The "lie" is that some Bézier-spline drawing programs let you restrict on-curve points to a "symmetric" configuration where the control points are at an equal distance on opposite sides of the on-curve point, but this doesn't necessarily make the curve itself more symmetric or more smooth. The proposed alternative is to control the bend radius instead, and ensure that the curve bends the same on both sides.
It’s trading one property for another, isn’t it? Standard beziers with symmetric handles are C1 continuous but not necessarily G2 continuous; author’s scheme is the other way around, which makes them better for some use cases and worse for others.
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The "lie" is that some Bézier-spline drawing programs let you restrict on-curve points to a "symmetric" configuration where the control points are at an equal distance on opposite sides of the on-curve point, but this doesn't necessarily make the curve itself more symmetric or more smooth. The proposed alternative is to control the bend radius instead, and ensure that the curve bends the same on both sides.
It’s trading one property for another, isn’t it? Standard beziers with symmetric handles are C1 continuous but not necessarily G2 continuous; author’s scheme is the other way around, which makes them better for some use cases and worse for others.
The C1 continuity you refer to is relative to the parametrization t=0..1 per segment. This is useless in practice.
For e.g. animation purposes, you need to reparametrize to arc length which destroys the apparent C1 continuity.