movement-notation-systems

What this skill does

# 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:

```python
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):

```python
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:

```python
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

```python
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

```python
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

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

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

    def generate