1
vote
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 $A,B,C$ ...
0
votes
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 ...
2
votes
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
vote
0answers
55 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: ...
1
vote
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 ...
0
votes
0answers
28 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
votes
1answer
47 views

How do I multiple these matrices together?

As a personal brain exercise, I've recently been trying to work out the math involved with rotating vertices around an arbitrary axis in 3D space. To do so, I've been relying very heavily on the ...
0
votes
2answers
38 views

How do I calculate the inverse of these matrices?

In learning how to rotate vertices about an arbitrary axis in 3D space, I came across the following matrices, which I need to calculate the inverse of to properly "undo" any rotation caused by them: ...
0
votes
1answer
51 views

rotation matrix to axis angle

from wikipedia the above rotation matrix has a rotation of -74 degrees. What does it mean "around the axis (−1⁄3,2⁄3,2⁄3)"? How can I determine how many degrees is rotated on X axis, Y axis and Z ...
1
vote
1answer
60 views

texture mapping from a camera image to a 3D surface acquired by a kinect

I have the following problem: A kinect camera capture a 3D surface and save it as a .obj files containing all the positions of the vertices (in the kinect coordinate system). If I take a picture ...
0
votes
0answers
70 views

Converting Euler Angle z-y'-x'' sequence to heading

I'm trying to convert a set of Euler Angles to a heading $(0-360)$ degrees. The Euler Angles use the $\ x-y'-x''$ sequence headings, using $\ \psi, \theta, \phi$ as the rotation angles, respectively. ...
2
votes
1answer
84 views

Texture mapping from a camera image (knowing the camera pose)

I'm not sure if I should ask this question here or on stackoverflow, so forgive me if I'm wrong. I want to apply a texture (taken from a camera) on a 3D surface, let me explain my problem: I have ...
0
votes
0answers
91 views

$3$D transformation matrix to $2$D matrix

I have a $3$D affine transformation $4\times 4$ matrix. I need to convert it (project) to a $2$D affine transformation $3\times 3$ matrix, which looks like this: $3$D rotations are irrelevant and ...
0
votes
1answer
56 views

Which of these rotation matrices represents a positive rotation in three-space about the y-axis?

This is what Wikipedia says: \begin{bmatrix} \cos \theta & 0 & \sin \theta \\ 0 & 1 & 0 \\ -\sin \theta & 0 & \cos \theta \\ \end{bmatrix} This is what I think it should ...
0
votes
1answer
165 views

Direction Cosines and Rotation Angles

I'm rotating an object in 3D space with respect to a relative base, or reference frame. I'm using a normal vector to represent the rotation angles. Suppose you have an object parallel to the ...
0
votes
0answers
20 views

Resolving bearings for tilted structure (vector rotations)

I am trying to find a neat solution to resolving bearings for a tilted structure. For example, if I know that a hub is $268.74^{\circ}$ and offset ($X = -3.542 $m, $Y = -1.857$ m, $Z = 2.013$m) with ...
0
votes
0answers
162 views

Converting a 3x3 matrix to euler angles in various rotation orders

So let's say I have a 3x3 orientation matrix set up like: a b c d e f g h i which I have generated from euler angles in a left-handed, Y-vertical system. ...
0
votes
1answer
325 views

Explain 3d transformation matrix…

In programming language like css, there is a 3d matrix. https://developer.mozilla.org/en-US/docs/Web/CSS/transform-function#matrix3d() Though, i don't know matrix or matrix3d. I have tried to learn ...
0
votes
0answers
96 views

Inverse 3D transforms from matrix given. End formula needed.

This question came from CSS3 3D graphics question. After applying some transformations (translate, rotate, scale, etc.) I get a 3D transform matrix. The matrix is explained here and here. I hope it ...
0
votes
2answers
118 views

Rotation matrix - rotate a ball around a rotating box

I've a 3D box: center point = (a,b,c), width = w, height = h, ...
0
votes
1answer
495 views

Rotate a plane along a line in 3d space

I have a plane A in 3D which can be defined either by the scalar plane equation or by its normal n. I want to find a new plane B which is orthogonal to plane A but shares an edge with plane A. I.e. I ...
3
votes
0answers
73 views

How to solve a distance problem inside of a picture?

sorry for my bad english. I have the following problem: In the picture you can see 4 different positions. Every position is known to me (longitude, latitude with screen-x and screen-y). Now i want ...
2
votes
1answer
69 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 ...
0
votes
3answers
86 views

are 12 different rotation matrix the same?

If I want to rotate a vector $V$ from coordinate system $A$ to $B$, I could use the rotation matrix by $V_B=R\cdot V_A$, where $R$ is the rotation matrix. There are many rotation sequences for $R$, ...
0
votes
1answer
249 views

How would one use matrices to find a normal unit vector?

A recent class assignment involved finding a unit vector perpendicular to a plane, given two unit vectors to start with. The solution given involved using the cross product; I was wondering if such a ...
3
votes
1answer
696 views

Transformation matrix to go from one vector to another

I've two vectors $a = (a_1, a_2, a_3)$ and $b = (b_1, b_2, b_3)$. How to find transformation matrix for transform from a to b?
1
vote
1answer
463 views

Find rotation matrix to match one 3D vector pair onto another

I have two pairs of 3D vectors named $(A_1, B_1)$ and $(A_2, B_2)$. All four vectors have unit length. I'd like to match one pair onto the other. As I am permitted to assume the angle between $A_1$ ...
11
votes
7answers
17k 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
960 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 ...
2
votes
3answers
936 views

3D to 2D rotation matrix

I have been trawling through this forum but am struggling to understand the maths a bit. Currently I have a 2D plane within a 3D space and I have the coordinates for them. I want to work on this 2D ...
1
vote
1answer
344 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?
1
vote
1answer
581 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
votes
1answer
154 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 ...
5
votes
1answer
748 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 ...
0
votes
2answers
59 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 ...
2
votes
1answer
1k 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 = ...
2
votes
2answers
4k 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 ...
1
vote
1answer
269 views

Identifying 3D shape from matrices analytically

I have a set of matrices (a 3D matrix, that represents a quantized body), for instance: (the size 5x5 here is just an example, the real size is a lot higher) $ M_1 = \left[ {\begin{array}{cc} 0 ...
0
votes
1answer
515 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 ...
0
votes
1answer
871 views

Help with matrix mathematica

Hi I am wondering how best to explain this, I am working with WebGL (effectively OpenGL) and I have the ray cast from clicking in 3d space. I have the far and near values of the ray cast, the camera ...