在 PyQt 中绘制具有多个偏离曲线点的贝塞尔曲线

Question

I would like to draw a TrueType Font glyph with PyQt5 QPainterPath. Example glyph fragment: (data from Fonttools ttx )

<pt x="115" y="255" on="1"/>
<pt x="71" y="255" on="0"/>
<pt x="64" y="244" on="0"/>
<pt x="53" y="213" on="0"/>
<pt x="44" y="180" on="0"/>
<pt x="39" y="166" on="1"/> 

on=0 means a control point and on=1 means a start/end point I'm assuming this would not use (QPainterPath) quadTo or cubicTo as it is a higher order curve.

Answer 1

True type fonts actually use only quadratic Bézier curves. This makes sense, they are pretty simple curves that don't require a lot of computation, which is good for performance when you have to potentially draw hundreds or thousands of curves even for a simple paragraph.

After realizing this, I found out strange that you have a curve with 4 control points, but then I did a bit of research and found out this interesting answer .

In reality, the TrueType format allows grouping quadratic curves that always share each start or end point at the middle of each control point.

So, starting with your list:

Start  <pt x="115" y="255" on="1"/>
C1     <pt x="71" y="255" on="0"/>
C2     <pt x="64" y="244" on="0"/>
C3     <pt x="53" y="213" on="0"/>
C4     <pt x="44" y="180" on="0"/>
End    <pt x="39" y="166" on="1"/> 

We have 6 points, but there are 4 curves, and the intermediate points between the 4 control points are the remaining start/end points that exist on the curve:

start	control	end
Start	C1	(C2-C1)/2
(C2-C1)/2	C2	(C3-C2)/2
(C3-C2)/2	C3	(C4-C3)/2
(C4-C3)/2	C4	End

To compute all that, we can cycle through the points and store a reference to the previous, and whenever we have a control point or an on-curve point after them, we add a new quadratic curve to the path.

start	control	end
115 x 255	71 x 255	67.5 x 249.5
67.5 x 249.5	64 x 244	58.5 x 228.5
58.5 x 228.5	53 x 213	48.5 x 106.5
48.5 x 106.5	44 x 180	39 x 166

The following code will create a QPainterPath that corresponds to each <contour> group.

path = QtGui.QPainterPath()
currentCurve = []
started = False
for x, y, onCurve in contour:
    point = QtCore.QPointF(x, y)
    if onCurve:
        if not currentCurve:
            # start of curve
            currentCurve.append(point)
        else:
            # end of curve
            start, cp = currentCurve
            path.quadTo(cp, point)
            currentCurve = []
            started = False
    else:
        if len(currentCurve) == 1:
            # control point
            currentCurve.append(point)
        else:
            start, cp = currentCurve
            # find the midpoint
            end = QtCore.QLineF(cp, point).pointAt(.5)
            if not started:
                # first curve of many
                path.moveTo(start)
                started = True
            path.quadTo(cp, end)
            currentCurve = [end, point]