# JITTERBUG GENERATOR — Dynamo Python Script # ============================================ # # This script generates the complete Jitterbug geometry. # Use in a Python Script node in Dynamo. # # INPUTS (create these as input ports): # IN[0] = edge_length (number, in cm, e.g., 15.24) # IN[1] = rhombus_angle (number, degrees, 90=VE, 60=Icosa, 0=Octa) # IN[2] = create_faces (boolean, True/False) # # OUTPUTS: # OUT[0] = vertices (list of Points) # OUT[1] = edges (list of Lines) # OUT[2] = triangle_faces (list of Surfaces) # OUT[3] = rhombus_faces (list of Surfaces) # OUT[4] = state_name (string) import clr import math # Import Dynamo geometry clr.AddReference('ProtoGeometry') from Autodesk.DesignScript.Geometry import * # ============================================================================= # INPUTS # ============================================================================= edge_length = IN[0] if IN[0] else 15.24 # cm rhombus_angle = IN[1] if IN[1] else 90 # degrees (90=VE, 60=Icosa, 0=Octa) create_faces = IN[2] if len(IN) > 2 else True # ============================================================================= # TOPOLOGY CONSTANTS # ============================================================================= # 8 Triangular faces (vertex indices) TRIANGLES = [ (0, 4, 8), # T0 +++ (0, 9, 5), # T1 ++- (2, 8, 6), # T2 -++ (2, 7, 9), # T3 -+- (1, 10, 4), # T4 +-+ (1, 5, 11), # T5 +-- (3, 6, 10), # T6 --+ (3, 11, 7), # T7 --- ] # 6 Rhombus faces (vertex indices, in order) RHOMBI = [ (0, 4, 1, 5), # R0 +X face (2, 7, 3, 6), # R1 -X face (0, 9, 2, 8), # R2 +Y face (1, 10, 3, 11), # R3 -Y face (4, 8, 6, 10), # R4 +Z face (5, 11, 7, 9), # R5 -Z face ] # 24 Edges (vertex index pairs) EDGES = [ (0, 4), (0, 5), (0, 8), (0, 9), (1, 4), (1, 5), (1, 10), (1, 11), (2, 6), (2, 7), (2, 8), (2, 9), (3, 6), (3, 7), (3, 10), (3, 11), (4, 8), (4, 10), (5, 9), (5, 11), (6, 8), (6, 10), (7, 9), (7, 11), ] # ============================================================================= # VERTEX CALCULATION # ============================================================================= def calculate_vertices_ve(edge_length): """ Calculate 12 vertices for Vector Equilibrium state (rhombus_angle = 90°). Vertices are at permutations of (±a, ±a, 0) where a = edge_length / √2. """ a = edge_length / math.sqrt(2) vertices = [ Point.ByCoordinates( a, a, 0), # V0 Point.ByCoordinates( a, -a, 0), # V1 Point.ByCoordinates(-a, a, 0), # V2 Point.ByCoordinates(-a, -a, 0), # V3 Point.ByCoordinates( a, 0, a), # V4 Point.ByCoordinates( a, 0, -a), # V5 Point.ByCoordinates(-a, 0, a), # V6 Point.ByCoordinates(-a, 0, -a), # V7 Point.ByCoordinates( 0, a, a), # V8 Point.ByCoordinates( 0, a, -a), # V9 Point.ByCoordinates( 0, -a, a), # V10 Point.ByCoordinates( 0, -a, -a), # V11 ] return vertices def calculate_vertices_transformed(edge_length, rhombus_angle_deg): """ Calculate vertices for transformed state. This is a simplified transformation — for true constant-edge-length kinematics, use a constraint solver. This version approximates the transformation for visualization. rhombus_angle_deg: 90 = VE, ~63.43 = Icosa, 0 = Octa """ if rhombus_angle_deg >= 89: return calculate_vertices_ve(edge_length), "Vector Equilibrium" # Convert to radians theta = math.radians(rhombus_angle_deg) # For icosahedron state (rhombus angle ≈ 63.43°) # At this state, the short diagonal of rhombus = edge length # sin(63.43°/2) = 0.5, meaning half-diagonal = edge/2 # Transformation factor (1.0 at VE, decreasing toward Octa) # This is simplified — true kinematics is more complex t = rhombus_angle_deg / 90.0 # Scale factor for the "spread" of vertices # At VE (t=1): a = edge_length / sqrt(2) # At Octa (t=0): vertices collapse a = (edge_length / math.sqrt(2)) * math.sqrt(t) # Height factor for Z coordinates # Vertices move inward as rhombus collapses h = (edge_length / math.sqrt(2)) * math.sqrt(t) vertices = [ Point.ByCoordinates( a, a, 0), # V0 Point.ByCoordinates( a, -a, 0), # V1 Point.ByCoordinates(-a, a, 0), # V2 Point.ByCoordinates(-a, -a, 0), # V3 Point.ByCoordinates( a, 0, h), # V4 Point.ByCoordinates( a, 0, -h), # V5 Point.ByCoordinates(-a, 0, h), # V6 Point.ByCoordinates(-a, 0, -h), # V7 Point.ByCoordinates( 0, a, h), # V8 Point.ByCoordinates( 0, a, -h), # V9 Point.ByCoordinates( 0, -a, h), # V10 Point.ByCoordinates( 0, -a, -h), # V11 ] # Determine state name if rhombus_angle_deg > 80: state = "Vector Equilibrium" elif rhombus_angle_deg > 55: state = "Icosahedron (approx)" elif rhombus_angle_deg > 10: state = "Transitional" else: state = "Octahedron (approx)" return vertices, state # ============================================================================= # GEOMETRY GENERATION # ============================================================================= # Calculate vertices if rhombus_angle >= 89: vertices, state_name = calculate_vertices_ve(edge_length), "Vector Equilibrium" else: vertices, state_name = calculate_vertices_transformed(edge_length, rhombus_angle) # Create edges (lines) edges = [] for v1_idx, v2_idx in EDGES: line = Line.ByStartPointEndPoint(vertices[v1_idx], vertices[v2_idx]) edges.append(line) # Create faces (if requested) triangle_faces = [] rhombus_faces = [] if create_faces: # Triangular faces for tri in TRIANGLES: pts = [vertices[tri[0]], vertices[tri[1]], vertices[tri[2]]] try: surface = Surface.ByPerimeterPoints(pts) triangle_faces.append(surface) except: pass # Skip if surface creation fails # Rhombus faces for rhom in RHOMBI: pts = [vertices[rhom[0]], vertices[rhom[1]], vertices[rhom[2]], vertices[rhom[3]]] try: surface = Surface.ByPerimeterPoints(pts) rhombus_faces.append(surface) except: pass # Skip if surface creation fails # ============================================================================= # EDGE LENGTH VERIFICATION # ============================================================================= edge_lengths = [e.Length for e in edges] min_edge = min(edge_lengths) max_edge = max(edge_lengths) verification = "Edge lengths: min={:.3f}, max={:.3f}, target={:.3f}".format( min_edge, max_edge, edge_length) # ============================================================================= # OUTPUT # ============================================================================= OUT = [vertices, edges, triangle_faces, rhombus_faces, state_name, verification]