receive yaw pitch and roll from a 4x4 Matrix
Author
hi,
sorry if this is a newbee question.
i´m using ode.net and it uses a 4x4Matrix for the orientation, how do i extract yaw, pitch and roll since they are only 3 3dimensinal vetors??
does pitch(yaw or roll) equal Matrix position 1.1, 1.2, 1.3(horizontal) or is the vertical 1.1, 2.1, 3.1 ?
if so what are is the fourth dimension for ... ?
is there a standard or is it used differently in other projects ?
thnx greetz the Dude
Quote:Original post by mauzi_the_Dude
hi,
sorry if this is a newbee question.
i´m using ode.net and it uses a 4x4Matrix for the orientation, how do i extract yaw, pitch and roll since they are only 3 3dimensinal vetors??
You want to extract the Euler orientation out of a 4x4 matrix?
Quote:
does pitch(yaw or roll) equal Matrix position 1.1, 1.2, 1.3(horizontal) or is the vertical 1.1, 2.1, 3.1 ?
No, it's not nearly that simple.
Sorry, I can't remember the math off the top of my head, but it's more complicated that just looking at a single component of the matrix.
Yaw, pitch, and roll are angles, not vectors. So, since you're looking for vectors I think you're not looking for "yaw, pitch, and roll", but simply the basis vectors for the oriented object's local coordinate frame.
You basically got that right! That is, the 3 basis vectors are EITHER the 3 rows or the 3 columns of the upper 3x3 part of the transformation matrix. Whether it is rows or columns depends on how ODE is applying multiplications, e.g., whether it treats the transformation as "row-wise" or "column-wise". I haven't looked at it carefully enough to know how its working, and the docs don't seem to say explicitly.
As to why there's a 4th row and column, this is because coordinates are being represented in so-called "homogeneous" coordinates. It makes for quite convenient pure-matrix transformations that include translation, rotation, and scale all in one step. The OpenGL red book is a one place to learn about homogeneous transformations:
Homogenous Coordinates and Transformation Matrices
You basically got that right! That is, the 3 basis vectors are EITHER the 3 rows or the 3 columns of the upper 3x3 part of the transformation matrix. Whether it is rows or columns depends on how ODE is applying multiplications, e.g., whether it treats the transformation as "row-wise" or "column-wise". I haven't looked at it carefully enough to know how its working, and the docs don't seem to say explicitly.
As to why there's a 4th row and column, this is because coordinates are being represented in so-called "homogeneous" coordinates. It makes for quite convenient pure-matrix transformations that include translation, rotation, and scale all in one step. The OpenGL red book is a one place to learn about homogeneous transformations:
Homogenous Coordinates and Transformation Matrices
Author
found something: ( and sorry, i didn´t say i was looking for the direction Vector3 :( my bad )
Q5. How do matrices relate to coordinate systems?
--------------------------------------------------
With either 3x3 or 4x4 rotation, translation or shearing matrices, there
is a simple relationship between each matrix and the resulting coordinate
system.
The first three columns of the matrix define the direction vector of the
X, Y and Z axii respectively.
If a 4x4 matrix is defined as:
| A B C D |
M = | E F G H |
| I J K L |
| M N O P |
Then the direction vector for each axis is as follows:
X-axis = [ A E I ]
Y-axis = <br> Z-axis = [ C G K ]<br><br><br>source: http://www.j3d.org/matrix_faq/matrfaq_latest.html#Q5<br><br><br>thnx didn´t see your post, i´ll look up the source, but thats what i was looking for ….
Q5. How do matrices relate to coordinate systems?
--------------------------------------------------
With either 3x3 or 4x4 rotation, translation or shearing matrices, there
is a simple relationship between each matrix and the resulting coordinate
system.
The first three columns of the matrix define the direction vector of the
X, Y and Z axii respectively.
If a 4x4 matrix is defined as:
| A B C D |
M = | E F G H |
| I J K L |
| M N O P |
Then the direction vector for each axis is as follows:
X-axis = [ A E I ]
Y-axis = <br> Z-axis = [ C G K ]<br><br><br>source: http://www.j3d.org/matrix_faq/matrfaq_latest.html#Q5<br><br><br>thnx didn´t see your post, i´ll look up the source, but thats what i was looking for ….
I know nothing about 4x4 equations. But here is the math for 3D rotations
that solved my problem with airplane control in DirectX7 that allowed total roll, pitch, and yaw.
I'm doing this from memory so if i'm in error please forgive me.
--------------------------------------------------------
in this equation:
The Code:
If i'm in error, then the error will mostlikely be in the
Cos(Roll)
and
Sin(Roll)
portions of the code.
that solved my problem with airplane control in DirectX7 that allowed total roll, pitch, and yaw.
I'm doing this from memory so if i'm in error please forgive me.
--------------------------------------------------------
in this equation:
UP: Z+ is up. (pitch)To rotate in a stationary location: Distance = 1To move the point along the new angles: Distance = Distance To Move Along new Roational AnglesEleminate the: X + ( Y + ( Z + ( Result is rotation around the world's 0,0,0 axis.Pi = 3.14....ect180 / pi = Radients value of angleThe Code:
Pitch = PitchAngle * (180 / pi)Yaw = YawAngle * (180/pi)Roll = rollAngle * (180/pi)NewX = X + (Sin(Pitch) * Cos(Yaw) * Cos(Roll) * Distance)NewY = Y + (Sin(Pitch) * Sin(Yaw) * Cos(Roll) * Distance)NewZ = Z + (Cos(Pitch) * Sin(Roll) * Distance)Point.x = NewXPoint.Y = NewYPoint.Z = NewZIf i'm in error, then the error will mostlikely be in the
Cos(Roll)
and
Sin(Roll)
portions of the code.
Euler angle extraction:
http://q12.org/pipermail/ode/2004-September/013862.html
http://www.acm.org/pubs/tog/GraphicsGems/gemsiv/euler_angle/ (many permutations)
http://www.acm.org/pubs/tog/GraphicsGems/gemsiv/euler_angle/EulerAngles.c
http://q12.org/pipermail/ode/2004-September/013862.html
http://www.acm.org/pubs/tog/GraphicsGems/gemsiv/euler_angle/ (many permutations)
http://www.acm.org/pubs/tog/GraphicsGems/gemsiv/euler_angle/EulerAngles.c
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