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Curvature Beziers

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Steven Wittens

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Description

Curvature Beziers is a technical article on Steven Wittens' acko.net blog that rethinks interactive editing of cubic Bézier splines. Instead of dragging classic tangent handles whose length does not encode curvature directly, the post introduces curvature handles that make the geometric meaning of each control more explicit.

Wittens derives the constraints that relate control-point positions to desired curvature, explains why multiple mathematical solutions appear for a single edit, and documents heuristics that pick stable solutions during mouse drags. Interactive diagrams let readers experiment with the handle model in the browser.

The piece assumes comfort with differential geometry of plane curves, spline continuity, and CAD-style curve tooling. Graphics programmers building path editors, font tools, or vector UI will get the most from the derivations and UI discussion.

The article is a single long-form post with embedded demos rather than a multi-part series. It is freely readable on acko.net and pairs well with Wittens' other visual math essays on splines and computational geometry.

Wittens' acko.net essays are frequently linked in graphics and tools circles for clear interactive explanations, though this specific curvature-handle formulation is a specialized follow-on for curve-editor authors.