Physically Accurate Light Painting Photography Prompt

INTENT drawing in a space rather than photographing it; the mark and what it revealed are one gesture UNKNOWNS T = shutter (seconds–minutes) ; path p(s) of the source ; intensity/dwell ; gel colour LAWS two records, one source (a) the TRACE: wherever the source faced the lens it draws a continuous curve; brightness ∝ DWELL time ⇒ pauses bloom into blobs, fast sweeps go dim, a bright core clips white with a coloured halo (b) the DEPOSIT: E(x) = ∫ I(s)·(n̂·r̂(s)) / |r(s)|² ds along the path ⇒ the path behaves as an EXTENDED source SHAPED LIKE ITSELF soft, swept shadows a moving source sweeps its shadow ⇒ the union is a fanned penumbra, not a single hard cast. A hard-edged shadow implies the source PAUSED there - and the trace must show that pause. inverse-square along the path surfaces nearest the trace are hot and fall off steeply; a wall lit evenly end-to-end implies the source travelled parallel to it, and the trace must show that travel OCCLUSION (the decisive one) the trace is real light at a real 3D position ⇒ anything in FRONT of it hides it. A streak that ran behind a tree disappears behind the trunk and resumes on the far side. chromatic lock a gelled source tints the trace AND everything it lit - one hue for both the painter invisible if they kept moving and never lit themselves; ghosted if they lingered or turned the source on their own body ambient still integrates over the same T ⇒ stars trail, cloud streaks, water silks ⇒ T̂_trail = T̂_stars = T̂_water (direct callback) reflections the trace reflects in water and glass under the ordinary mirror map OVERDETERMINATION the path recovered 3× ⇒ 2 redundant equalities from the drawn trace · from where the surfaces are brightest (nearest approach) · from the direction and softness of every swept shadow - all describe ONE trajectory HONEST one path, one T, one hue; every lit surface explained by the visible trace and vice versa FORBIDDEN a light streak drawn OVER an object it must have passed behind ; a glowing trace that illuminates nothing - surfaces beside it unlit ; surfaces brightly painted with no trace anywhere near them ; hard single-direction shadows under a source the trace shows in continuous motion ; a coloured trace depositing white light, or vice versa ; even illumination along a wall with a trace that never travelled its length ; a fully visible, sharply rendered person holding the light at the end of a 60-second exposure ; a static frozen sky above a minutes-long trace.