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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2answers
43 views

Calculate coordinate of any point on triangle in 3D plane

I am really stuck and can't find right way to write a formula(s) that will calculate Z coordinate of point on triangle plane in 3D plane. I know all coordinates of triangle points ( Ax, Ay, Az, Bx, ...
-1
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1answer
38 views

Finding how “spreaded” a point cloud in 3D

I don't know the proper term for "spreaded" but what I want to find is, a value that indicates how far is an average point from the centroid. I think this is standard deviation of the point set, but ...
1
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2answers
71 views

Rotate XYZ frame in 3D space

Given a XYZ frame in 3D space at origin O(0,0,0). And given a plane equation: ...
0
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1answer
23 views

Area of triangle on a sphere (not spherical triangle)

How do I find the area of a triangle on a sphere, and the triangle is not a spherical triangle, for example, the triangle is formed with two geodesics and a line of latitude. Is there a specific ...
1
vote
1answer
23 views

Given an axis of rotation and an angle, work out the rotation angles around x,y,z axis

I want to convert from one 3D rotation convention to another. The first convention has an axis of rotation, $\boldsymbol{r}$ and an angle $\theta_r$ to rotate about this axis. The second convention ...
0
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1answer
38 views

x(u,v), y(u,v), z(u,v) parametric equations for a special cycloid

I'm trying to find out a 3d parametric equations for a cycloid I know that a cycloid is a 2d curve it is generated by a point on a rolling circle. but my circle is rolling around another circle both ...
0
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1answer
31 views

Euler angles for mapping three points on a sphere to three other

Let $\mathbf{a}$, $\mathbf{b}$, $\mathbf{c}$ be points on the unitary sphere, so that $\|\mathbf{a}\| = \| \mathbf{b} \| = \| \mathbf{c} \| = 1$. Let $\mathbf{a'}$, $\mathbf{b'}$, $\mathbf{c'}$ be ...
0
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2answers
38 views

Collision detection between two accelerating spheres with no initial velocity?

We have two non-touching spheres of radii r1 & r2 are lying in space at rest. Both of them are then given accelerations a1 & a2 respectively at time t=0. Find whether they will ever come in ...
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0answers
23 views

Mapping between two unknown 3D coordinate systems from common motion

Coordinate systems A and B are rigidly linked in an unknown way. The platform then moves and the motion vectors [RA|TA] and [RB|TB] are calculated in each coordinate system. They are parallel but not ...
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2answers
60 views

Difference between Euclidean space and vector space?

I often hear them used interchangeably ... they are very complicated to make any use of. Wikipedia words: Euclidean space: One way to think of the Euclidean plane is as a set of points ...
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0answers
23 views

Famous graphs with nice 3D embeddings

The Petersen graph has an interesting 3D embedding. Take a tetrahedron. Add a midpoint to each edge. Connect opposing midpoints for a Petersen graph. The Perkel graph or 57-cell has an interesting ...
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0answers
12 views

rotating vector based on plane normal

This is probably very basic, but here is a drawing of what I'm trying to achieve : Explanation : Those are 3D normalized vectors and I'm trying to change v1 to v1' based on vn. As shown in the ...
2
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0answers
25 views

Volume of overlap between two convex polyhedra

I have two convex polyhedra represented by triangle meshes. I can easily determine if they are in contact or not, but when they are in contact then I would like to determine the volume of their ...
0
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1answer
19 views

Incorporating an error ellipse from eigenvalue/vectors into 3D geometry

I have a 3D point with a covariance matrix, and an associated 3D vector that begins at the point. I would like to be able to consider alternative points for the starting position of the vector, ...
0
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1answer
26 views

Intersection of a plane and a surface of revolution

I'm am stuck on the following problem: I have the equation of a curve in the plane $(x,z)$: $z=f(x)$. I build a surface of revolution in the space rotating this curve around the $z$ axis. I need to ...
2
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1answer
24 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
votes
1answer
59 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 ...
0
votes
0answers
15 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
votes
1answer
33 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 ...
1
vote
1answer
97 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
73 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
53 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 ...
0
votes
2answers
38 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 ...
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0answers
15 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
votes
1answer
41 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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votes
1answer
26 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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votes
3answers
101 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
41 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
votes
2answers
69 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 $c$ ...
0
votes
2answers
39 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
votes
1answer
66 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
38 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, ...
0
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0answers
19 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
60 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: ...
0
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0answers
27 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 ...
1
vote
2answers
106 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 ...
1
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1answer
52 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 ...
0
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0answers
21 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 ...
1
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1answer
88 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 ...
1
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1answer
19 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
64 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 ...
1
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1answer
30 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
27 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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votes
2answers
40 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
124 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
65 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. ...
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1answer
42 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
votes
1answer
58 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
42 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 ...