{"slug":"heygen-com-cut-the-curve","name":"cut-the-curve","description":"The technique catalog: five velocity-matched SEAMS (zoom-through, INVERSE zoom-through, cut-the-curve, waterfall cut, rack-focus blur-cut) plus the two in-scene techniques — waterfall ENTRY (staggered arrival cascades for title cards / segment openers) and the nudge curve (slow-fast-slow three-phase group slides). Covers partial-travel (~12% of frame) velocity matching via mirrored power4 eases, the Z scale-sign rule, size-scaled blur (10px text / 18-20px full-frame), word-by-word staggered cuts, cascade pacing by element weight, and the 10/65/25 slide ratio. Read before authoring any transition, text-beat handoff, kinetic text entry, or group reposition. [depth, zoom, inverse-zoom, scale-sign, mirrored-zoom, rack-focus, pacing, velocity, cut-the-curve, waterfall, stagger, cascade, kinetic-text, title-card, segment-opener, nudge, slide, easing, group-motion, z-depth, motion-graphics, cinematic, transition, blur, directional-continuity]","long_description":"---\nname: cut-the-curve\ndescription: \"The technique catalog: five velocity-matched SEAMS (zoom-through, INVERSE zoom-through, cut-the-curve, waterfall cut, rack-focus blur-cut) plus the two in-scene techniques — waterfall ENTRY (staggered arrival cascades for title cards / segment openers) and the nudge curve (slow-fast-slow three-phase group slides). Covers partial-travel (~12% of frame) velocity matching via mirrored power4 eases, the Z scale-sign rule, size-scaled blur (10px text / 18-20px full-frame), word-by-word staggered cuts, cascade pacing by element weight, and the 10/65/25 slide ratio. Read before authoring any transition, text-beat handoff, kinetic text entry, or group reposition. [depth, zoom, inverse-zoom, scale-sign, mirrored-zoom, rack-focus, pacing, velocity, cut-the-curve, waterfall, stagger, cascade, kinetic-text, title-card, segment-opener, nudge, slide, easing, group-motion, z-depth, motion-graphics, cinematic, transition, blur, directional-continuity]\"\n---\n\n# Cut the Curve — the technique catalog\n\nFive SEAM techniques, one principle: **cut at peak velocity, match direction and speed\non both sides of the cut** — plus the two in-scene techniques (§6 arrivals, §7 slides).\nThe seam LAW — vector law, the current, the ledger, the Seam Gate — lives in\n`motion-doctrine`; read it first. This skill is the parameters and mechanics.\nAll GSAP code templates (worker + registry): `examples/gsap-implementation.md`.\n\n## Catalog\n\n| # | Technique | Scope | Axis | Use for |\n| --- | -------------------------- | ------------------------------ | ------------------- | ------------------------------------------------------ |\n| 1 | **Zoom-Through** (forward) | Within-scene text swap | Z, toward viewer | progressing deeper into the same thought |\n| 2 | **Inverse Zoom-Through** | Arrival / payoff beat | Z, away from viewer | something bigger lands |\n| 3 | **Cut the Curve** | Between scenes | X / Y | the default boundary, the film's current |\n| 4 | **Waterfall Cut** | Text-to-text seam | X, per-word | word-level handoff between big-text beats |\n| 5 | **Rack-Focus Blur-Cut** | Same-surface state swap | X / Y / Z | the one cut you want SEEN — a DSLR focus-pull flourish |\n| 6 | **Waterfall Entry** | In-scene ARRIVAL (no seam) | Y, from below | title cards, segment openers, list intros |\n| 7 | **Nudge Curve** | In-scene group slide (no seam) | X / Y | repositioning a composed group to make room |\n\n## Z direction is a sign\n\n\"Same axis\" is not enough on Z — the sign of d(scale)/dt must match across the cut:\n\n| Z vector | Exit scale | Entry scale | Variant |\n| -------------- | ------------------- | -------------------- | -------------------- |\n| Push (forward) | growing `1 → 1.2` | growing `0.75 → 1` | zoom-through |\n| Pull (back) | shrinking `1 → 0.8` | shrinking `1.25 → 1` | inverse zoom-through |\n\nBanned mirrors: a receding exit answered by a grow-from-small entry (pull flips to push —\nthe common one, since grow-from-small is the default element entrance), and a push exit\nanswered by an oversized retraction. This binds the incoming scene's OWN entrances during\nthe seam window (cut + ~0.5s), not just the wrapper tween: hold the incoming frame\ncomposed, or author its entrance to match the sign. Verify per Seam Gate rule 7.\n\n## Blur logic (all Z variants)\n\n| Subject | Peak blur | Why |\n| --------------------------------------------- | ----------- | -------------------------------------------------------------- |\n| Text-scale (headline, word group) | **10px** | 20px smears letterforms — the cut reads as a glitch, not speed |\n| Full-frame surface (window, card, screenshot) | **18–20px** | lighter blur on a big surface reads as a rendering hiccup |\n\nSame peak blur on both sides at the swap frame. Blur the WRAPPER, never children.\n\n---\n\n## 1. Zoom-Through (forward)\n\nZ-axis velocity-matched cut; **never both texts visible.** Everything GROWS: the outgoing\ntext accelerates toward camera, a hard swap hides at peak blur, the incoming text keeps\ngrowing into the focal plane. Headlines and short phrases only. Total ≈ 0.4s.\n\n| Phase | Scale | Blur | Opacity | Ease | Duration |\n| -------------- | -------- | -------- | ----------------- | ------------------------------------------ | -------- |\n| Exit | 1 → 1.2 | 0 → 10px | 1 → 0.15 | power3.in (opacity: separate `none` tween) | 0.2s |\n| Cut (`tl.set`) | in: 0.75 | 10px | out: 0 / in: 0.15 | — | — |\n| Entry | 0.75 → 1 | 10 → 0px | 0.15 → 1 | expo.out | 0.5s |\n\nExit opacity MUST be its own linear tween — `power3.in` holds opacity near 1 too long.\nOn entry all properties share `expo.out`.\n\n## 2. Inverse Zoom-Through (backward)\n\nThe pull-back mirror: the outgoing element RECEDES; the incoming arrives OVERSIZED (as if\njust behind camera) and retracts into the focal plane. Everything SHRINKS. Spend on\nARRIVAL/payoff beats — a payoff line, a giant reply, a held end-state — never ordinary\nboundaries. Total ≈ 0.7s (30% exit / 70% entry).\n\n| Phase | Scale | Blur | Opacity | Ease | Duration |\n| -------------- | -------- | -------- | ----------------- | ------------------------------------------ | -------- |\n| Exit | 1 → 0.8 | 0 → 10px | 1 → 0.15 | power3.in (opacity: separate `none` tween) | ~0.2s |\n| Cut (`tl.set`) | in: 1.25 | 10px | out: 0 / in: 0.15 | — | — |\n| Entry | 1.25 → 1 | 10 → 0px | 0.15 → 1 | expo.out | ~0.5s |\n\nBlur is 10px text-scale; 18–20px only when both sides are full-bleed surfaces.\n\n**Sign discipline:** the incoming scene arrives as a composed frame inside the retracting\nwrapper — no grow-from-small intro in the seam window. Staged entrances happen after the\nretraction settles, or start ≥1 and retract.\n\n## 3. Cut the Curve (default scene boundary)\n\nX/Y velocity-matched cut — the default for ALL scene-to-scene boundaries, in the film's\ncurrent, not an accent. The outgoing hero accelerates in one direction, the cut lands\nmid-motion, the incoming hero continues the SAME direction and decelerates. Total ≈ 0.6s;\ndirections LEFT / RIGHT / UP / DOWN (default LEFT).\n\n**Partial travel:** ~12% of frame (≈230px at 1920) — never full off-screen moves.\n\n| Direction | Exit | Entry start → end |\n| --------- | ------------- | ----------------- |\n| Leftward | `x: 0 → −230` | `x: +230 → 0` |\n| Rightward | `x: 0 → +230` | `x: −230 → 0` |\n| Upward | `y: 0 → −230` | `y: +230 → 0` |\n| Downward | `y: 0 → +230` | `y: −230 → 0` |\n\nMechanics:\n\n- **Mirrored eases:** exit `power4.in` + entry `power4.out`, same distance and duration —\n the two halves of one `power4.inOut`, so velocity matches exactly at the cut.\n- **The fade trick:** exit opacity completes at ~25–30% of its travel (fade ≈ 0.18–0.3s\n vs motion 0.3–0.34s); entry ignites at ~0.35 opacity mid-path. Time the last fading\n element to die right at the cut — a gap where nothing moves reads as dead air.\n- Exit 0.2–0.4s; entry ≥ exit. Optional blur 8–10px.\n- **Stage ground:** `#root` must be opaque\n (`background: var(--canvas-deep, var(--canvas, #000))`) — the mid-window cut opens a\n summed-opacity < 1 window that flashes white otherwise (see `seam-craft`).\n\n`push-slide` exists but violates partial-travel and mid-motion phase; prefer cut-the-curve.\n\n## 4. Waterfall Cut (word-by-word cut-the-curve)\n\nCut-the-curve at WORD granularity — the strongest leftward cut for text-to-text seams.\nOutgoing words ramp out on their own curves; incoming words cascade in mid-flight — a\nwave the eye rides across the seam.\n\n**Scope:** worker-authored inside one multi-beat comp (stacked full-frame `.beat` layers),\nNOT a registry/injector type — it tweens word spans, not clip wrappers. The boundary into\nand out of the text-beat block still gets a normal registry transition. Does not count\nagainst the 2–3 transition budget.\n\n| Parameter | Value | Why |\n| ------------------- | --------------------- | ------------------------------------------- |\n| Travel | ±230px (~12% frame) | partial travel + velocity > full-frame push |\n| Exit | 0.34s `power4.in` | the acceleration IS the cut |\n| Exit fade | 0.18s, starts with x | word gone by ~25–30% of travel — no smear |\n| Exit stagger | +0.022s reading order | the line peels, not a block slide |\n| Entry | 0.3s `power4.out` | back half of the composite — velocity match |\n| Entry start opacity | 0.35 | mid-path ignition; binary 0→1 pops |\n| Entry gaps | 0.05s × 0.84 decay | accelerating cascade, resolves composed |\n\nRules:\n\n- One direction per chain, riding the current. Inverse zoom is the chain's ARRIVAL beat only.\n- Pre-set all words to `x: +230, opacity: 0` at build time — `immediateRender: false`\n alone leaves un-started words visible at rest.\n- A short first beat may exit whole-line: its fade ends ~0.02s before the cut so it is\n still streaking when the next words ignite — no dead gap.\n- Transform/opacity only (seek-safe); opaque stage ground applies.\n\n## 5. Rack-Focus Blur-Cut (the visible cut)\n\nThe one variant where the cut is SEEN: a defocus blur SPIKE hides a single-frame hard\nswap — a handheld-DSLR focus-pull. Use as an occasional flourish for a state swap of the\nSAME surface within one visual theme; never the default boundary.\n\nDifferences from the others: outgoing stays FULLY OPAQUE until the cut (the blur hides\nthe swap — no early fade); eases `power2.in` / `power2.out` (soft optics, not momentum).\n\nRules:\n\n- Fire only at a narrative beat, ≤ once per ~8s; never mid-caption or during a hold.\n- Cut at PEAK blur (≥6px; peak 8–12px, ≤16–18px max) — swapping on the way up shows the cut.\n- A subtle scale (~1.06 lens-breathing) sells it as optics.\n- Same direction on both sides — the vector law still holds. Entry ≥ exit duration.\n- Blur the wrapper; never blur + opacity in one tween on one element (headless\n compositing bug); never blur a `