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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Describing a plane in three dimensions

When describing a plane in three dimensions, one uses a point P and a vector N normal to the plane, where N describes the "tilt" or orientation of the plane.Is it possible to describe a plane using a ...
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1answer
61 views

How to calculate homography matrix of plane using the homography of its orthogonal plane?

I have an image of a 3D object cast on two orthogonal planes. I have a homography matrix of one of these planes. I want get the homography for the other plane. my question explicitly is: 1- Can I ...
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1answer
70 views

What is the math behind this art project?

This is a fascinating piece of art that makes me wonder how the cut out was created. Can anyone explain to me, in layman mathematical terms, how the position and angle of the black stick, when ...
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1answer
26 views

Find a 3d equation that goes through a series of points?

I have a series of points in 3d space and I need to find an equation that goes through all of them. What would be the best way to do this? Points: (3.7, 0.45, 0.7) (5.2, 0.8, 0.96) (6, 1.04, 1.15) ...
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1answer
31 views

How to find a 3d equation from a series of points

I have 6 points and I need to find the equation, or an equation, that will go through all of them. How would I go about doing this? The points are as follows. (3.7, 0.45, 0.7) (5.2, 0.8, 0.96) (6, ...
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2answers
25 views

Projection of vectors?

Suppose I want to find the projection of vector $u$ onto $v$ . To me it makes sense to just make a right triangle with $u$ as the hypotenuse, and the problem is to find the base of this triangle. The ...
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0answers
31 views

Integrating Frenet Serret Equations

Using Frenet-Serret formulas how to find positions of curves in 3-space when calculating the two space curves: $ \kappa= 1, \tau=1; $ $ \kappa= \cos (s/a), \tau= \sin(s/a). $ Next, when $ \ Q = ...
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2answers
25 views

Finding equation of plane normal to a line.

How to find the equation of the plane which passes through the point $(3, -3, 1)$ and normal to the line joining the points $(3, 2, -1)$ and $(2, -1, 5)$ ?
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1answer
66 views

Why can't I measure the distance this way?

The problem is to find the distance between the point $(3, -2, 4)$ and the plane $2x-5y+z=10$ I tought of doing it like this: The shortest line between the point and the plane is orthogonal to the ...
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3answers
65 views

Intersection of 2 planes?

The question asks to find the parametric equations of the line of intersection between the planes $3x+2y-z=28$ $x-4y+2z=0$ I think I know how to do it and I think I got the right answer, but I ...
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2answers
33 views

3D geometry - equation of line

Question: Suppose we have the two lines: $$\frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{4}$$ and $$\frac{x-2}{3} = \frac{y-4}{4} = \frac{z-5}{5}$$ Find the equation of the line which covers the ...
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1answer
65 views

Point between two points given time? [closed]

Let's say there are two separate points in a 3 dimensional space. An object at point A can move to point B at any speed given (let 'S' be units per second). If I start moving the object from point A ...
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2answers
82 views

Rotating a set of anges (pitch/yaw/roll) by another set of angles (pitch/yaw/roll)

I want to rotate a set of angles (pitch/yaw/roll) by another set of angles (pitch/yaw/roll). By using Google I only found information about rotating a vector by angles, which is not what I need. ...
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0answers
62 views

Placement of protons and neutrons in the nucleus

So, I'm creating a program that would represent a given atom (also different isotopes) in 3d view. I'd need some kind of formula to calculate the position of protons and neutrons to form a nucleus. ...
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1answer
54 views

Canonical equation of a line in space: horizontal and vertical lines

I have a question about canonical equation of a line in 3d space: how can I handle vertical and horizontal lines? One of direction vector's values will be just $0$, but this will mess up the equation, ...
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1answer
42 views

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 ...
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2answers
38 views

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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1answer
59 views

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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0answers
10 views

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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0answers
57 views

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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1answer
174 views

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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2answers
37 views

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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1answer
40 views

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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1answer
123 views

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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2answers
72 views

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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1answer
85 views

**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 ...
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1answer
30 views

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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1answer
40 views

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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2answers
57 views

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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1answer
48 views

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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1answer
51 views

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 ...
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1answer
69 views

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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1answer
82 views

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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1answer
45 views

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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2answers
71 views

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 ...
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0answers
55 views

. 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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1answer
33 views

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 ...
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1answer
28 views

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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1answer
203 views

Calculate 3D Vector out of two angles and vector length

What is the easiest way to calculate vector coordinates in 3D given 2 angles vector length? Input: Angle between X and Y axis: $$\alpha \in [0, 360).$$ Angle between Y and Z axis: $$\beta\in [0, ...
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0answers
12 views

3D Linear-geometry with coordinates

Truncated pyramid has a smaller opening with sides ABCD, and a bigger opening with sides FGHE ( where F is o top of A, G on top of B, H on top of C and E on top of D). This figure has 3D coordinate ...
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1answer
93 views

Intersection of Three Planes proof

I'm supposed to be making a study guide answer for this question, but I'm struggling with proof. Show that the three planes intersect at the point provided that Note that the ...
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2answers
33 views

Width of rotated plane

I'm trying to get the width of a rotated plane, but my knowledge of trig functions didn't really help me get what I want. I have a plane, that is $310$ units wide, and is $200$ units away from the ...
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2answers
48 views

Final transformation matrix

I have a 3d object, to which I sequentially apply 3 4x4 transformation matrices, $A$, $B$, and $C$. To generalize, each transformation matrix is determined by the multiplication of a rotation matrix ...
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1answer
99 views

3 Points in 3D Space to Develop an Arc or Circle

Background: I'm a Robotics Engineer and I am trying to develop a more flexible, modular, and robust program for our welding robots, which will minimize teaching time for new robots and also minimize ...
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4answers
73 views

Points on 3d line

Say we have $2$ points on a 3d line, point $A(x,y,z)$ and point $B(x,y,z)$. If we want to get the coordinates of a third point, beyond point $B$ but a certain distance from point $A$, how would we do ...
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4answers
50 views

How to find perpendicular vectors in 3D

Find all values of a such that the vector $q = \langle 2, a, –2\rangle$ is perpendicular to the vector $p = \langle –3, a, 5 \rangle$.
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1answer
58 views

8 cubes ($2$x$2$x$2$) crossed by a straight line

There are 8 cubes forming a bigger cube whose dimension is $2$ x $2$ x $2$. Let a straight line (or a laser) try to pierce through as many small cubes as possible. At most how many small cubes can be ...
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0answers
32 views

Intersection of two moving objects in 3D

There are two objects, where the known data is the position and velocity in 3D vector format. I`m interested in the time and position of the intersection between the two, and possibly without ...
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2answers
408 views

puzzle 3-d visualization

729 small cube are painted pink on each face and then arranged to form 27 identical middle-size cubes.Each middle size cube is painted black and then arranged together to form one large cube. And ...
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1answer
42 views

Perpendicular vectors in $\Bbb R^3$

Hi I am struggling with this simple question. Let $\vec{v}$ be a unit vector in $\Bbb R^3$. How can I construct two periodic functions $\vec{x}(\theta)$ $\vec{y}(\theta)$ such that $\vec{v}$, ...