Movement Notation Systems

This skill provides guidance for creating systems that encode, analyze, and generate human movement for choreography, animation, and movement analysis.

Core Competencies

• Movement Notation: Labanotation, Benesh, Motif notation
• Computational Geometry: Skeletal representation, joint angles
• Procedural Animation: Rule-based movement generation
• Effort-Shape Analysis: Laban Movement Analysis (LMA)
• Temporal Structures: Rhythm, phrasing, dynamics

Movement Notation Fundamentals

The Challenge of Movement

Movement is inherently multidimensional:

• 3D spatial paths
• Temporal evolution
• Body part coordination
• Qualitative dynamics (effort)
• Relational context (other bodies, objects, space)

Major Notation Systems

System	Strengths	Use Cases
Labanotation	Complete, precise	Archival, reconstruction
Benesh	Compact, visual	Ballet, therapy
Motif	Abstract, readable	Teaching, analysis
Motion Capture	Exact coordinates	Animation, research

Laban Movement Analysis Framework

Body Component

What body parts are moving:

Body Organization:
├── Core-Distal (center outward)
├── Head-Tail (spinal connection)
├── Upper-Lower (horizontal division)
├── Body-Half (left-right)
└── Cross-Lateral (diagonal connections)

Body Parts Hierarchy:
Center (pelvis)
├── Torso (spine, chest)
│   ├── Head
│   ├── Shoulders
│   └── Arms → Elbows → Hands → Fingers
└── Hips
    └── Legs → Knees → Feet → Toes

Space Component

Where the body moves:

class KinesphereModel:
    """The reachable space around the body"""

    DIMENSIONS = {
        'vertical': {'up', 'down'},
        'horizontal': {'left', 'right'},
        'sagittal': {'forward', 'backward'}
    }

    LEVELS = ['low', 'middle', 'high']

    # 27 directions in the kinesphere
    DIRECTION_SYMBOLS = {
        'place_high': (0, 1, 0),
        'place_middle': (0, 0, 0),
        'place_low': (0, -1, 0),
        'forward_high': (0, 1, 1),
        'forward_middle': (0, 0, 1),
        'forward_low': (0, -1, 1),
        # ... all 27 combinations
    }

    # Spatial scales
    SCALES = {
        'near': 0.3,    # Close to body center
        'mid': 0.6,     # General reach
        'far': 1.0      # Full extension
    }

Effort Component

How movement is performed (qualitative dynamics):

class EffortFactors:
    """Laban Effort qualities"""

    FACTORS = {
        'weight': {
            'light': {'sensation': 'buoyant', 'value': -1},
            'strong': {'sensation': 'powerful', 'value': 1}
        },
        'time': {
            'sustained': {'sensation': 'leisurely', 'value': -1},
            'quick': {'sensation': 'urgent', 'value': 1}
        },
        'space': {
            'indirect': {'sensation': 'flexible', 'value': -1},
            'direct': {'sensation': 'focused', 'value': 1}
        },
        'flow': {
            'free': {'sensation': 'fluent', 'value': -1},
            'bound': {'sensation': 'controlled', 'value': 1}
        }
    }

    # Basic Effort Actions (combinations of weight, time, space)
    ACTIONS = {
        'punch': {'weight': 'strong', 'time': 'quick', 'space': 'direct'},
        'dab': {'weight': 'light', 'time': 'quick', 'space': 'direct'},
        'slash': {'weight': 'strong', 'time': 'quick', 'space': 'indirect'},
        'flick': {'weight': 'light', 'time': 'quick', 'space': 'indirect'},
        'press': {'weight': 'strong', 'time': 'sustained', 'space': 'direct'},
        'glide': {'weight': 'light', 'time': 'sustained', 'space': 'direct'},
        'wring': {'weight': 'strong', 'time': 'sustained', 'space': 'indirect'},
        'float': {'weight': 'light', 'time': 'sustained', 'space': 'indirect'}
    }

Shape Component

How the body changes form:

class ShapeQualities:
    """Body shape changes"""

    MODES = {
        'shape_flow': {
            'description': 'Internal shaping, self-oriented',
            'examples': ['breathing', 'growing/shrinking']
        },
        'directional': {
            'description': 'Bridge to environment',
            'subtypes': ['spoke-like', 'arc-like']
        },
        'carving': {
            'description': 'Sculpting 3D space',
            'relationship': 'Interacting with environment'
        }
    }

    AFFINITIES = {
        'rising': {'effort': 'light', 'direction': 'up'},
        'sinking': {'effort': 'strong', 'direction': 'down'},
        'spreading': {'effort': 'indirect', 'direction': 'horizontal'},
        'enclosing': {'effort': 'direct', 'direction': 'in'},
        'advancing': {'effort': 'sustained', 'direction': 'forward'},
        'retreating': {'effort': 'quick', 'direction': 'back'}
    }

Computational Movement Representation

Skeletal Data Structure

class Skeleton:
    """Hierarchical skeletal representation"""

    def __init__(self):
        self.joints = {
            'pelvis': Joint('pelvis', parent=None),
            'spine': Joint('spine', parent='pelvis'),
            'chest': Joint('chest', parent='spine'),
            'neck': Joint('neck', parent='chest'),
            'head': Joint('head', parent='neck'),
            'l_shoulder': Joint('l_shoulder', parent='chest'),
            'l_elbow': Joint('l_elbow', parent='l_shoulder'),
            'l_wrist': Joint('l_wrist', parent='l_elbow'),
            'r_shoulder': Joint('r_shoulder', parent='chest'),
            # ... etc
        }

    def get_world_position(self, joint_name):
        """Compute global position from local transforms"""
        joint = self.joints[joint_name]
        position = joint.local_position

        current = joint
        while current.parent:
            parent = self.joints[current.parent]
            position = parent.rotation.apply(position) + parent.local_position
            current = parent

        return position

    def compute_joint_angles(self):
        """Extract joint angles for analysis"""
        angles = {}
        for name, joint in self.joints.items():
            if joint.parent:
                angles[name] = joint.rotation.as_euler('xyz')
        return angles


class Joint:
    """Single joint in skeleton hierarchy"""

    def __init__(self, name, parent=None):
        self.name = name
        self.parent = parent
        self.local_position = np.array([0, 0, 0])
        self.rotation = Rotation.identity()
        self.constraints = {}  # Joint limits

Motion Trajectory

class MotionTrajectory:
    """Temporal sequence of poses"""

    def __init__(self, fps=30):
        self.fps = fps
        self.frames = []  # List of Skeleton states
        self.annotations = []  # Qualitative markers

    def duration(self):
        return len(self.frames) / self.fps

    def get_velocity(self, joint_name, frame_idx):
        """Compute instantaneous velocity"""
        if frame_idx < 1:
            return np.zeros(3)

        pos_current = self.frames[frame_idx].get_world_position(joint_name)
        pos_prev = self.frames[frame_idx - 1].get_world_position(joint_name)

        return (pos_current - pos_prev) * self.fps

    def extract_effort_features(self, joint_name, window=10):
        """Estimate Laban Effort qualities from motion"""
        features = {
            'weight': self._compute_acceleration_magnitude(joint_name, window),
            'time': self._compute_temporal_change_rate(joint_name, window),
            'space': self._compute_path_directness(joint_name, window),
            'flow': self._compute_flow_continuity(joint_name, window)
        }
        return features

Procedural Movement Generation

Rule-Based Choreography

class ChoreographyGenerator:
    """Generate movement sequences from rules"""

    def __init__(self):
        self.vocabulary = self._load_movement_vocabulary()
        self.grammar = self._load_grammar_rules()

    def generate_phrase(self, theme, duration_beats=16):
        """Generate choreographic phrase"""

        # Start with motif based on theme
        motif = self._select_motif(theme)

        # Develop through phrase
        phrase = [motif]
        current_beats = motif.duration_beats

        while current_beats < duration_beats:
            # Apply development rules
            if random.random() < 0.3:
                # Repeat with variation
                variation = self._vary_motif(phrase[-1])
                phrase.append(variation)
            elif random.random() < 0.5:
                # Contrast
                contrast = self._generate_contrast(phrase[-1])
                phrase.append(contrast)
            else:
                # Transition
                transition = self._smooth_transition(phrase[-1])
                phrase.append(transition)

            current_beats += phrase[-1].duration_beats

        return phrase

    def _vary_motif(self, motif):
        """Create variation of movement"""
        variations = [
            self._change_level,      # Same movement, different level
            self._mirror,            # Left-right reversal
            self._change_size,       # Larger or smaller
            self._change_tempo,      # Faster or slower
            self._change_direction,  # Face different direction
            self._fragment,          # Part of the movement
            self._extend,            # Add onto the movement
        ]
        return random.choice(variations)(motif)

Effort-Driven Animation

class EffortAnimator:
    """Generate movement with specified Effort qualities"""

    def animate_action(self, skeleton, target_position, effort_state):
        """Move body part with specified Effort"""

        # Time factor affects duration
        if effort_state['time'] == 'quick':
            duration = 0.3
            ease_type = 'exponential'
        else:  # sustained
            duration = 1.2
            ease_type = 'sine'

        # Weight factor affects acceleration
        if effort_state['weight'] == 'strong':
            acceleration_curve = self._strong_curve()
        else:  # light
            acceleration_curve = self._light_curve()

        # Space factor affects path
        if effort_state['space'] == 'direct':
            path = self._linear_path(skeleton.current, target_position)
        else:  # indirect
            path = self._curved_path(skeleton.current, target_position)

        # Flow factor affects continuity
        if effort_state['flow'] == 'bound':
            path = self._add_micro_pauses(path)
        # free flow is smooth by default

        return self._create_animation(
            path=path,
            duration=duration,
            acceleration=acceleration_curve
        )

Spatial Pattern Generation

class FloorPatternGenerator:
    """Generate spatial pathways"""

    def generate_path(self, pattern_type, space_bounds, duration):
        """Generate floor pattern"""

        patterns = {
            'circular': self._circular_path,
            'spiral': self._spiral_path,
            'figure_eight': self._figure_eight,
            'diagonal_cross': self._diagonal_cross,
            'zigzag': self._zigzag_path,
            'random_walk': self._random_walk
        }

        generator = patterns.get(pattern_type, self._random_walk)
        return generator(space_bounds, duration)

    def _spiral_path(self, bounds, duration, turns=3):
        """Generate spiral floor pattern"""
        center = bounds.center
        max_radius = min(bounds.width, bounds.height) / 2

        points = []
        num_points = int(duration * 30)  # 30 points per beat

        for i in range(num_points):
            t = i / num_points
            angle = t * turns * 2 * np.pi
            radius = max_radius * (1 - t)  # Spiral inward

            x = center[0] + radius * np.cos(angle)
            y = center[1] + radius * np.sin(angle)

            points.append((x, y, t * duration))

        return points

Notation Output

Textual Notation Format

class MovementScore:
    """Text-based movement score"""

    def to_notation(self, phrase):
        """Convert phrase to readable notation"""
        score = []

        for movement in phrase:
            notation = {
                'beat': movement.start_beat,
                'duration': movement.duration_beats,
                'body': self._notate_body(movement),
                'space': self._notate_space(movement),
                'effort': self._notate_effort(movement),
                'description': movement.description
            }
            score.append(notation)

        return score

    def _notate_effort(self, movement):
        """Effort notation symbols"""
        symbols = {
            ('strong', 'quick', 'direct'): '⚡',   # Punch
            ('light', 'sustained', 'indirect'): '☁️',  # Float
            ('strong', 'sustained', 'indirect'): '🌀',  # Wring
            # ... etc
        }
        effort_tuple = (
            movement.effort['weight'],
            movement.effort['time'],
            movement.effort['space']
        )
        return symbols.get(effort_tuple, '○')

Visual Score Representation

Time →
|    0    |    1    |    2    |    3    |    4    |
├─────────┼─────────┼─────────┼─────────┼─────────┤
│ ◊ HEAD  │         │    ○    │         │         │
│ ═ ARMS  │  ═══════│════     │   ═════ │═════    │
│ ║ TORSO │    ║    │   ║║    │    ║    │  ║║║    │
│ ‖ LEGS  │   ‖‖    │  ‖  ‖   │   ‖‖    │ ‖    ‖  │
├─────────┼─────────┼─────────┼─────────┼─────────┤
│ Level:  │   High  │   Mid   │   Low   │   Mid   │
│ Effort: │   ⚡    │    ☁️   │    🌀   │   ⚡    │
└─────────┴─────────┴─────────┴─────────┴─────────┘

Best Practices

Encoding Principles

1. Preserve intent: Capture what the choreographer wants, not just positions
2. Layer information: Structure > Shape > Dynamics
3. Allow interpretation: Don't over-specify unless needed
4. Support variation: Enable controlled improvisation

Analysis Guidelines

• Extract both quantitative (positions) and qualitative (effort) features
• Consider cultural and stylistic context
• Validate with practitioners

References

• references/labanotation-symbols.md - Symbol reference for Labanotation
• references/lma-glossary.md - Laban Movement Analysis terminology
• references/motion-capture-formats.md - Common mocap data formats