2005-04-17 23:56:48 UTC
Cross product is a mathematical convention where X, Y and Z are concerned
Given one conventional definition for the crossproduct x, we have
X = Y x Z
Y = Z x X
Z = X x Y
Drawing axes is also another convention, a pictorial one. If you use the crossproduct convention above (purely mathematical) with a pictorial convention similar to DirectX (the coordinate system is stated with y upwards, x to the right and z forward) then the mathematical convention must be represented by the pictorial convention, eg AxB = C and like X x Y= Z then C must be in the same picture representation as Z.
Note you can change the pictorial convention without changing the mathematical convetion. If OpenGl coordinate system is used then it is a mirror picture of the DirectX system, but C and Z still coincides.
Note you could change the mathematical convention
X = Z x Y
Y = X x Z
Z = Y x X
Here mathematically the result is different
Everything is ok when you stick to one convention throughout your representation :) I have not read through all of the context from
http://www.euclideanspace.com/maths/algebra/vectors/
but the diagram is just on element out of the entire context, so I cant agree or disagree with you
