0
votes
0answers
7 views

Stable equilibrium position of 3d models.

I have 2 models, described by vertices arrays. The aim is to find stable equilibrium position of one of the models upon the other. The algorithm should consider the possibilities of transformation of ...
0
votes
1answer
22 views

Translation of basis for a vector space on the specified distance

In the Euclidean space $XYZ$ is a basis $X_1Y_1Z_1$ defined that is specified by the vectors $\overrightarrow {O_1X_1}$, $\overrightarrow {O_1Y_1}$ and $\overrightarrow {O_1Z_1}$. How to calculate ...
0
votes
1answer
40 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
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 ...
0
votes
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
93 views

Big axis of an ellipse

I drew a circle in this square and I transformed them (view in 3d). How to find the angle between the big axis and $y$ or $x$ axis? Blue plane rotated by 36° around $y$ axis; azimut is 30° and ...
1
vote
1answer
78 views

Rotation formalisms in three dimensions

I'm little bit confused. The Rotations are described by various means Direction Cosines Matrix (DCM); Euler Angles; Euler Axis/Angle; Quaternion. What is the difference between them. How I can ...
0
votes
0answers
95 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
0answers
19 views

How to find the values of transformstion and its center/axis? [duplicate]

I have system of two planes. Each plane is defined by three points, so I have their equations. One of these plane is stable, I can't perform any transformation. The second one is modifiable - rotation ...
0
votes
1answer
52 views

3D coordinate Transformation

I am currently trying to align two bodies which do not have similar sizes and shapes. But both of these two bodies share some keynodes(similar nodal position with 0.1% error difference). How can I ...
1
vote
0answers
70 views

Determining pose of an object in 3d space

Given a 3D model of an object centred at the origin, if I place a camera at position (x,y,z) and make it face the origin, from the image rendered the object appears ...
3
votes
1answer
2k views

How to find an all-in-one 2D to 3D Transformation Matrix for perspective projection, rotation, and translation?

I have read Finding a 3D transformation matrix based on the 2D coordinates but I think my situation is different because I think I need a 4x3 matrix, not a 3x3 matrix. I'm not sure but this might be ...
1
vote
1answer
35 views

Calculating transformation from origin to point

I have an icosahedron of radius $x$ with 12 vertices at known coordinates. If I have a point at $(0,0,x)$ where $x > 0$ and a vertex of this icosahedron at $(a,b,c)$ how can I find the rotation ...
1
vote
1answer
586 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 ...
1
vote
1answer
109 views

Creating a 3D surface from 2D graphs

So I have two sets of equations: $\mathcal{A}$ = \begin{equation} \{ f(y_{0},x), \, f(y_{1},x) , \;... \;, f(y_{n},x) \} \end{equation} $\mathcal{B}$ = \begin{equation} \{ g(y,x_{0}), ...
1
vote
1answer
42 views

Multi 3D Screen to POV

See, im a simple hardcore Programmer. In fact i wrote some 3D-Programs till now. I had nothing to do this weekend, so i made a 3D-based filemanager. My desktop is multihead so the point-of-view of ...
3
votes
1answer
753 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
2answers
44 views

Optimally projecting a point onto a line whose orientation is known

I have a line $l$ starting at origin ending at 0,0,1 along the $z$ axis. $l$ is rotated $P$ degrees around the $x$-axis and then $Q$ degrees around the $y$-axis. So I have a new endpoint for the line. ...
7
votes
2answers
5k views

How to transform a set of 3D vectors into a 2D plane, from a view point of another 3D vector?

I googled around a bit, but usually I found overly-technical explanations, or other, more specific Stackoverflow questions on how 3D computer graphics work. I'm sure I can find enough resources for ...
2
votes
0answers
126 views

Transform 3D vectors between planes using a matrix

I've got 6 points in 3D space: $A,B,C,D,E,F$, that represent 4 vectors. $AB$ is perpendicular to $AC$ and $DE$ is perpendicular to $DF$. I need to find a transformation matrix M, that transforms $AB$ ...
4
votes
2answers
626 views

3d transformation two triangles

I have two triangles in 3d. I need to calculate transformation matrix(3X3) between two triangles in 3D. 1)How can I calculate the transformation matrix(rigid) while fixing one of the points to the ...
1
vote
1answer
592 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. ...
2
votes
1answer
1k views

Extracting perspective transformation from a 2D projection

I have a 2D projection of a flat, rectangular object in 3D space, like this one: I know all sorts of information about this shape—its opposite sides have the same length, the sides meet at right ...
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 ...
0
votes
1answer
516 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 ...