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
37 views

Area of projection of cube in $\mathbb{Z}^3$ onto a hyperplane

A cube with vertices $(\pm 1, \pm 1, \pm 1)$ gets projected into the plane perpendicular to vector $\mathbf{n}\in S^2$. The projection is a hexagon, how do I find the area? I think I can just ...
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2answers
13 views

Why one V-axis and two H-axis on 3D? [on hold]

Why when drawing a 3D graphic there are one vertical axis and two horizontal axis and it is not vice-versa?
1
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1answer
44 views

To find the volume of the region that is bordered by 4 points in 3D space

To find the volume of the region that in the points $A(x_1,y_1,z_1),B(x_2,y_2,z_2),C(x_3,y_3,z_3),D(x_0,y_0,z_0)$. Let's define a 4X4 matrix to determine plane equation that are on $A,B,C$ ...
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2answers
18 views

Parametric equation for intersection of curve

Here's the three part question: A) Find parametric equations for curve which is the intersection of the cylinder $x^2 + z^2 = 1$ and the plane y = -x. B) Show that the curve lies on the surface $x^2 ...
6
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1answer
68 views

Probability that two circles in space are linked

Let $C_0$ be a circle centered on the origin, and $C_1$ a circle centered on $(1,0,0)$, center distance of $1$. Q1. If both $C_0$ and $C_1$ are randomly oriented and have the same radius $r ...
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0answers
380 views
+100

Fitting Expanding Spheres in the Irregular Surface

This is a kind of a puzzle: I have a convex hull filled with $N$ small spheres(with radius $r$). Now, the balls grow in size till it hit any side of the Cavity (Convex hull) or any other ball. ...
-1
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0answers
22 views

What is the use of direction cosines? [closed]

What is the use of direction cosines and direction ratios? Is there any practical problems related to direction cosines? Why we tagged the word 'direction'? If possible explain me through photos or ...
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1answer
15 views

What is and what are the use for an “ AINV preconditioner ” or “ SAINV ”?

In an article that I'm reading there is a mention to this "thing" and I absolutely don't know anything about it, for me it could be anything. I noticed that this thing is somehow related to the math ...
0
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0answers
18 views

Rotation of point with infinite child objects. (Chain rotation)

More of a thought experiment here, knowledge for knowledges sake. Let's say you can create infinite points that rotate smoothly and at the same speed as each other through a full revolution - let's ...
2
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2answers
36 views

Finding a 3rd coordinate of the rectangle points in 3d

I have a 4 3-D-points, each of them has only 2 of 3 known coordinates, as follow (? is unknown here): P5 (P5x, P5y?, P5z) P6 (P6x, P6y?, P6z) P3 (P3x, P3y, P3z?) P4 (P4x, P4y, P4z?) They build ...
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1answer
27 views

Volume of Cavity between intersecting multiple Spheres

I want find an equation for this problem: Problem Statement:: I have different size sphere, for example say $R_1$ for Red balls and $R_{2}$ for white Balls, overlapping each other. 1.) I want to ...
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3answers
37 views

What 3D graph does $x^2+2z^2=1$ give?

I am missing the 3D graph for the equation $x^2+2z^2=1$.
0
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1answer
11 views

Calculate position of N points around given point in 3d space?

Sorry if I used wrong words - English is not my native language, and I never actually studied geometry. For a project I'm working on, I need to calculate set of points, that: are in given, ...
2
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1answer
26 views

Creating a surface from a path of 3D cubic bezier curves

I have a list of cubic bezier curves in 3D, such that the curves are connected to each other and closes a cycle. I am looking for a way to create a surface from the bezier curves. Eventually i want ...
0
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1answer
25 views

transform line and point in 3d and 2d space [closed]

I have a line which is described with two point and I know (x0,y0,z0) and (x1,y1,z1). After that I transform it to 2d space dividing with -z0 and -z1 values. Problem is that if I know (a,b) how can ...
0
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0answers
21 views

Seams/net of curved surfaces

Like with the seams of a piece of clothing or inflatable, what would the methodology be to creating a flat net of a curved 3d object? I would like to create a model of a mobius torus, and would like ...
5
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1answer
69 views

Find all such functions defined on the space

$f:\mathbb{R}^3\to \mathbb{R}^{\ast}$ is such that for any non-degenerate tetrahedron $ABCD$ with $O$ the center of the inscribed sphere, we have : $$f(O)=f(A)f(B)f(C)f(D) $$ Prove that $f(X)=1$ for ...
0
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1answer
25 views

How can I transform a 3D triangle to xy plane

Suppose I am given a triangle ABC and its corresponding vertex coordinates in 3D. I want to transform ABC in such a way so that vertex A lies on global (0,0,0) coordinate, B lies on (dist, 0, 0) ...
0
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0answers
38 views

Proving the 3-d pythagorean theorem on surface areas of oblique triangular pyramid

I would like suggestions if possible, other than the really sloppy picture, I'll edit that once my dad gets me Microsoft office. I got a snip of the shape, and edited it as best as I could. The ...
0
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0answers
44 views

How to average 3D Scale Vector?

I'm working in a 3D application and I'm trying to average scale values together, but I'm missing a step. The x, y, z scale values in my problem will all be the same so even though my values will be ...
0
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1answer
21 views

Given a point origin, find ray that intersects two lines

I'm working on a specific shadow calculation for a graphics project. I have a point light source obscured by a straight edge object, and I want to find where the edge of the shadow intersects a ...
0
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1answer
34 views

Triangle in 3D space point X and Y coordinate know find Z

I have a triangle in a 3D space. I know the points X an Y coordinate but I dont know the Z. How can the Z be calculated by knowing the points of the triangle and the X an Y coordinate of the point ...
2
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2answers
32 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, ...
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1answer
35 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 ...
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2answers
62 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: ...
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0answers
16 views

Transforming euler rotations to other coordinate system

I have a global $3D$ coordinate system, and it's transform matrix is an identity matrix. I also have an object with it's own, local coordinate system and it's transform is not identity matrix. Now I ...
0
votes
1answer
22 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
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1answer
15 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
30 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
25 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 ...
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2answers
36 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
19 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 ...
0
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2answers
50 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
19 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 ...
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0answers
18 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
16 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
22 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
20 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
50 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
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1answer
71 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
56 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
49 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
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2answers
36 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
14 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
39 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}, ...
0
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1answer
25 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 ...