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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59 views

Book on coordinate transformations

I am looking for a book that covers various coordinate systems in 3 dimensions, various methods of representing rotations and other transformations like rotation matrices and quarternions, including ...
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0answers
15 views

Calculation viewpoint location of a 3d object.

I am tring to get 2D viewpoint cooridnates of 3D object. This 3D object is on a plain. Things I have: 1) Plain size (ex 800x600) with center of 0,0,0. 2) Relative position of a 3D objects corner ...
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3answers
28 views

In $\Bbb R^3$, I want to find the point on a line that is a distance R away from another point (not on the line). [closed]

I have a point $A:\left(x_{A}, y_{A}, z_{A}\right)$ and a line $\vec{G}:\vec{g}+t\vec{u}$. I want to find the point on $\vec{G}$ that is a distance R away from $A$. I know that $A$ is not on $\vec ...
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1answer
24 views

Prove that Euclidean, spherical, and hyperbolic 3-manifolds are THE only three-dimensional geometries that are both homogeneous and isotropic.

The book Introduction to Topology by C. Adams and R. Franzosa says : There are only three three-dimensional geometries that are both homogeneous and isotropic: the Euclidean, spherical, and ...
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1answer
42 views

Are there computational short cuts to calculating the distance from a large number of points to 3 different planes?

I have three planes, and i want to calculate distance of my point to each of them. However, there are 68000 points in the space, so it does not make sense( computationally) to calculate the distance ...
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0answers
35 views

Coordinate system construction and change for a (X, Y, Z) cloud of points

I’m working on a project in an aerospace company. I have to post process a cloud of points with X Y Z coordinates in Excel spreadsheet. I need to build different coordinate frame (origin and x y z ...
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1answer
38 views

3D rotation of a square

Suppose we have a square in 3D space with its normal pointing in the direction of the positive $z$ axis, i.e. $(0,0,1)$. The four vertices of the square are $(1,1,0)$, $(-1,1,0)$, $(-1,-1,0)$, ...
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2answers
42 views

Find equations of the line through a given point that meets another line at certain distance

Find the vector and parametric equation of the line through point $P(1,0,1)$ that meets the line with vector equation $$p = (1,2,0) + (2,-1,2)t$$ at points a distance $3$ from $P_0(1,2,0)$ ...
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1answer
23 views

point inclusion in a half-plane 3D

I have a 3D half-plane defined using a line segment an a point (as shown in picture taken from here). I am wondering how I can detect if a point belongs to the half-plane. Is there any way to ...
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1answer
28 views

3-D Geometry - line

Question: A line makes the same angle $\theta$ with the x and z-axis. If the angle $\beta$ which it makes with the y-axis is such that $\sin^2\beta = 3\sin^2\theta$ then find the value of ...
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0answers
26 views

Determining deflection of a cylinder

I have a cylinder of length l and radius r and I am trying to work out how far off straight it is. (What I mean by that is assuming the other end of the cylinder is at 0,0 what is the deflection from ...
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1answer
47 views

Looking at three wires, can I make it look like they meet?

I was walking down the street and there were three wires (used by the tram) above my head. I looked up and by hazard it looked to me like they intersected all three in the same point. I asked myself ...
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2answers
68 views

Does a line intersect a box in a 3D space?

Known parameters: Coordinates of the $8$ corners of the box: $\{(X_1;Y_1;Z_1), ..., (X_8;Y_8;Z_8)\}$ The box is alligned with the global coordinate system Begin and end coordinates of the line: ...
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1answer
20 views

Find the feet of perpendiculars on a plane

Perpendiculars are drawn from points on the line $\frac{x+2}{2}=\frac{y+1}{-1}=\frac{z}{3}$ to the plane $x+y+z=3$. The feet of perpendiculars lie on the line ...
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2answers
39 views

If three planes intersect pairwise along parallel lines, then their normal vectors are coplanar

Suppose we know that when the three planes $P_1$, $P_2$ and $P_3$ in $\mathbb{R}_3$ intersect in pairs, we get three lines $L_1$, $L_2$, and $L_3$ which are distinct and parallel. How can I show ...
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0answers
23 views

Figuring x,y,z end points

I'm trying to calculate x,y,z endpoints based on a length and two angles. So if my starting point is 0,0,0, length (l) = 100, Angle 1 (A1) is 35 and Angle 2 (A2) is 15, what would be the equation to ...
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0answers
22 views

How to restore 3d figure from two main cuts?

Imagine we have two perpendicular cuts of the 3d figure, that has vertical axis of symmetry as it shown on the picture: [ We know all the data from which these two cuts consists of(0X,0Y and 0Z data ...
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0answers
21 views

Angular velocity and it's dependence on rotation vectors

This question is about rotational dynamics. Starting with an inertial and a body frame of reference, and using some sequence of 'euler' rotations, I can arrive at the expression of angular velocity. ...
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2answers
52 views

Calculating the vector to intercept a falling object

Given two objects with known positions in a three dimensional space, of which: One is a ballistic projectile (that is, it is free-falling with constant gravitational acceleration), and The other ...
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1answer
29 views

Rotate along outside of sphere

Although this is related to programming, I don't want to know the programming end of this, just the math. Based on mouse movement, I want to rotate around the origin and always face it like in Google ...
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2answers
72 views

Parametric Equations for the tangent line of a vector function at a given point

I am working on a homework problem and am not sure if I am understanding it correctly. The problem reads: Find parametric equations for the tangent line to the curve with the given parametric ...
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3answers
84 views

Check if a point is inside a rectangular shaped area (3D)?

I am having a hard time figuring out if a 3D point lies in a cuboid (like the one in the picture below). I found a lot of examples to check if a point lies inside a rectangle in a 2D space for example ...
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3answers
169 views

Line L intersects perpendicularly both the lines $\frac{x+2}{2}=\frac{y+6}{3}=\frac{z-34}{-10}$ and $\frac{x+6}{4}=\frac{y-7}{-3}=\frac{z-7}{-2}$

A straight line L intersects perpendicularly both the lines $\frac{x+2}{2}=\frac{y+6}{3}=\frac{z-34}{-10}$ and $\frac{x+6}{4}=\frac{y-7}{-3}=\frac{z-7}{-2}$,then square of the perpendicular distance ...
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0answers
66 views

3D vector rotation in android

I need to rotate the data from 1 sensor with information from another one. I want to ask if my approach is feasible. The plan is the following: 1) Get accelerometer 3d vector 2) Turn in into a unit ...
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1answer
64 views

The angle between two rays in 3D space

This is a problem from Mathematics GRE Subject Test - #42. In the xyz-space, what is the degree measure of the angle between the rays $z= (x>=0), y=0$ and $z= (y>=0), x=0$? a)0; b)30; ...
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1answer
73 views

How do you find the angle between two vectors? [closed]

How to solve this question? Find the acute angle between the line joining $(1,3,2)$ to $(2,5,-1)$ and the line joining $(-1,4,3)$ to $(3,2,1)$.
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1answer
27 views

Given a normal vector, what information can you extract?

In my textbook, $n = 3i +2j + 6k$ which lies on the $y$-axis. Can you explain how is that because I understand that it should go $3$ units on $x$ then $2$ on $y$ then $6$ on $z$ which is not on the ...
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1answer
103 views

How to find the equation of the plane passing through the intersection of two other planes and whose perpendicular distance from the origin is given?

I've been trying to find a way to work this out for hours now with no luck. The question is: Find the equation of the plane(s) passing through the intersection of the planes $x+3y+6=0$ and ...
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2answers
40 views

Calculating the Surface Normal of a Triangle

If a point looks like this: $$\textbf{point = [x, y, z]}$$ I have a triangle made up of these points: $$p_a = [0.3333, 0, 0.05]$$ $$p_b = [0.4333, 0, 0.05]$$ $$p_c = [0.3317, 0.0327, 0.05]$$ I ...
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0answers
206 views

Finding the area of a parallelogram on a 3D coordinate plane

I'm stuck on the following question; I've attempted it but I'm not sure if I've done it right. Find the area of the parallelogram on the plane (−x + 3y + 3z = 6) defined by 0 ≤ x ≤ 3, 0 ≤ y ≤ 2. So ...
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1answer
87 views

Finding ray direction with smallest angle from a ray to a disc in 3D

In 3D I have been given a ray and a disc: $$Ray=\mathbf{r_o}+t*\mathbf{\hat{r_d}}$$ $$Disc=\mathbf{\hat{d_n}} \cdot \langle x\;y\;z \rangle=0, ||\mathbf{d_o}-\langle x\;y\;z \rangle||<d_r$$ where ...
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0answers
95 views

What is this shape called?

I've encountered an unusual shape that I have no idea the name of. We have a sticker on the shape that tells us the equation $z^2 = \frac{x^2}{a^2-y^2}$ Here is a picture of the shape itself: ...
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0answers
47 views

find resultant XYZ points in a laser 3D scanner

I am working on a 3D scanner using a laser and camera and some other stuff needed, the idea is that the camera captures an image to the target when the laser is on, then use the image to gain the ...
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2answers
130 views

Shortest Distance between Two Parallel Lines in 3D

On Wikipedia, I found the following explanation for the distance between two skew lines: According to me, the logic of the formula should work for parallel lines too. I was trying to tweak the ...
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3answers
76 views

General equation of a plane through $3$ points. [closed]

Find the general equation of the plane through the points $A(1,1,0),\, B (1,0,1),$ and $C(0,1,2)$. How is this done?
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0answers
70 views

Transforming components of angular velocity vector in a rotating reference frame into time derivatives of Euler's angles

We've got a standard SO(3) setup: two Cartesian coordinate systems, one that is stationary (in the sense that we will refer everything to that one), and has the axes $X$, $Y$ and $Z$, and the second ...
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1answer
54 views

Linear correlation in 3D?

What's the name of a statistical method used to determine the goodness of fit of a series of points in 3D space that are to be fitted on a regression line ? I can calculate a regression line and the ...
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0answers
23 views

Find the equation of the intersection of $x^2+y^2=1$ and $y + z = 2$. Find the angle between the two surfaces at their intersection.

I solved for the intersection. I parameterized the first function, for the cylinder, into $r(t) = (\cos(t), \sin(t))$. Then solved for the $z$ parameter using $z = 2-y = 2-\sin(t)$. Thus, for curve ...
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0answers
28 views

Show that the curve given by r(t)=<cos4t,t,sin4t> has constant curvature.

How do I prove this? I can use k=mag(T')/mag(r') but the derivations get extremely hairy. I think I'm over complicating it for myself.
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2answers
31 views

Which axis is which in 3 Dimensional system? [closed]

i'm a little confused. 1)Which axis is which in 3 Dimensional system? 2)Does it matter if I switch the x-axis to y-axis?
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2answers
108 views

How to calculate the quaternion from/and axis angle having parent and target position (camera and its target)?

I want to calculate the orientation (quaternion) of the virtual 3d camera that is looking at some point in 3d space. The illustration: According to this explanation the quaternion be calculated ...
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1answer
27 views

Can anyone explain what frame multiple 3D rotations are in relation to?

When I do multiple rotations in 3D, how do I do the second rotation in relation to the original frame, how do I do the second rotation in relation to the rotated frame? I think if I multiply the ...
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0answers
54 views

What is the difference between isometric deformation and conformal defomation?

What is the difference between an isometric deformation and a conformal deformation? In fact, even the definition of both deformations is still unclear clear for me. Is it possible to define an ...
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1answer
32 views

Calculating which two points are the closest together given a series of points.

I'm in a position where I need to calculate the distance between two points to determine which is the closest point. Now, the proper formula to do this is: $$distance = \sqrt{(x2-x1)^2 + (y2-y1)^2 + ...
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1answer
225 views

Finding ray direction with smallest angle from a ray to a rectangle in 3D

In 3D I have been given a ray and a rectangle: $$Ray=\mathbf{r_o}+t*\mathbf{r_d}$$ $$Rect=\mathbf{p_o}+p*\mathbf{p_x}+q*\mathbf{p_y}$$ where $\mathbf{r_o}$ is the ray origin $\mathbf{r_d}$ is ...
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2answers
54 views

Plane of all points equidistant from two other points?

Find the equation of the plane that contains all the points that are equidistant from the given points $(-9, 3, 3), (6, -2, 4)$ I think the plane described lies in the midpoint of these points, and ...
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2answers
54 views

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
60 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
69 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 ...
0
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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) ...