On 1/16/07, Matthias Schabel <boost@schabel-family.org > wrote:
...
My humble knowledge may have confused me but I thought that the same
temperature by Centigrade and by Kelvin will always differ by about 273 (i.e. the conversion is linear). Which is not right in case of Farenheit.
What I mean by linear vs. affine is that, while the scale factor for converting temperature differences in Kelvin to/from centigrade is one, there is a nonzero translation of the origin (MathWorld has a good description of linear and affine transformations):
http://mathworld.wolfram.com/LinearTransformation.html http://mathworld.wolfram.com/AffineTransformation.html
The point that Ben was making in his post is that, while absolute temperature conversion between Kelvin and centigrade requires an offset, conversion of temperature differences does not. As far as I can tell, to integrate this directly into the library would require strong coupling between a special value_type flagging whether a quantity was an absolute temperature or a difference, which I think is undesirable. By defining special value_types
class absolute_temperature; class temperature_difference;
and defining the operators between these so that you can add or subtract temperature_differences to/from absolute_temperatures to get another absolute_temperature, add or subtract two temperature_differences to get another temperature difference, and subtract two absolute_temperatures to get a temperature_difference you should be able to get the correct behavior. Maybe I'll try to put together a quick example of this...
I do think it would be great to distinguish between affine and vector spaces in a library like this, but in practical terms it seems like there are three levels of commitment that users might have to dimensional analysis: 1. Type of dimension (length versus temperature). 2. Units of measure (meters versus feet). 3. Absolute versus relative quantities (°C = K+273.15 versus °C = K). It seems to me that these are separate problems, each building upon the one before it, and that an ideal library would let the user work at any of these levels. I think 1 and 2 can be handled with appropriate dimensional types and casts among them; 3 can be handled by separate types for absolute and relative quantities. I think these could be implemented independently in that order. I'm thinking usage like this: // First: type of dimension quantity<double, distance> x1 = 42.0 * distance; // Second: units of measure quantity<double, meters> x2 = 20.0 * meters; // Casting to explicitly add units of measure to unitless quantities. x2 = quantity_cast<quantity<double, meters> >(x1); // The user claims x1 is in meters. // Allow casting a reference or pointer, too (important for interfacing with numerical solvers). quantity<double, meters>& xref = quantity_cast<quantity<double, meters>&>(x1); quantity<double, meters>* xptr = quantity_cast<quantity<double, meters>*>(x1); // Third, since most people won't want to get into this, let quantity be what // most would expect (i.e., a linear space) but add absolute_ and relative_ to be clear. absolute_quantity<double, temperature> t1 = 1000.0 * temperature; // Unspecified temperature type. absolute_quantity<double, temperature> t2 = 1010.0 * temperature; relative_quantity<double, temperature> tdiff = t2 - t1; // tdiff is now 10 temperature units. quantity<double, kelvin> t3 = 1020.0 * kelvin; // General kelvin quantity. relative_quantity<double, kelvin> t3rel = quantity_cast<relative_quantity<double, kelvin> >(t3); // Explicitly say it's relative. // So now t3rel is 1020.0 K absolute_quantity<double, celsius> t3C = quantity_cast<absolute_quantity<double, celsius> >(t3); // Explicitly say it's absolute. // Now t3C is 746.85°C. t3C /= 2.0; // Specialize absolute temperatures to have scalar multiplication. // Now t3C is 236.85°C = (1 020.0K/2) absolute_quantity<double, seconds> t = 10.0 * seconds; // t2 *= 2.0; // This shouldn't compile because absolute time doesn't have scalar multiplication. —Ben PS Temperature is particularly odd in that absolute temperature it is (almost) a linear space even though temperature differences are in a different linear space. That is, 0°C × 2 = 273.15K × 2 = 546.3K = 273.15°C. (I say "almost" because there's no negative absolute temperature, so it can't really be a linear space.) PPS Where can I find the code under discussion?