Interactive application
Interactive
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Curve Atlas

An atlas of how curves are constructed, constrained and intersected. Compare classical splines with local Yuksel interpolation, inspect when exact polynomial constraints produce poor shape, and follow predictor–corrector steps along intersections of implicit surfaces.

Shape, continuity and intersection
ControlEvaluateIntersect
Brochure →Open project ↗
  1. ∿

    Choose a construction

    Compare bases, interpolation rules and rational weights on shared controls.

  2. ∂

    Impose constraints

    Specify positions and derivatives; inspect residuals and unwanted excursions.

  3. κ

    Read the geometry

    Reveal curvature, moving frames and the extent of local influence.

  4. ×

    Trace intersections

    Follow tangent predictions, corrective solves and discovered branches.

Satisfying the equations is only one part of producing useful geometry.

Rational Bézier construction with control weights and Bernstein basis contributions.
Rational Bézier construction with control weights and Bernstein basis contributions.
A predictor-corrector trace of a sphere and oblique cylinder intersection.
A predictor-corrector trace of a sphere and oblique cylinder intersection.