builder_3d.py

import numpy as np
from itertools import combinations
from typing import List, Dict, Tuple


def build_panes(speakers: List[Dict]) -> List[Dict]:
    panes = []
    # Create optimized list of (id, position) for iteration
    speaker_nodes: List[Tuple[int, np.ndarray]] = [
        (s["id"], np.array(s["pos"])) for s in speakers
    ]

    for triplet in combinations(speaker_nodes, 3):
        (id1, pos1), (id2, pos2), (id3, pos3) = triplet

        # Calculate Triangle Surface Normal
        edge_vector_a = pos2 - pos1
        edge_vector_b = pos3 - pos1
        surface_normal = np.cross(edge_vector_a, edge_vector_b)

        # Skip degenerate (area ~ 0) triangles
        if np.linalg.norm(surface_normal) < 0.001:
            continue

        # Convex Hull Check: A valid external face has all other points on ONE side
        is_external_face = True
        has_positive_side_points = False
        has_negative_side_points = False

        for other_id, other_pos in speaker_nodes:
            if other_id in [id1, id2, id3]:
                continue

            distance_from_plane = np.dot(surface_normal, other_pos - pos1)

            if distance_from_plane > 0.001:
                has_positive_side_points = True
            elif distance_from_plane < -0.001:
                has_negative_side_points = True

            # If points exist on both sides, the triangle intersects the volume
            if has_positive_side_points and has_negative_side_points:
                is_external_face = False
                break

        if is_external_face:
            basis_matrix = np.array([pos1, pos2, pos3]).T
            try:
                inverse_matrix = np.linalg.inv(basis_matrix)
                panes.append(
                    {
                        "type": "3D",
                        "ids": [id1, id2, id3],
                        "inv_matrix": inverse_matrix.tolist(),
                    }
                )
            except np.linalg.LinAlgError:
                continue

    return panes