Wormhole Throat Geometry (2D)

This 2D companion draws the same wormhole physics as the 3D scene as a flat Morris-Thorne embedding-diagram cross-section: two flared mouths are joined by a neck whose exact radius profile is r(z)=√(z²+b₀²), reshaped live by the throat-radius and flare-length sliders. Launching a light ray sends a marker along the true meridian geodesic through the throat while a second marker races along an external "long way around" path of length D in ordinary space — the same numerically-integrated arc length and travel-time readout used to size the wormhole scene's shortcut, here shown side by side so the time saved is visible directly, with narrow-throat, wide-throat and long-throat presets.