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From: Reece Dunn (msclrhd_at_[hidden])
Date: 2004-12-18 14:22:36

Reece Dunn wrote:
> Andy Little wrote:
>> Despite my previous remarks regarding automatic conversions, after
>> reviewing
>> what I have done on this previously I now conjecture that the two
>> types of
>> space (device space and logical space) have very different properties and
>> their types cannot be directly compared against each other eg using
>> operator
>> < without some subtleties ( I now remember this is the reason that I
>> havent
>> completed a 'pixel' type). There needs to be a device available, to
>> provide
>> the 'context' of pixels_per_inch() or whatever, however, by changing the
>> device mode( screen resolution) or the device itself( display <-->
>> printer))
>> ,the comparison of two constants, one of each type, may give different
>> results at different times. I am not sure that is a wise move! (I have
>> always ended up using physical units for very much the above reasons and
>> contrive to keep device units as a low level implementation detail..
>> It is a
>> major reason that I ended up looking for and eventually writing a
>> physical
>> quantities library, to solve the problem once and for all! )
> Hmm. This is a complex issue! It makes sense to have some sort of
> metric_type that supports pixels, percentages, picas/points, millimeters
> and inches. As you hint at, these need a device to resolve or convert.
> In general, you will only want to manipulate a value using one specific
> metric type (e.g. specifying a font in points). You only really need to
> perform conversions when evaluating a value (e.g. when drawing a line
> from two coordinates). However, there may be a need for conversions in
> other areas, e.g. when getting the size that a string will take when
> rendered to a device using a specific font, you may want this to be in
> inches.

Taking a look at the CSS3 module on values and units
(, we have the
following unit types:

px (pixels) -- pixel units relative to the resolution of the viewing
device. CSS3 gives a recommendation for rescaling to various devices
(e.g. printer).
in (inches)
mm (millimeters)
cm (centimeters)
pt (points)
pc (picas)
% (percentage)
sf (scalefactor) -- a multiplier for the size value
em -- 'font-size' of the relevant font
ex -- x-height of the relevant font

Here, the CSS3 units em and ex are not really relevant because we have
no font property to use to calculate the relative em/ex values.

Looking at the values, it is possible to split them into 3 groups:
* pixels -- device-specific unit size
* inches -- logical unit size
* scalefactor -- relative unit size

All values are reducible to one of the three groups:

    1px = 1px
    1in = 25.4mm = 2.54cm = 72pt = 6pc
    using the relationships:
       1in = 2.54cm
       1cm = 10mm
       1pt = 1/72in
       1pc = 12pt
    1sf = 100%

Now the problem is conversion between pixels, inches and scalefactor.

scalefactor <--> pixels:
    required = max px
    sf --> px: px = max * sf
    px --> sf: sf = px / max
scalefactor <--> inches
    required = max in
    sf --> in: in = max * sf
    in --> sf: sf = in / max
pixels <--> inches
    required = pixels-per-inch (ppi)
    px --> in: in = px / ppi
    in --> px: px = in * ppi

The above max px and max in can be reduced to max in since it is
possible to convert max in --> max px, Thus we have:

    metric convert_to
       metric val, metric::type to, float max, float ppi

Thoughts? Comments?


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