Are these enough nodes to draw up an oval with just 2 points? Nothing to do with hinting

AbiRasheed
AbiRasheed Posts: 248
in Type Design Technique & Theory
I disagree and think it needs a total of 4  here's an image of what I'm talking about  https://imgur.com/gallery/JbmJ9HE
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  • AbiRasheed
    AbiRasheed Posts: 248
    edited September 16
    I can't bring up a good argument to say one does need 4 control points for this to be a good oval  except from my experience in drawing vectors. On a different note are ovals or an ellipse or  are they both another form of a circle? They're eucledian I know that much.
  • John Hudson
    John Hudson Posts: 3,504
    In what context are you asking the question? If this relates to font making, then I would ask what your two-node oval looks like when converted to quadratic curves? That’s always one of my thoughts when creating font outlines, because even if I am not planning to ship TTFs, plans change and I’d rather not create cubic shapes that may even up unacceptably distorted when converted.
  • John Hudson
    John Hudson Posts: 3,504
    edited September 16
    On a different note are ovals or an ellipse or  are they both another form of a circle?
    Ovals and circles are both kinds of ellipse. A circle is an ellipse in which all points along the circumfrence are equal distance from the centre. An oval is an eccentric ellipse in which the distance from the circumfrennce to the centre varies, but is equal on a straight line from any point on the circumfrence through the centre to an opposite point.
  • AbiRasheed
    AbiRasheed Posts: 248
    edited September 16
    @John Hudson John Hudson said:
    In what context are you asking the question? If this relates to font making, then I would ask what your two-node oval looks like when converted to quadratic curves? That’s always one of my thoughts when creating font outlines, because even if I am not planning to ship TTFs, plans change and I’d rather not create cubic shapes that may even up unacceptably distorted when converted.
    Not in the context of font making but just general best practices for cubic curves
  • Thomas Phinney
    Thomas Phinney Posts: 3,083
    edited September 16
    For most font purposes, and at least some graphics purposes, I would say that designing an oval that way is “bad.”

    But the context matters—a lot. Otherwise we don’t know what might be rendering these curves. Nor do we know how much value is being gained by using half as many points. Is not having points at major extrema a problem? Maybe.
  • Ray Larabie
    Ray Larabie Posts: 1,465
    edited September 16
    I've experimented with 2-point ellipses for fonts with decorative dots, going all the way back to Fake Receipt in 1997. But as John pointed out, the quadratic curve conversion is a problem. Try it, and you'll see. It kind of works, but whenever I needed economical not-so-pretty dots, I built them from quadratic curves with four points, and a single control piont on each corner. That way they could usually be converted back and forth with no curve loss.
  • Linus Romer
    Linus Romer Posts: 210
    edited September 17
    Not in the context of font making but just general best practices for cubic curves
    On a different note are ovals or an ellipse or  are they both another form of a circle?
    Cubic Bézier curves cannot describe circular and elliptic arcs exactely.
    The semicircle shown, for example, would normally be approximated using the Bézier control points (1, 0), (1, 4/3), (-1, 4/3), and (-1, 0). This ensures that the Bézier curve passes through (1, 0), (0, 1), and (-1, 0) and that the directions at these points are correct. Try it out in GeoGebra with 
    Curve[(1-t)^3*1 + 3*(1-t)^2*t*1 + 3*(1-t)*t^2*(-1) + t^3*(-1), (1-t)^3*0 + 3*(1-t)^2*t*(4/3) + 3*(1-t)*t^2*(4/3) + t^3*0, t, 0, 1]
    At the point at time t = 0.23534171 (intersection of the curve with the line y=x), the radial deviation from a true semicircle is greatest: The distance to the origin is 1.018 instead of 1. However, as soon as the semicircle is approximated by two Bézier curves, the approximation improves.
    The same applies to ellipses, since ellipses are the images of affinely transformed circles.
  • John Butler
    John Butler Posts: 343
    I could have sworn that at one point there was a tool (Ikarus?) that generated circles using eight on-curve cubic Bezier points instead of the usual four, for greater fidelity to perfect circles. Or there was a foundry who handled circles this way.

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