> any hope for general convolutions (or at least more general ones than with circles)
Interesting question.
Knuth's METAFONT can describe glyphs not simply as filled outlines, but ALSO as strokes of pens shaped by circles, ellipses, and EVEN convex polygons (e.g., a an acute triangular wedge perhaps).
And the description of a METAFONT glyph is all parameterized (it's really a program! -- hence the META) so there's not even an actual outline for a glyph but a tunable family of glyph variations.
METAFONT's model is humanistic as human ideographs and letter forms were (once) scratchings, engravings, and pen strokes. However the shape of movable type, as captured with Bezier splines by TrueType and Postscript outline glyphs, lack a first-class stroking capability.
So could you support the humanistic METAFONT-style approach efficiently in today's world of GPU rendering? Yes, if you could, as suggested above, efficiently convolve a pen's shape with a stroke trajectory.
Circles for pens are no problem; and ellipses are just squished transforms of circular stroking. But (convex) polygonal pens for stroking?
Polar stroking provides a starting framework for such a convolution approach for convex polygonal pens (say, a triangular wedge or other convex polygonal shape). Step in small changes in gradient direction change. Rather than assuming a conventional circular or nib pen shape, snap each tessellated rib to the closest polygonal pen vertex. The result is the polygonal convolution you seek.
So a question almost nobody is asking: What if we could revive METAFONT for the 21st century?
Imagine a Jurassic Park scenario applied -- not to dinosaurs -- but rather to Knuth's Computer Modern.
Interesting question.
Knuth's METAFONT can describe glyphs not simply as filled outlines, but ALSO as strokes of pens shaped by circles, ellipses, and EVEN convex polygons (e.g., a an acute triangular wedge perhaps).
And the description of a METAFONT glyph is all parameterized (it's really a program! -- hence the META) so there's not even an actual outline for a glyph but a tunable family of glyph variations.
METAFONT's model is humanistic as human ideographs and letter forms were (once) scratchings, engravings, and pen strokes. However the shape of movable type, as captured with Bezier splines by TrueType and Postscript outline glyphs, lack a first-class stroking capability.
So could you support the humanistic METAFONT-style approach efficiently in today's world of GPU rendering? Yes, if you could, as suggested above, efficiently convolve a pen's shape with a stroke trajectory.
Circles for pens are no problem; and ellipses are just squished transforms of circular stroking. But (convex) polygonal pens for stroking?
Polar stroking provides a starting framework for such a convolution approach for convex polygonal pens (say, a triangular wedge or other convex polygonal shape). Step in small changes in gradient direction change. Rather than assuming a conventional circular or nib pen shape, snap each tessellated rib to the closest polygonal pen vertex. The result is the polygonal convolution you seek.
So a question almost nobody is asking: What if we could revive METAFONT for the 21st century?
Imagine a Jurassic Park scenario applied -- not to dinosaurs -- but rather to Knuth's Computer Modern.
https://en.m.wikipedia.org/wiki/Computer_Modern
"Your scientists were so preoccupied with whether or not they could, they didn't stop to think if they should."