Glyphs to Paths - Quadratics & Cubics in CoreText

Pressing on with the conversion of the file that deals with glyphs I need to obtain the path that represents a glyph. CoreText provides the function CTFontCreatePathForGlyph that returns a CGPath of an individual glyph. The final thing to do then is to convert the path to the output format.

Core Graphics provides a function CGPathApply that will apply a user defined function to each element a part is composed of. So your user function is applied to al the moveto, lineto and curveto operations that make up the path.

To make getting to the path elements a little easier in C++ I have written a visitor class. The class is quite trivial, little more than a switch statement, that calls through to virtual moveto, lineto and curveto methods that can be overridden. Another way of doing this would be to write an iterator.

A slight complication is that the CGPath can contain both cubic and quadratic curves. In the target file format all curves are cubic. This means that any QuadCurveToPoint calls have to be converted to the cubic CurveToPoint. I am not yet in the position to test any of this - but I think it is reasonable to assume that there is a high probability that some font outlines may be expressed in quadratic curves - simply because quadratic curves are the native curve type of TrueType fonts. I would expect the Postscript (Type-1 fonts and friends) to appear as quadratics as that is the native curve type of these fonts.

Converting the QuadCurveToPoint so that it calls through to CurveToPoint is not too bad. The key thing is to have the previous end-point - and the rest is maths. I did not work out the maths that does this conversion myself - but it is something that I have had to use before. The function (or method) drops out quite simply. A link to some maths that seems strangely consistent with my old notes can be fond here.

void CGPathVisitor::QuadCurveToPoint(const CGPoint &q1, const CGPoint &q2)
{
CGPoint    c0 = m_lastPt; // last point

CGPoint c1 = { c0.x + 2.0 * (q1.x - c0.x) / 3.0,
c0.y + 2.0 * (q1.y - c0.y) / 3.0 };
CGPoint c2 = { q2.x + 2.0 * (q1.x - q2.x) / 3.0,
q2.y + 2.0 * (q1.y - q2.y) / 3.0 };
CGPoint c3 = q2;

this->CurveToPoint(c1, c2, c3);
}

I have not tested this code yet - if there are problems with it I will come back and correct this post.