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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1answer
705 views

Finding the distance between the centre of an arbitrarily rotated cylinder and a point on that cylinder

this is a bit more complicated than the post title suggests because I was running out of words. I suppose the full title would be: "Finding the distance between the centre of an arbitrarily rotated ...
3
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1answer
82 views

Periodical reflection conditions in a sphere.

A perfect mirror covered the inside surface of a sphere (assumption: there is no any loss during reflection and reflections continue endless) and there is a very small laser on point $A$ in the ...
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3answers
1k views

3-D equation of a circle

I came across a sum but could not solve it as i dont know the 3d equations of a circle : The sum is If $A(3,-2,2)$ and $B(2,9,5)$ are the end points of a diameter of a circle,then the third pt that ...
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1answer
2k views

Icosahedron coordinates

Wikipedia says (link)that cartesian coordinates of icosahedron are: (0, ±1, ± φ) (±1, ± φ, 0) (± φ, 0, ±1) Where φ = (1 + √5) / 2 is golden ratio ≈ 1.618. I ...
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1answer
405 views

Calculating angle of human joint beyond 180° in 3D

I'm having some trouble calculating the angle of an human joint in 3D using the Microsoft Kinect. Here's an example of the angle of the elbow (using the shoulder and wrist joint): Image of example ...
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1answer
198 views

How to fly a curve from one heading to another using only roll and pitch.

I have 3 perpendicular vectors representing an object in 3d space... Heading Right Up ...and I would like to be able to 'fly' this object so that it ends up at a ...
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1answer
424 views

Determining angle of tilt from length of axes?

When taking a picture of a cross, if the center of the cross is known, is there any way to determine the angle at which the picture was taken based on the number of points on the y axis above and ...
5
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2answers
666 views

“Normalizing” Points on a Sphere

I have a set of points on a unit sphere representing different orientations: Now I need to apply rotation(s) such that the points will lay on the horizon as tightly as possible: The ideal ...
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2answers
91 views

Normal from multiple vectors

I have a several 3D vectors $X_{i}$ which lay approximately in a plane. Now I need to find a single vector, which is normal (as much as possible) to all of them. For two vectors, I can use a cross ...
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2answers
229 views

Need to define an integral expression to find the area of intersection of a Plane and a Cone.

How can the integral expression be defined to find Area (S) on $x+y+z=1$ and bordered with intersection of the cone ($x^2+y^2-z^2=0$) and the plane ($x+y+z=1$) ?
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1answer
4k views

Finding an equation of a sphere for a specific plane

I am not sure how to proceed with this question from Stewart's SV Calculus text: Find equations of the sphere's with center $(2, -3, 6)$ that touch (a) the $xy$-plane, (b) the $yz$-plane, (c) ...
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3answers
626 views

What is the tangent plane equation on the 3 spheres?

3 spheres are on $z=0$ plane and touch each other as shown in the picture. Coordinates of their centers are $O_1=(0,0,5),O_2=(0,y_2,3),O_3=(x_3,y_3,2)$. What is the tangent plane equation on 3 ...
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3answers
32k views

how to calculate area of 3D triangle?

I have coordinates of 3d triangle and I need to calculate its area. I know how to do it in 2D, but don't know how to calculate area in 3d. I have developed data as follows. ...
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1answer
148 views

Find P points inside ABCD tetrahedron so that volume of ABCP = volume of ABDP

Find all $P$ points inside $ABCD$ tetrahedron, so that $V_{ABCP} = V_{ABDP}$ Thanks in advance for any help.
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1answer
181 views

Should/do parallel lines curve when rendered with perspective?

Simple perspective calculations used in rendering 3D points onto a 2D screen take the form of dividing the camera-relative coordinates by distance from camera and multiplying by a field-of-view ...
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1answer
191 views

Calculate equivalent (X,Y) given (X,Y,Z)

I'm working on generating a 3D-looking application (in 2D) and am having difficulty generating my graphing points equally. I can only graph in 2D, but want to have a 3D look to it (similar to a ...
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4answers
2k views

Quaternions and spatial translations

From my understanding, in spatial applications (3D rendering, games and similar applications) quaternions can only be used to describe rotations/orientations and not translations (like a ...
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0answers
132 views

polygon inside a polygon

i have several point patches lie on different planar faces. then, I obtained enclosing polygons to represent points so that i have several planar polygons (for example A,B,C,D). when i examine the ...
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0answers
401 views

differentiation of polygons, having cross borders

I have point data set and I segmented the data into different planar objects. after that, using contouring (convex hull), I obtained the boundary points. Please assume all points relevant to one ...
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2answers
2k views

How are 3D coordinates transformed to 2D coordinates that can be displayed on the screen? What is the formula for this?

The title asks it all, and could someone please also explain the formula as well? Thanks.
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1answer
543 views

Finding radius r of the overlappable sphere(s) in 3D image

My current problem: I have an input 3D binary image (a 3D matrix that has only 0 and 1) that consists of random numbers of sphere with radius r. We do not know how many spheres are there in the ...
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1answer
786 views

Find 3D rotation vector and angle to transform a rectangle into a given quadrilateral

I have a given rectangle that I need to transform into a given quadrilateral shape that resulted from a rotation and translation in 3D space, and subsequent projection. ...
0
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1answer
168 views

Chain Rule and Homogenous Coordinates

I have a vector $\tilde{p} = (x,y,z)$ (homogenous coordinates). The corresponding non-homogenous vector is $p = (x/z, y/z)$. Now the $\tilde{p}$ is a result of some linear transform $R(\theta)$ of ...
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2answers
833 views

Extend angle between two 3D vectors to x-y plane.

I would like to know how I can extend the angle between two vectors in 3D space to the x-y plane. So, there are two vectors in 3D space, and the angle between them is found using the definition of ...
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1answer
1k views

How to calculate rotation angle to get a set distance between two vector end points

The situation: In 3D space there are two vectors (A, B) of equal length L, but with different directions. The beginning points of these vectors are located at a distance of L as well. They could be ...
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1answer
658 views

line projection on top of a plane

If I have a horizontal line (a 3d point and 3d vector with zero z component) and another plane (could be an oblique or a horizontal; i have normal vector of the plane); then how do we get the ...
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1answer
168 views

Euclidean Geometry a triangle problem

In the three dimensional figure below, is there a way to prove that $$ \angle MNK = 90^ \circ $$ $\hspace{2.8in}$
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1answer
737 views

Find third 3d coordinate given two other coordinates

Given the 3d coordinates of the 2 spheres (see image below) and the length of the Box, how can find the 3d coordinates at the end of the box using an equation?
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1answer
1k views

Extracting perspective transformation from a 2D projection

I have a 2D projection of a flat, rectangular object in 3D space, like this one: I know all sorts of information about this shape—its opposite sides have the same length, the sides meet at right ...
3
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0answers
876 views

Three-dimensional vectors and force systems

Full disclosure: this is a homework problem. However, I find myself stuck in the middle. The problem is below As shown, a system of cables suspends a crate weighing W = 350 . (Part C 1 figure) ...
3
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1answer
4k views

linear interpolation in 3 dimensions

Say that I have 2 points in 3 dimensional space specified in Euclidean coordinates $p_0(x_0,y_0,z_0)$ and $p_1(x_1,y_1,z_1)$. How would I go about finding the coordinates of an unknown point that ...
7
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1answer
1k views

3D Rotation Matrix Uniqueness

Given a 3D rotation matrix R in a basis B. Can we consider R as being unique in B? Is there any other 3d rotation matrix R' representing the same 3D rotation in B? How could I prove that? Note: I do ...
2
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0answers
494 views

points of intersection on a randomly situated plane and ellipsoid (spherical) in 3d space

if i have an ellipsoid and a plane oriented in any way in a 3 dimensional coordinate system, and they intersect; is there a way to find an equation that describes (or at least approximates) all points ...
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1answer
253 views

Finding the radius of a particular center voxel in 3D cylinder-like structure

From the image above, assume that it is a 3D image that is of m*n*o size. Each voxel can only be either 0 or 1. White is 1. Black is 0. In this 3D environment, there is one cylinder-like ...
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2answers
62 views

All the matrices that are orthogonal and have $q_1,q_2$

"Determine all the orthogonal matrices $Q=[q_1,q_2,q_3]$ that have as the first two columns the vectors $q_1=\frac{1}{\sqrt{6}}(-1,2,-1)^T, \ q_2=\frac{1}{\sqrt{3}}(1,1,1)^T$". I used the ...
12
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2answers
202 views

Mathematical description of a corncob

I'm trying to figure out how I can make a paper model of the corncob water tower in Rochester, Minnesota for my N-scale train layout. The best I can find is this: ...
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1answer
2k views

(Graphics Gems IV, Shoemake) From matrix to euler angles explanation

I am trying to understand matrix to Euler angles conversion. So I read Graphics Gems IV, page 222 from Ken Shoemake. It states: "Suppose we have code to convert a rotation matrix to XEDS angles, $R = ...
30
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3answers
914 views

will 3 lights illuminate convex solid

Can 3 lights be placed on the outside of any convex N dimensional solid so that all points on its surface are illuminated?
1
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1answer
252 views

What is the intuition behind the solution of Hilbert's third problem?

I have read a book called "Proofs From The Book", but it defined many terms and contains much terminology, so I couldn't understand how to obtain a proof by using Bricard's condition. However, I ...
3
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7answers
853 views

Software to display 3D surfaces

What are some examples of software or online services that can display surfaces that are defined implicitly (for example, the sphere $x^2 + y^2 + z^2 = 1$)? Please add an example of usage (if not ...
2
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2answers
6k views

How to multiply vector 3 with 4by4 matrix, more precisely position * transformation matrix

All geometry in computer graphics are transformed by position * transform matrix; The issue is the fact that position is a vector with 3 components (x,y,z); And transform matrix is a 4 by 4 with one ...
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3answers
1k views

Analytically compute signed distance of ellipsoid

I'm trying to generate a 3d signed distance field for a origin centered ellipsoid. For a sphere this is pretty easy: $$\sqrt{x^2 + y^2 + z^2}-r$$ where $r$ is the radius. I'm not sure what the best ...
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1answer
227 views

Why are the coefficients of the base states of a qubit complex numbers?

Why are qubits represented as $$\left|{q}\right\rangle = \alpha\left|{0}\right\rangle+\beta\left|{1}\right\rangle\equiv\alpha\left[{1 \ 0}\right]^T+\beta\left[{0 \ 1}\right]^T; ...
0
votes
1answer
582 views

3D parametric equations with polar coordinates

I'm currently studying for my calc 2 midterm and came across this and it completely lost me. I'm not even completely sure where to begin with it. Any ideas? Put $\langle x[r,t],y[r,t],z[r,t] \rangle ...
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2answers
1k views

How can I determine the radius of a dodecahedron?

I am making a dodecahedron that needs to fit inside of a sphere. The sphere has a diameter of 56mm. What is largest possible measurement of one segment of a pentagon side of a dodecahedron that would ...
3
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2answers
9k views

Line and plane intersection in 3D

How would one calculate the intersection of a line and a plane in 3D ? Given for example are 4 points which form a plane (x1,y1,z1)...(x4,y4,z4) and 2 different ...
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1answer
501 views

Equation to a Perpendicular Line Along A Plane

I have the following problem, which Google has not yet been able to answer. I have the equations to two lines in 3D space. I also have the co-ordinates of a single point on each line. I can therefore ...
0
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1answer
518 views

3D correlation visualization?

Incomer per person (x axis) correlates with life expectancy (y axis). These two indicators change over time (z axis). x correlates with y. Moreover, x and y both correlate with z. The question is: ...
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3answers
6k views

Vector Rotation in 3D

Given: Two points: ($x_1$, $y_1$, $z_1$), ($x_2$, $y_2$, $z_2$) A vector that is parallel to the $x$-axis and points to ascending numbers (intuitively stated, the vector points 'East'). I am ...
0
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1answer
73 views

Geometry: problem with defining the vertices of a tunnel around a given path

I'm trying to create some kind of demo that rushes through a tunnel. I have made a random path generator that creates smooth looking paths in 3D space (just some 3D points) Now I would like to ...