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From: Andy Little (andy_at_[hidden])
Date: 2004-10-22 14:44:19

"Patrick Kowalzick" <Patrick.Kowalzick_at_[hidden]> wrote in message
> Hi Andy,
> I just read your post in boost.devel list, and took a brief look on your
> angle page:
> I searched for the question:
> "Should angles be modulo? (IOW should 361 degrees ---> 1 degree etc.)"
> and was not really surprised to find it. I wanted to know how you treat
> this problem :).
> Here just my opinion:
> -we encountered here a problem with weights in calculations, meaning an
> angle was weighted via its a-priori error, which is an angle as well.
> Setting this angle to 360 degree was fatal. The programm crashed setting
> the error back to 0, what is not recommend in a division 1/error (hihi).

I wonder if never allowing the angle to be 0 could solve this in this
case( ie using 360 instead) , or would that cause more confusion?

> It was fatal, but 361 degree would have been even worse, producing a
> result what is definitly not expected.
> -So we discussed if an angle bigger than 360 degree exists, and IMO -
> yes. Imagine you turn yourself 2 times, than you have a rotation of 720
> degree and not 360 degree.

Absolutely. I think that there are various entirely separate uses of
angles. One is in trigonometry using sines, cosines and so on. Another is in
dividing a circle into a discrete series of steps. The classic example here
is an analogue clock where the second hand particularly often moves in a
discrete series of steps. A third is in measuring angular velocity eg in
radians per second. A fourth is in measuring distance say using a quadrature
decoder. In the last examples the number of revolutions travelled is

In some cases an angle is being used as a number, usually when using
radians, in others it is certainly not, though in these cases it may be
required to convert to radians at the latest possible stage, say for
conversion from polar to cartesian coordinates.

I have attempted to address this by creating two classes of angles, one
irrational (ie radians, ( though not grads ;-0 ),, and one as discrete
fractions of revolution( ie degrees, minutes etc), which can legitimately
have an integer as a value_type.

Overall I arrived pretty early at the conclusion that automatically making a
calculation result modulo was a bad idea.

> I like more your idea with the modulo function, but keep in mind, that
> some applications use -180 to 180 degree and other 0 to 360 degree.

Thanks for bringing that up. I hadnt really considered that, so I will look
into this aspect. I havent implemented modulo functions yet. There are a
lot of things of this type to consider.

> And last, what is your opinion here: you might use clockwise-angles or
> counter-clockwise-angles. Is it necessary to distinguish these types?

Where the angle is being used to count revolutions obviously the sign of the
numeric value is the obvious choice. This does imply that the angle follows
a convention, which is an obvious cause of mistakes in coordinating between
different systems. Similar problems occur in graphics systems. I guess I
will have to look into ways and means of enforcing conventions. However that
is notoriously difficult to do at this building block level as it implies
human/physical verification in most cases. eg try_move( +1)... have I
actually rotated anti-clockwise ? etc.

Thanks for the feedback.


On a more general note, the other purpose of the OP was to try to gauge
enthusiasm for making this a proposal for a boost library. Any feedback on
that would be personally appreciated.

OTOH ... hmmm ... perhaps the impact would be too big... the bike shed is
certainly nice and warm ;-)

Andy Little

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