tags:

views:

36

answers:

1
Q: 

Should I always normalise a point after a homogenous transformation?

I'm just starting out with 3D math/programming and I have a question about point normalization:

When doing transformations such as rotations, scaling, camera and perspective projections should I always normalize points so that w is 1 between transformations, or is it better to leave it until I'm ready to display them? Is there any reason not to, other than performance?

Thanks,

Jason

+1  A: 

Normally, you don't apply a series of linear transformations to vectors. You apply one: the composition of all the linear transformations you'd like to apply (including model and camera transformations) and you do this right before displaying the point.

It doesn't matter anyway, because none of the standard transformations affect w anyway. I mean, there isn't even any rounding error, w will always be 1.

Dietrich Epp  2010-02-08 00:25:43
So, is it fair to say that P is equivalent to N(P)? At least for transformation and projection? (pardon the pun)
Jason Hernandez  2010-02-08 01:10:37
No. Only the w component stays the same. A more accurate formula would be E_w T = T E_w = E_w for all transformations T, where E_w is the orthogonal projection onto span{w}.
Dietrich Epp  2010-02-08 07:45:31
Six Months later... that all makes sense. thx.
Jason Hernandez  2010-07-14 17:59:41

related questions

Matrix artihmetic in PHP?
Better (non-linear) binning
Is there around a straightforward way to invert a triangular (upper or lower) matrix?
Binning in matlab
Looping in a spiral
.Net Matrix
How can I calculate the inverse of a matrix?
Database Bejewelled Puzzle- How does this solution work?
How can I implement a RESTful webservice using C++?
Does anyone have any experience using math.net
Best way to represent a 2-D array in C++ with size determined at run time
MySource Matrix - Opinions
Python Inverse of a Matrix
What is the easiest way to align the Z axis with a vector?
determining points from set of pairwise distances
Invert 4x4 matrix - Numerical most stable solution needed.
Is there a library for Linear algebra matrix handling in Java?
How can I sort a 2-D array in MATLAB with respect to one column?
3d to 2d Projection Matrix
GPU programming on Xbox 360
How do I get the current size of a matrix stack in OpenGL?
int matrix with pointers in C - memory allocation confusion
How do you rotate a two dimensional array?
A Transpose/Unzip Function in Python
LaTeX: How to add a matrix in a LaTeX document?