## Errata > Some things

Thank you for taking the time and interest to submit your observations.

Regarding "The coordinate systems on page 119 and following: As I learned in school the arrows of a coordinate system define where the higher (positive) numbers are."

I suspect different schools and text books may use different styles for diagrams. In this case, the arrows indicate increasing magnitude regardless of sign (as I learned in school). The axis vectors are conceptually no different from other vectors using arrows to indicate direction. A negative vector will have an arrow pointing in the opposite direction of a positive vector. Each cardinal axis extends infinitely in both positive and negative directions.

Regarding "Page 124 'Orders Matter'. In my opinion they don't." Translation applied to a matrix is a "Commutative" operation similar to addition. ( a + b == b + a) Both rotation and scaling applied to a matrix are "Noncommutative" operations like division. (a / b != b / a) There is a nice summary with a matrix example at https://en.wikipedia.org/wiki/Commutative_property.

Regarding "The coordinate systems on page 119 and following: As I learned in school the arrows of a coordinate system define where the higher (positive) numbers are."

I suspect different schools and text books may use different styles for diagrams. In this case, the arrows indicate increasing magnitude regardless of sign (as I learned in school). The axis vectors are conceptually no different from other vectors using arrows to indicate direction. A negative vector will have an arrow pointing in the opposite direction of a positive vector. Each cardinal axis extends infinitely in both positive and negative directions.

Regarding "Page 124 'Orders Matter'. In my opinion they don't." Translation applied to a matrix is a "Commutative" operation similar to addition. ( a + b == b + a) Both rotation and scaling applied to a matrix are "Noncommutative" operations like division. (a / b != b / a) There is a nice summary with a matrix example at https://en.wikipedia.org/wiki/Commutative_property.

May 28, 2013 |
Erik Buck

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2) The coordinate systems on page 119 and following: As I learned in school the arrows of a coordinate system define where the higher (positive) numbers are. So making a 3D coordinate system with six arrows makes no sense to me.

3) Page 124 "Orders Matter". In my opinion they don't. They only do if you configure the transformations in a wrong way. If you only change the order of the transformations without changing the values and the axes than you would get a different result, of course. But if you also change the values and the axes than you would get the exact same results. Look at these screenshots of your app:

S1) http://s1.directupload.net/images/130527/j5buo6ha.png

S2) http://s7.directupload.net/images/130527/iefgksqe.png

They produce the same output with switched order.

Have a nice day !