PAD Emotional Model

The PAD (Pleasure, Arousal, Dominance) model is the canonical type used to represent emotional state across the VIVA ecosystem. Coined by Mehrabian (1996), it places every emotion on three orthogonal axes in [-1, 1]³.

The Vec3 type

import viva_math/vector.{type Vec3, Vec3}

let fear = vector.pad(-0.64, 0.60, -0.43)
//                    ↑       ↑       ↑
//                Pleasure  Arousal  Dominance

vector.pad/3 constructs a clamped Vec3 — the constructor enforces each axis in [-1, 1], so out-of-range inputs are saturated rather than silently corrupting downstream calculations.

The 8 basic emotion attractors

Mehrabian (1996) places each octant of the PAD cube at a known attractor. viva_math/attractor exposes them with empirically calibrated coordinates:

import viva_math/attractor
import viva_math/vector

// Classify the nearest attractor by Euclidean distance in PAD space.
let state = vector.pad(-0.3, 0.7, -0.2)
attractor.classify_emotion(state)
// -> "fear"

Operations on Vec3

viva_math/vector is the full algebra layer over PAD vectors:

import viva_math/vector

let a = vector.pad(0.5, -0.2, 0.7)
let b = vector.pad(0.1, 0.3, -0.4)

vector.add(a, b)           // pointwise
vector.scale(a, 0.5)       // scalar
vector.dot(a, b)           // inner product
vector.distance(a, b)      // L2
vector.lerp(a, b, 0.3)     // linear interpolation
vector.normalize(a)        // unit vector

See also

• viva_math/cusp — sudden mood transitions via Thom (1972) catastrophe theory.
• viva_math/free_energy — Friston (2010) Free Energy Principle for interoception.
• viva_math/ou — Ornstein-Uhlenbeck stochastic mood dynamics over PAD vectors.
• viva_math/transport — distances between PAD distributions for population-level analysis.

References

• Mehrabian, A. (1996). Pleasure-arousal-dominance: A general framework for describing and measuring individual differences in temperament.
• Russell, J. A. (2003). Core affect and the psychological construction of emotion.