impactface

VELOCITY VERLET

x′ = x + v·dt + ½a·dt²

a′ = F(x′) / m

v′ = v + ½(a + a′)·dt

3-pass: pos → forces → vel

SOFTENED N-BODY GRAVITY

r² = Δx²+Δy²+ε²

r³ = r² · √r²

aᵢ += G·mⱼ·Δr / r³

aⱼ -= G·mᵢ·Δr / r³

ε softens r→0 blowup
N(N-1)/2 pairs via 3rd law

GOAL SPRING (FORMATION)

ρ = (t − t_d) / t_r

ρ = clamp(ρ, 0, 1)

F = k · ρ · (x* − x)

t_d = drift delay
t_r = ramp duration
x* = target pixel

VELOCITY DAMPING

v ← v · d

d = d_b if t < t_d

d = d_f if t ≥ t_d

d_b = burst damp (looser)
d_f = form damp (tighter)

LOCK CONDITION

|x − x*| < r_lock

→ v = 0, a = 0

→ frozen in place

r_lock = 4 px snap radius

HUNGARIAN ASSIGNMENT

cost(i,j) = |pᵢ − t_j|²

min Σ cost(i, σ(i))

O(n³) Jonker-Volgenant
optimal particle↔pixel map

LIVE INPUT

camera inactive

EMOTION DETECTION

joy

anger

fear

sadness

surprise

MANUAL OVERRIDE

COLLISION

particles 50

ASTEROID SELECTION

ASTEROID DATA

—

diam—

mass—

albedo—

type—

SMA—

—

diam—

mass—

albedo—

type—

SMA—

PHYSICS

gravity 50000

spring 15

drift s 1.0

ramp s 3.0

b.damp 0.985

f.damp 0.96

SIMULATION STATS

particles 0

formed 0%

phase idle

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