face and side after a rotation is performed. And also ...
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### Rotations of a cube

I am trying to create a program using Python 3 which must simulate the rotations of a cube. However, I am struggling to figure out how to rotate that cube. I have the following formulas: ...
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### Smallest convex polyhedron containing integer points of a cylinder [closed]

A cylinder has height $6$ and radius $3$. The centers of the two bases are $(0,0,0)$ and $(0,0,6)$. Find the volume of the smallest convex polyhedron that encloses every lattice point inside the ...
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### How are 3d images rendered in 2d space?

There was a similar question asked on this same site a few years ago (How to transform a set of 3D vectors into a 2D plane, from a view point of another 3D vector?), but the answerer seemed to kind of ...
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### Paramaterization of paraboloid and plane.

Consider the paraboloid $z=x^2+y^2$. The plane $2x-4y+z-6=0$ cuts the paraboloid, its intersection being a curve. Find "the natural" parameterization of this curve. I have set each equation equal ...
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### Find the point at which the line intersects the plane. Is the intersection perpendicular?

Find the point at which the line $$x = 1 - t \\ y = 3 + t \\ z = 7 + 2t \\$$ intersects the plane $$x + 2y + z = 20$$ Is the intersection perpendicular? I have found the point of intersection to be (...
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### **Location** of shortest distance between two skew lines in 3D?

I can find the shortest distance $d$ between two skew lines $\vec{V_1}$ and $\vec{V_2}$ in 3D space with $d=\left|\frac{(\vec{V_1}\times\vec{V_2})\cdot\vec{P_1P_2}}{|\vec{V_1}\times\vec{V_2}|}\right|$...
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### What is the perspective projection of a 3d point relative to a quarternion encoded camera?

I'm representing a camera on the cartesian space as a tuple of a 3d point (position) and a quarternion (rotation). I get the front, right and up vectors of the camera by applying the quaternion to the ...
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### How do I represent a Mobius Band Triangle Parametrically

I am trying to describe a Mobius band in the shape of a triangle like this: parametrically in terms of its $x$, $y$, and $z$ functions. Is this even possible? I know a basic mobius strip can be ...
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### What are the Eigenvectors in the following matrix?

I have the matrix A: \begin{bmatrix} 4 & 2 & 2\\ 2 & 4 & 2\\ 2 & 2 & 4\\ \end{bmatrix} I found $\lambda I_n - A$ to be: \begin{bmatrix} (\lambda -4) & -2 & -2\\ -2 &...
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### Determining the angle of a photograph containing known parallel objects/lines.

I have a photograph of a house and a window taken at an angle. I'm trying to determine the angle at which the photograph was taken. The house has wooden siding that can be safely assumed to be ...
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### Finding extreme point of a set determined by two planes in $\mathbb R^3$

Problem asks to find a extreme point the set $\{(x,y,z) \mid x-2y \leq 3 , 2y+3z \geq 4 \}$. But I don't think it has a extreme point, because it is intersection of two hyper planes in 3D, which doesn'...
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### Calculating the volume of a surfboard

I'm building a website for a client in which customers can customise the shape of their board (curvature, length, width, thickness, and so forth) and the client has asked if we can calculate the ...
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### How to get circle points in 3d given a radius and a vector orthogonal to the circle area?

I already know how to get a point on a circle (here), but I need a circle in 3d which should be the orthogonal to a given vector. I got: Angle in degree/radians Circle radius Orthogonal vector I ...
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### Fit a plane in data set which passes through maximum number of points in this data set and disregards noise

I have a set of 3D points (cartesian coordinates). I want to find the best fit plane. As I understand, there are many algorithms to get a best fit plane. One of them is this by Dan Couture. This fits ...
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### Showing that the image of a curve lies on a surface?

I am looking for an intuitive explanation to a problem in one of my practice tests. I'm given a parameterized curve from $\Bbb R$ to $\Bbb R^3$, called ${\bf r}(t) = (\sin t \cos t, \cos^2 t, \cos t)$....
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### . Find the projection of the triangle on the coordinate planes.

Given the following, three vectors: a⃗ =3i−2j+5k b⃗ =i−6j+6k c⃗ =2i+3j−k Relative to cartesian coordinate systems with origin O. I calculated the sides to be 4.58,11.45 and 7.87. I also calculated ...
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### Move point onto circle-outline in R3

I need to do all this in $\mathbb{R}^3$ a plane by $n \cdot p = -k$ a circle within this plane by radius = $r$ and center = $c$ a point $a$ on the inside on the circle (on the plane) a direction $d$...
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### Scaling 3D-Points in Plane

I have some points (3D) all on the same (known) plane. Now I want to scale these points within the plane as opposed to the whole 3D space (as in scalar-multiplication of points in 2D space) Is there ...
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### Small Stellated Dodecahedron, generating triangle vertices

I have been trying to draw a small stellated dodecahedron (would post an image if I had enough rep) using OpenGL, and would like to generate the vertices programmatically. I'm looking for a way to map ...
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### How to rotate cuboid to plane

I have a cuboid with 8 points that is axis aligned with its center at the origin 0,0,0. Now I have a plane and want my cuboid to rotate so that instead of being axis aligned, it is now aligned to this ...
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### How to find the points of intersection of the perpendicular vector two skew lines

Correct me if im wrong, but this is what i know so far The cross product of two skew lines is the perpendicular vector between both those lines. The perpendicular vector intersecting two skew lines ...
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### In an icosahedron subdivided n times, how can I find the coordinates of adjacent centroids?

I think it would be helpful to refer to this image when trying to follow my description: http://i.imgur.com/nRXQo3W.jpg (taken from http://experilous.com/1/blog/post/procedural-planet-generation). ...
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### 3D Shape with only coplanar faces?

I just thought of this problem, and it's bugging me that I can't find any sort of shape that fits it. Are there any 3D shapes with only faces that have coplanar matches with other faces in the shape? ...
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### can't figure out multilateration with xyz positions of each post and difference in time

I'm having some real issues figuring out multilateration. I'll start by saying I'm not a math whiz, but I am usually able to figure most things out, but this one has been throwing me through a loop ...
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### How can i reflect position and direction vectors from a plane

I'm now working on a project that has mirrors. I'd like to reflect a virtual camera and the way which i can do this is to reflect two vectors - position and normalized direction vectors of the camera. ...