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
46 views

proof for euler-rodrigues formula - matrix form

I need for a matrix representation. Exactly I want to know how to get the Euler-Rodrigues formula in a matrix form like here. Thanks!
1
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1answer
20 views

How to find the $ x,y$ coordinates of a point in between $2$ points in $3$ dimension

Point $1 = (0,0,0)$ Point $2 = (5,6,7)$ Given that point $3$ have a $z$-coordinate of $3$, how can I find the $x,y$ coordinates of point $3$?
2
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1answer
152 views

Find the equation of a plane tangent to two spheres

Given the equations of two spheres, how would I find the equation of any plane tangent to the two spheres? I tried something, but I realized that it failed, and I am not sure where to go from here. I ...
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0answers
18 views

Fitting by an ellipsoid with a known center?

Consider a set of $N$ points in 3D of coordinates : $$p_{i} = \left\{x_{i}, y_{i}, z_{i} \right\}$$ The very general question I ask is : how to fit these points by the surface of an ellipsoid ...
2
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1answer
38 views

How does a measurement error change the volume of a tetrahedron?

Consider that I have a tetrahedron $T$ whose the lengths of edges are $(a,b,c,d,e,f)$. I want to calculate the volume of the tetrahedron by Cayley-Menger Determinant. However, I know that, the ...
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1answer
184 views

Jacobian of exponential mapping in SO3/SE3

Following this post Jacobian matrix of the Rodrigues' formula (exponential map) What if I really need the Jacobian of the exponential mapping function in $\omega \neq 0$? Basically, I want to ...
1
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1answer
348 views

Finding the shortest distance between two planes using Lagrange multipliers

A problem (among a list of Lagrange multipliers problems in Earl Swokowski's Calculus) states as follows: find the shortest distance between $2x+3y-z = 2$ and $2x+3y-z=4$. I can see that the ...
0
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1answer
66 views

3D Geometry Contest Math Problem

The problem is as follows: Six solid regular tetrahedra are placed on a flat surface so that their bases form a regular hexagon H with side length 1, and so that the vertices are not lying in the ...
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2answers
42 views

Transformation of the points on a plane

How do I transform a point $(x,y,z)$ on plane $\Pi (ax + by + cz = 0)$ to a point $(x',y',z')$ on plane $\Phi(ax+by+cz+d=0)$? What matrix should I use? Here is a 2-D representation of what I'm ...
0
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0answers
17 views

Generate rotations about X & Y axes between certain 3D vectors

Given a semi-arbitrary 3D vector (the z will always be positive for my purposes), how could I find rotation about the X and Y axis? Alternatively, how might I simplify an XYZ rotation to the X and Y ...
0
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1answer
51 views

N points in a circle around a point on a sphere.

Consider a 3D sphere: $(x_{c}, y_{c}, z_{c})$ : cartesian coordinates of the center $r$ : the radius Consider a random point on the surface of this sphere of coordinates : $(x_{0}, y_{0}, ...
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1answer
28 views

Multiplication with vectors.

Well, I'm not quite sure if I chose right terms for my problem but I will give it a chance. Here, I have some tasks and examples ( http://www.mif.vu.lt/matinf/asm/gr/p12.pdf ). On the bottom of the ...
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3answers
103 views

Can you find a ellipse so that its image is a circle?

This is a "fun" question and I have already a solution. I asked this question so that I may see a different approach or an elegant solution. Let $P$ be a plane with equation $x+y+z=1$. Find an ...
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2answers
328 views

slope of a line in 3D coordinate system

Suppose I have $2$ points in a 3D coordinate space. Say $p_1=(5,5,5)$, $p_2=(1,2,3)$. How do I find the slope of the line joining $p_1$ and $p_2$? After getting the slope (which I assume will be an ...
3
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2answers
86 views

Find point in 3D space based on plane and known point

I'm struggling with drawing geometry in 3D spaces via OpenGL. My current task is to find coordinates of point. Assume we have such input data: Points $a$, $b$ and $k$ define a plane. Point $c$ ...
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2answers
47 views

Projecting 3D Point to Plane

I have a plane defined by the equation $Ax + By + Cz + D = 0$. It does not pass through the origin. I have projected the origin of my global coordinate system onto the plane, so it is at $(a, b, c)$. ...
3
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1answer
67 views

the surface area of the cream white colored surface wants to be calculated using integral

I Want to calculate the area of the cream colored surface illustrated on the image below using integral. variables are $\beta$ and $\phi$ and constants are R and r
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2answers
39 views

What is the difference between $z=0$ plane and $26z=0$ plane

I'm using this site to calculate a plane equation. The points are $(2,3,0)$, $(5,1,0)$ and $(6,9,0)$. The result is $26z = 0$ plane. Is there a difference between $26z =0$ and $z = 0$? Moreover, ...
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0answers
25 views

Numerical evaluation of an infinite 3D sum of cosine?

Consider the following function: $$f\left(x, y, z\right) = \sum_{\left(n, m, l\right)\in \mathbb{N}_*^3}e^{-\alpha\left(n^2+m^2+l^2\right)}\frac{\cos\left(\omega nx\right)\cos\left(\omega ...
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0answers
73 views

Map points between 3D Coordinate systems

I am trying to find a way to relate two 3D coordinate systems. I have 24 points for each system and found this, but it only works for 2D coordinate systems: ...
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0answers
47 views

Intersection volume of two oriented bounding boxes

I have been searching the web for a while now, but to my surprise I haven't found a algorithm to the following problem yet: Given are two oriented bounding boxes, that is, they generally are not axis ...
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2answers
110 views

How to rotate a plane in 3-D using standard form?

I have a set of points $N = \{n_1, n_2, ...\}$ on a plane $z = 0$. And I have another set of points $M = \{m_1, m_2, ...\}$ on plane $ax + by + cz + d = 0$. $|N| = |M|$ $\forall n_i, n_j \in N$ and ...
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1answer
99 views

number of planes possible such that it is equidistant from 4 non coplanar points

If there are for non coplanar points find the number of planes such that all four of them are equidistant from the plane . Sorry one of those problems where dont know what to do . How should i do this ...
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0answers
28 views

Rotating by the pivot point and store the result as rotation by the (0,0,0) + translation.

I have an object in 3D space, but I guess that problem is dimension-independent - you can assume it's 2D as well. I have an object (box) - I store only its ...
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1answer
114 views

Finding the missing coordinate of a point within a 3D triangle

We have an equilateral triangle $ABC$ in 3-dimensional space. The points are known, such as: $A = (x_1,y_1,z_1)$ $B = (x_2,y_2,z_2)$ $C = (x_3,y_3,z_3)$ Point $P$ is on triangle $ABC$. If I know ...
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1answer
24 views

Vectors to Matrices in algebraic equations

This question is based off of Dave Eberly's 3D Game Engine Design, 2nd Edition. I am reading it slowly to gain a larger algebraic grasp of 3D graphics, which this book seems to offer. When finding a ...
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2answers
81 views

Calculating Intersection of Three Spheres Step by Step

How do I calculate the intersection of three spheres step by step? Assume that the spheres are $S_i(c_i, r_i)$ where $i = 1,2,3$, $c_i$ is the center coordinates of $S_i$ and $r_i$ is the radius of ...
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1answer
41 views

Equation of a plane passing through a point

Write an equation of the plane with normal vector n=<-6, 9, -8> passing through the point (-1, 3, 4) in scalar form. The equation should equal 2. I just learned this topic and I am having ...
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2answers
28 views

Plane in 3 Dimensions

I just learned this topic and I'm having trouble with this homework problem... Find an equation of the plane through the three points given: $P = (0, 2, 0)$ $Q = (-4, 6, 2)$ $R = (3, 3, -1)$ The ...
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2answers
56 views

Unreliable algorithm for determine if points lie along a line?

So lets say I have some points $A,B,C$. A method I have been shown for determining if the lie along a straight line is thus: $\mathrm{If}\space|AC|=|AB|+|BC| \space\mathrm{then\space A,B\space ...
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0answers
192 views

Transform a vector to global frame and ignore rotation about one axis or Full tilt compensated magnetometer

Good day everyone. I would like to lock the rotation about one specified axis. For example, let`s imagine that we have a quaternion which desribes the orientation of our rigid body relative to the ...
0
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0answers
131 views

Function of an object that has a shape of circle, square and triangle on 3d projection

What is the function of this kind of object (solid on the bottom right)? I got a lot of material for pondering with keyword cylindrical wedge and hoof, but this is something inverse compared to it. ...
1
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1answer
65 views

How do I calculate the dimensions of this Frustum?

So, I saw this question in a book, You have been given a cone. The cone's base angles are both equal to 75° and the vertical angle is (of course) 30°.The radius of the cone is 7 metres.Now, ...
0
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1answer
59 views

Rays in the space

I have a nice problem from a mathematical circle: Let n be a positive integer. Determine the smallest n with the property in the space having
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1answer
60 views

Ellipsoid intersection

Let $E$ be an ellipsoid centered at $p = (x,y,z) \in \mathbb{R}^3$ and let $T:\mathbb{R}^3 \to \mathbb{R}^3 $ be a linear transformation which transforms $E$ to a unit sphere. Let $R$ be the ray $p_0 ...
1
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2answers
63 views

Rotate $z = 0$ plane in 3D

I have 100 points on $z=0$ plane. I want to rotate those points, such that they lie on any plane $P(a,b,c,d)$, preserving distances. Hence, I need a rotation matrix. For instance, if my points are ...
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1answer
37 views

Distortion in spherical coordinates

I'm trying to realized 3d models of stones. My idea was to create a 2D random angular distribution with opportune correlation, namely $R(\theta,\varphi)=rand(\theta,\varphi,c_l)$ where ...
2
votes
1answer
31 views

is there a higher dimensional analogue of the first isogonic center?

I'm curious to know if, given four points $a, b, c, d$, you can always find a point $p$ such that last lines $pa, pb, pc, pd$ form equal angles pairwise. I'd also appreciate resources on 3d geometry ...
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0answers
36 views

Intersection of a line on a plane

I have two points $P_1=(x_1,y_1,z_1)$, and $P_2=(x_2,y_2,z_2)$, also I have my plane values $A,B,C $ and $D$ too. I know that $P_1$ lies on a side of the plane, and $P_2$ lies on other side of the ...
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0answers
23 views

Collision of two moving lines (3D)

I have two lines / edges moving with linear velocity in timesteps. How do I determine whether the lines collide / intersect in the intervening period? My lines are (P1,Q1) and (P2,Q2). The endpoints ...
0
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1answer
64 views

Calculation of an average plane without using a covariance matrix

I need to calculate the normal to an average plane using the positions of >3 points (for 3 points, I know how to do it with a cross-product). My main problem is that it needs to be a simple method ...
0
votes
1answer
29 views

Vectors In Three Dimensions

Hi! I am working on some online homework for my calc2 class and I am having trouble with this problem. I first set $r_1$ and $r_2$ equal to one another to get $(-1-4t, 2+2t, -14+2t)=(-13+4t, 8-2t, ...
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0answers
56 views

Rotation rate around one axis transformed to a different axis at an angle to the first

Suppose I have a motor with axis M on my diagram rotating at rate $r$ [rad/sec]. Connected to the motor is a gyroscope, the axis G of which is at an angle a to to that of the motor (the gyroscope ...
2
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1answer
261 views

Find normal vector of circle in 3D space given circle size and a single perspective

I don't really know what to search up to answer my question. I tried such things as "ellipse matching" and "3d circle orientation" (and others) but I can't really find much. But anyways... I have ...
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0answers
29 views

How do I do the math necessary to make these five matrices multiplied together equal the result shown?

I'm currently studying the math involved with rotating vertices around an arbitrary axis in 3D space. For this, I have found the following page to be very helpful: ...
0
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1answer
167 views

Volume between paraboloid and plane

I need to find the volume of the finite region enclosed between the surface $$ y = 1 - x^2 - 4z^2 $$ and the plane $$y = 0$$ Here's what I've done: $$ \int\int ...
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vote
2answers
288 views

Finding a normal to an ellipsoid

Let $E$ be an ellipsoid centered at $v = (x,y,z) \in \mathbb{R}^3$ and let $T:\mathbb{R}^3 \to \mathbb{R}^3 $ be a linear transformation which transforms $E$ to a sphere $S$ with a radius of length ...
0
votes
1answer
40 views

Converting 3D into 2D

I have a quad and I'm trying to convert its vertices so that they're facing the camera which is lying at 0,0,1 looking down the Z, or not even specifically facing the camera, just so they're facing up ...
0
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1answer
22 views

Find close-enough points in 3d space

I have 2 sets of points in 3d space , each set of size n. I need to calc. all the points from the first set the are close enough (dist between 2 points < TH, TH is given) to at least one of the ...
2
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1answer
59 views

Collinear points in 3dimension

Given three $3D$ points: $A,B$ and $C$, what is the procedure to check if they are collinear? In general, given $n$ points in $m$-dimension, how should one find out, if these $n$-points defines a ...