Tagged Questions

-1
votes
0answers
24 views

Imaginary line passing through non-collinear points in R3.

I have come to a problem where n points are provided in 3-Dimensional plane. I need a imaginary line which can be assumed that it is passing through these points.
0
votes
1answer
18 views

Commutative applying rotations around three axis

Rotating an object in a 3 dimensional space by euler angles might be intuitive but comes with some problems. First, the order of applied rotations around the different axis matters. Second, there is ...
2
votes
1answer
43 views

Disable one angle of rotation

I'd like to disable one angle of rotation of an object rotating in 3D space. Imagine a camera rotating around and displaying objects as they are in space. I'd like this object to be fixed on the ...
1
vote
4answers
43 views

Find the equation of plane containing line described by

Please help me in this really easy task Find the equation of plane containing line described by $x+3y-2z=1$, $2x-y+2z=3$, containing point $(1,1,3)$
0
votes
3answers
67 views

How to calculate triangle-line collision in 3D?

If there is a given triangle (tx1, ty1, tz1), (tx2, ty2, tz2), (tx3, ty3, tz3) and two given point of a line ...
3
votes
1answer
64 views

Why does aliasing cause loss of a degree of freedom in Euler angles?

I'm reading a book on 3D game math where the author points out that when using Euler angles the same orientation can be reached by doing two different operations; say rotating a cube 90 degrees around ...
0
votes
1answer
92 views

Apply Euler vector to translate vector

This is a problem for 3d graphics programming. I have an object in 3d space, an airplane, who's position is (x1, y1, z1). The orientation (rotation) specified as a Euler vector in radians, (x2, y2, ...
2
votes
2answers
120 views

Rotating one 3-vector to another

I have written an algorithm for solving the following problem: Given two 3-vectors, say: $a,b$, find rotation of $a$ so that its orientation matches $b$. However, I am not sure if the following ...
2
votes
2answers
111 views

How to calculate the rotation of a vector?

So, let's say I have vector $\vec{ab}$ and vector $\vec{ac}$. How do I calculate the amount of rotation from $b$ to $c$? Note, this is in a 3D space, of course...
0
votes
1answer
86 views

Is there a formula to know the angle of an object, on a Cartesian plane, when it is rotated by arbitrary x, y, z degrees?

Example: If I have a line rotated (at its center) by -45 degress on the x, y, and z axis what formula would I used to determine what angle that object is at if you put it back on a cartesian plane? ...
0
votes
1answer
203 views

Ray Plane Intersection Calculation

I am currently having issues with calculating plane intersection of a ray. I start with the following equation $P = P_0 +tR_t$ $R_t$ is the Unit Vector of the Trajectory. Now we have a plane ...
0
votes
1answer
242 views

Finding a 3D transformation matrix based on the 2D coordinates

I have a square with the length of the sides being 1. This square is transformed by an unknown transformation matrix in the 3D space and then projected back to the plane (the projection is known). I ...
0
votes
0answers
41 views

Convert point coordinates

I have to create some transformations for a 3D application but I'm not very good at math. I have 2 objects in space (let's call them ...
0
votes
2answers
164 views

3D Cartesian Coordinates System revolve around a specified axis

I have a 3d cartesian coordinates system and now I want to rotate a point $p(x_0, y_0, z_0)$ arround a specified axis $v(v_x, v_y, v_z)$ like $(1,1,1)$,and the angle is $\theta$,finally I want to get ...
2
votes
1answer
515 views

How to calculate the rotation matrix between 2 3D triangles?

I need to calculate the rotation matrix and the translation vector between 2 given triangles in Euclidean space. This is really just a rotation and a translation, the lengths of sides of the triangle ...
7
votes
3answers
4k views

Calculate Rotation Matrix to align Vector A to Vector B in 3d?

I have one triangle in 3d space that I am tracking in a simulation. Between time steps I have the the previous normal of the triangle and the current normal of the triangle along with both the current ...
0
votes
0answers
414 views

Explicit calculation of 3x3 rotation matrix from combining three angle-unit axis rotations?

I need to remove dependence on a programming library from a computer application I'm working on and instead hand code a geometric operation. Please can you show explicitly (for someone with little ...
0
votes
1answer
318 views

General solution for 3D line intersection

I've been trying to get the intersection point of 2 3D lines (in general, so i can code an algorithm) using the following equations: $$ x_0 + k_0 a_0 = x_1 + k_1 a_1 \tag{1}$$ $$ y_0 + k_0 b_0 = y_1 ...
1
vote
0answers
202 views

Calculating an average plane from a series of points using Numpy

Given N, 3D position vectors, I want to find the best-fit plane of those vectors. I found a suggested answer here that said: Calculate the average of the points (easy) Calculate the Covariance ...
1
vote
1answer
256 views

Closed-form for eigenvectors of rotation matrix

For matrices that are elements of $SO(3)$ is there a formula for the eigenvectors corresponding to the eigenvalue $1$ in terms of the entries of the matrix?
2
votes
1answer
147 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 ...
0
votes
0answers
198 views

3D Mathematics Projecting One Vector onto Another

I have a Vector function which takes two Vectors and and attempts to "project" these vectors together. The method used is to separate the larger of the two vectors (the larger value calculated via ...
3
votes
1answer
336 views

Determining which side of a 3D cube is facing the viewer

Me and a friend are trying to render a rotating cube on a 2D plane(the screen) using java. Here's the problem The cube has 6 sides, each with a specific normal vector of the form (0,0,1), (0,-1,0) ...
0
votes
1answer
436 views

how to perform a rotation around a point which itself is rotating?

I'm working on rotating human limbs in a 3d game. I use Linear Algebra matrix rotations and translations to achieve moving the human and limbs. I currently can rotate around a pivot point by first ...
2
votes
1answer
463 views

calculating coordinates from a flattened 3D array when you know the size, index and ordering

If I have a grid that I know is RxCxD in size, and I have number that corresponds to an element in that grid, and the grid is mapped in Row major format, how can I find out the ordered triplet that ...