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I remember being told that Type 1 fonts support cubic Bezier curves (start position + scaled direction, end position + scaled direction), while TrueType fonts only support quadratic curves (start point, end point, control point).

This has got me wondering:

  • Which of the three font formats/standard has "glyph expressivity" which subsumes one or both of the others?
  • For those pairs which don't subsume each other's expressivity, what are the features which each of them has and the other doesn't

Note: I'm not interesting in this like max number of characters and various Unicode-related tricks - just th encoding of glyphs.

  • Opentype is just a container that includes features of both. So a opentype font can be a truetype font or a off font so either cubic or quadratic. Offcourse since quadratic is a subset of cubic cubic could be enough – joojaa Dec 10 '17 at 14:35
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PostScript (PS) Outlines are described with Cubic Bézier curves. TrueType (TT) Outlines are described with Quadratic Bézier Curves.

Now, a Bézier curve of degree n can be converted into a Bézier curve of degree n+1 with the same shape (see Bézier Curve Degree Elevation). This means you can describe a TT Outline (Degree 2) exactly with a PS Outline (Degree 3), while you cannot do the same in the opposite direction (though you can do it as accurately as required).

Talking about formats:

  • PostScript Type 1 fonts use PS Outlines,
  • TrueType (TTF) fonts use TT Outlines, and
  • OpenType (OTF) fonts can use both (TT or PS flavor).

Note that sometimes, OpenType TT flavor fonts can have the TTF file extension.

So the answer for the first question: Type 1 and OTF with PS Outlines can describe the other formats exactly but only the glyph shape.

Now, some information of the formats.

Type 1:

  • Is described with PS Outlines.
  • Supports hinting.
  • Has encrypted parts.
  • Supports subroutines.
  • Depending on the platform, requires 2 or 3 files per font.

TrueType:

  • Is described with TT Outlines.
  • Supports hinting (by describing glyph outline distortion, which can lead to more powerful hinting, but requires more work and the result is highly dependent on the quality of the hinting program by the designer).
  • Has very basic Digital Rights Management.
  • Can have bitmap embedding.

OpenType:

  • Can be described with PS or TT Outlines.
  • Supports hinting.
  • Can have bitmap embedding.
  • Can have much more glyphs per font.
  • Has advanced typographic capabilities.
  • Is Cross-platform.

Answering the second question, I guess the only scenario in which I could choose TrueType over OpenType (since Type 1 is basically superseded by OT) is when I need the more advanced hinting capabilities of TT, e.g., for very low resolution devices. As I mentioned, it will depend on the quality of the hinting of the font.

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