a3 – Parabolic Caustics (Reflection Envelope)

Rays from a point reflect off a parabola y = a x² producing a bright caustic envelope. Adjust curvature, source position, ray density, and reflection length.

Parameters

Geometry Curvature a Ray count Ray spread (deg) Reflection length Source X Source Y

Animation Animate (rotation) Breathing a-mod Time speed

Animate?

Rendering Ray opacity Caustic intensity Stroke width Color rotation Color spread

Show parabola

Show caustic hull

Controls

Formula

Parabola: y = a x^2. Source S=(Sx,Sy). Ray i initial direction angle θ_i inside spread. Intersection: solve a x^2 = Sy + m (x - Sx), m=tan θ_i. Surface tangent slope at x0: y' = 2 a x0. Reflect direction using R = D - 2(D·n) n with normal n normalized from ( -y', 1 ).

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Parameters