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 https://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
Thanks very much for the correction I have updated the page.
As Richard pointed out the problem was that I drew the diagram with a
left hand coordinate system although I am standardising the site with
a right hand coordinate system (for compatibly with OpenGL and X3D). I
have redrawn the diagram with a right hand coordinate system and because
it is difficult to represent the 3 dimensions I have added an example.
Although both right and left hand conventions are commonly used for the
coordinate systems, does anyone know if it is common to use different
conventions for cross products?
Where I can, I have put links to Amazon for books that are relevant to
the subject, click on the appropriate country flag to get more details
of the book or to buy it from them.
Introduction to 3D Game Programming with DirectX 9.0 - This is quite a small book
but it has good concise information with subjects like, maths introduction and
Mathematics for 3D game Programming - Includes introduction to Vectors, Matrices,
Transforms and Trigonometry. (But no euler angles or quaternions). Also includes
ray tracing and some linear & rotational physics also collision detection
(but not collision response).