"Matt Calabrese" wrote
On 10/13/05, Deane Yang wrote:
Mathematically, I think Andy is entirely correct in what he says above. Once you take the ratio of two measurements of the same dimension (or quantity), you end up with a pure number that really can't be distinguished from other ratios or pure numbers.
I tend to disagree here. A ratio of two lengths, for example, is in fact a value in radians.
As an example take two people. Person1 has a height of 1 m . Person2 has a height of 2 m. Person 1 is 1/2 as high as person 2. That 1/2 is certainly not measured in radians. it is just a number. [cut]
Take this situation, for example, if one were to choose to make the result of length / length simply a raw value. What happens if you have:
arc_length / radius + quantity< degrees >( 90 );
If you choose to have the result of the first operation be a raw value as opposed to a radian value, then what do we do here? Andy states that the operation shouldn't be allowed, however, I believe it should, since arc_length / radius is in fact an angle.
(Not sure what I am meant to have stated ) Actually this calc is entirely possible in pqs (See examples/angles.cpp). pqs uses angles as value_types. A sample calculation might look like this: // the angle value_type of arc_length signifies an arc length length_<of_angle::rad>::m arc_length(of_angle::pi/2); //[2] // the implicit double value_type of radius signifies a straight length length::m radius(1); std::cout << arc_length / radius + of_angle::deg(90) << '\n'; Outputs 3.141593 rad (The type of len1 / len2 is radians. radians and degrees are addable .) However // meant to be an arc length length::m arc_len1( pi/2); // the implied double value_type signifies a straight length length::m len2(1); std::cout << arc_len1 / len2 + of_angle::deg(90) << '\n'; // no operator + for (double, degrees). It does work (You can also use degrees etc as the value_type) but the implicit conversion from radians to/from numeric is also available if user wishes to work in a simpler way. cheers Andy Little [note1] To get the implicit conversion behaviour in pqs-2-00-02 you need to define PQS_IMPLICIT_RADIANS_STRAIGHTENING. It was an experimental behaviour but as it seems to work ok I guess it should be the default. However implicit conversion of degrees(minutes,seconds etc) to a numeric type was found to be unsatisfactory. [note 2] I really should change l 'of_angle, to just 'angle;' It would make much more sense ;-)