Fix interpolation: use offset backward lerp instead of forward extrapolation
Forward extrapolation caused visible teleporting at every direction change (ghosts jumping ~1.3 tiles at intersections). Replace with lerp(prev, current, 0.5 + t/2) which starts the visual at the midpoint (max 0.5 tile / 12px lag) and smoothly reaches the destination. No jumps, no teleporting, minimal hitbox offset. Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>
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@@ -262,9 +262,10 @@
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(+ a (* t (- b a))))
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(+ a (* t (- b a))))
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;; draw-pacman! :: pacman, number -> /
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;; draw-pacman! :: pacman, number -> /
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;; Draws Pac-Man with forward extrapolation from current position.
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;; Draws Pac-Man with offset backward interpolation. Uses
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;; Formula: current + (current - prev) * t — visual leads toward
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;; lerp(prev, current, 0.5 + t/2) so the visual starts at the
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;; the next tile so it aligns with the logical hitbox.
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;; midpoint (max 0.5 tile lag) and arrives at current by t=1.
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;; No jumps on direction changes unlike forward extrapolation.
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(define (draw-pacman! pacman progress)
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(define (draw-pacman! pacman progress)
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(let* ((pos (pacman 'position))
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(let* ((pos (pacman 'position))
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(row (pos 'row))
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(row (pos 'row))
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@@ -272,8 +273,9 @@
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(prev-row (pacman 'prev-row))
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(prev-row (pacman 'prev-row))
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(prev-col (pacman 'prev-col))
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(prev-col (pacman 'prev-col))
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(t (min progress 1))
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(t (min progress 1))
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(render-row (+ row (* t (- row prev-row))))
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(factor (+ 0.5 (* 0.5 t)))
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(render-col (+ col (* t (- col prev-col))))
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(render-row (lerp prev-row row factor))
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(render-col (lerp prev-col col factor))
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(direction (pacman 'direction)))
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(direction (pacman 'direction)))
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((pacman-sprite 'set-x!) (grid->pixel-x render-col))
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((pacman-sprite 'set-x!) (grid->pixel-x render-col))
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((pacman-sprite 'set-y!) (grid->pixel-y render-row))
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((pacman-sprite 'set-y!) (grid->pixel-y render-row))
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@@ -283,7 +285,7 @@
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((eq? direction 'down) ((pacman-sprite 'rotate!) rotation-down)))))
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((eq? direction 'down) ((pacman-sprite 'rotate!) rotation-down)))))
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;; draw-ghosts! :: list -> /
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;; draw-ghosts! :: list -> /
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;; Updates all ghost sprite positions with forward extrapolation.
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;; Updates all ghost sprite positions with offset backward interpolation.
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(define (draw-ghosts! ghosts)
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(define (draw-ghosts! ghosts)
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(for-each
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(for-each
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(lambda (ghost ghost-draw)
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(lambda (ghost ghost-draw)
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@@ -293,8 +295,9 @@
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(prev-row (ghost 'prev-row))
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(prev-row (ghost 'prev-row))
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(prev-col (ghost 'prev-col))
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(prev-col (ghost 'prev-col))
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(t (min (/ (ghost 'movement-timer) ghost-speed-ms) 1))
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(t (min (/ (ghost 'movement-timer) ghost-speed-ms) 1))
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(render-row (+ row (* t (- row prev-row))))
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(factor (+ 0.5 (* 0.5 t)))
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(render-col (+ col (* t (- col prev-col))))
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(render-row (lerp prev-row row factor))
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(render-col (lerp prev-col col factor))
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(dir (ghost 'direction)))
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(dir (ghost 'direction)))
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((ghost-draw 'update!) render-row render-col dir)))
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((ghost-draw 'update!) render-row render-col dir)))
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ghosts ghost-draw-states))
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ghosts ghost-draw-states))
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