# 피사의 사탑 (Torre di Pisa) — Blender Python 절차적 모델 # 높이 약 56m, 기단 지름 약 15.5m 의 대리석 원통 종탑을 실제 치수로 만들었다. # 1층은 15개의 붙임기둥과 블라인드 아치(마름모 상감), 2~7층은 기둥 30개짜리 회랑 6단, # 맨 위는 지름이 작은 종루(아치 개구부 12개와 청동 종)다. 아치 사이 벽(스팬드럴)은 # 원통 좌표로 bmesh 를 직접 짜서 휘어진 아치 띠를 만들고, 기둥·아치는 linked 복제로 메시를 공유한다. # 처마 돌림띠와 기단은 회전체(lathe)로 만들었다. 탑 전체를 남쪽(-Y)으로 약 4° 기울였고, # 공사 중 기울기를 바로잡으려 한 흔적처럼 종루는 0.8° 덜 기울게 했다. 바닥에는 기적의 광장 잔디와 포석을 깔았다. import math from atelier import * SHOT = {"azimuth": -8, "elevation": 9, "lens": 70, "light": "day", "background": "#24303f"} # ── 재질 ───────────────────────────────────────────── M_MARBLE = mat('CarraraMarble', '#e4dccb', rough=0.55) M_COLUMN = mat('ColumnMarble', '#ece5d6', rough=0.45) M_WALL = mat('GalleryWallMarble', '#b8ad97', rough=0.6) M_GREY = mat('GreyStoneBand', '#9a968c', rough=0.6) M_INLAY = mat('GreenInlay', '#6e7c70', rough=0.5) M_DARK = mat('DoorwayShadow', '#3b342c', rough=0.8) M_BRONZE = mat('BellBronze', '#8c6b3c', rough=0.38, metal=0.85) M_WOOD = mat('BellYokeOak', '#5a4129', rough=0.7) M_IRON = mat('WroughtIron', '#3a3c3e', rough=0.5, metal=0.6) M_LAWN = mat('PiazzaLawn', '#58733a', rough=0.92) M_PAVE = mat('Paving', '#cbbfa8', rough=0.8) M_ROOF = mat('LeadRoof', '#7b7e80', rough=0.5, metal=0.3) LEAN = math.radians(3.97) lean = bpy.data.objects.new('PisaTower_Lean', None) link(lean) lean.rotation_euler = (LEAN, 0, 0) belfry_pivot = bpy.data.objects.new('Belfry_Correction', None) link(belfry_pivot) belfry_pivot.parent = lean def own(ob, parent=None): ob.parent = parent or lean return ob # ── 메시 도우미 ────────────────────────────────────── def sector(name, r0, r1, a0, a1, z0, z1, seg=4, material=None): """원통 좌표의 휘어진 블록(r0~r1, 각도 a0~a1, 높이 z0~z1).""" bm = bmesh.new() rows = [] for i in range(seg + 1): a = a0 + (a1 - a0) * i / seg c, s = math.cos(a), math.sin(a) rows.append([bm.verts.new((r * c, r * s, z)) for r, z in ((r0, z0), (r1, z0), (r1, z1), (r0, z1))]) for i in range(seg): for j in range(4): bm.faces.new((rows[i][j], rows[i + 1][j], rows[i + 1][(j + 1) % 4], rows[i][(j + 1) % 4])) bm.faces.new(rows[0]) bm.faces.new(list(reversed(rows[-1]))) bmesh.ops.recalc_face_normals(bm, faces=bm.faces) me = bpy.data.meshes.new(name) bm.to_mesh(me) bm.free() ob = bpy.data.objects.new(name, me) link(ob) return assign(ob, material) def arch_bay(name, rref, r_in, r_out, half, ra, z_s, z_top, n=14, material=None): """아치 하나 분의 휘어진 스팬드럴 벽. u(호 길이)·z 평면의 '사각형 - 반원'을 원통에 감는다.""" H = z_top - z_s tc = math.atan2(H, half) ths = sorted(set([math.pi * i / n for i in range(n + 1)] + [tc, math.pi - tc]), reverse=True) arc, bnd = [], [] for t in ths: c, s = math.cos(t), math.sin(t) arc.append((ra * c, z_s + ra * s)) tt = min(half / abs(c) if abs(c) > 1e-9 else 1e9, H / s if s > 1e-9 else 1e9) bnd.append((tt * c, z_s + tt * s)) bm = bmesh.new() def V(u, z, r): p = u / rref return bm.verts.new((r * math.cos(p), r * math.sin(p), z)) ao = [V(u, z, r_out) for u, z in arc] ai = [V(u, z, r_in) for u, z in arc] bo = [V(u, z, r_out) for u, z in bnd] bi = [V(u, z, r_in) for u, z in bnd] m = len(ths) for k in range(m - 1): bm.faces.new((ao[k], ao[k + 1], bo[k + 1], bo[k])) # 바깥면 bm.faces.new((ai[k], bi[k], bi[k + 1], ai[k + 1])) # 안쪽면 bm.faces.new((ao[k], ai[k], ai[k + 1], ao[k + 1])) # 아치 안쪽(내륜) if abs(bnd[k][1] - z_top) < 1e-6 and abs(bnd[k + 1][1] - z_top) < 1e-6: bm.faces.new((bo[k], bo[k + 1], bi[k + 1], bi[k])) # 윗면 for k in (0, m - 1): # 기둥머리 위 받침면 bm.faces.new((ao[k], bo[k], bi[k], ai[k])) bmesh.ops.recalc_face_normals(bm, faces=bm.faces) me = bpy.data.meshes.new(name) bm.to_mesh(me) bm.free() ob = bpy.data.objects.new(name, me) link(ob) return assign(ob, material) def archivolt(name, rref, r0, r1, ra0, ra1, z_s, n=16, material=None): """아치 둘레를 따라 바깥으로 살짝 돋운 반원 테(아키볼트).""" bm = bmesh.new() rows = [] for i in range(n + 1): t = math.pi * i / n row = [] for r, ra in ((r0, ra0), (r1, ra0), (r1, ra1), (r0, ra1)): p = ra * math.cos(t) / rref row.append(bm.verts.new((r * math.cos(p), r * math.sin(p), z_s + ra * math.sin(t)))) rows.append(row) for i in range(n): for j in range(4): bm.faces.new((rows[i][j], rows[i + 1][j], rows[i + 1][(j + 1) % 4], rows[i][(j + 1) % 4])) bm.faces.new(rows[0]) bm.faces.new(list(reversed(rows[-1]))) bmesh.ops.recalc_face_normals(bm, faces=bm.faces) me = bpy.data.meshes.new(name) bm.to_mesh(me) bm.free() ob = bpy.data.objects.new(name, me) link(ob) return assign(ob, material) def ring_profile(name, pts, material, seg=96): """닫힌 (r,z) 단면을 회전시킨 돌림띠.""" ob = lathe(name, pts + [pts[0]], material=material, seg=seg, shade_smooth=False) return ob def column(name, h, rs, material, plinth=True, cap_scale=1.0): """로마네스크 기둥: 사각 주춧돌 + 아틱 주초 + 약간 배흘림 기둥몸 + 주두 + 사각 관판.""" parts = [] pl = 0.12 * cap_scale if plinth: parts.append(box(name + '_plinth', (rs * 2.7, rs * 2.7, pl), material=material, base=True)) zb = pl if plinth else 0.0 cap_h = 0.42 * cap_scale ab = 0.12 * cap_scale shaft_top = h - cap_h - ab prof = [(0, zb), (rs * 1.32, zb), (rs * 1.32, zb + 0.06 * cap_scale), (rs * 1.18, zb + 0.12 * cap_scale), (rs * 1.25, zb + 0.18 * cap_scale), (rs * 1.05, zb + 0.24 * cap_scale), (rs, zb + 0.3 * cap_scale), (rs * 1.03, zb + (shaft_top - zb) * 0.35), (rs * 0.9, shaft_top - 0.05), (rs * 1.0, shaft_top - 0.03), (rs * 1.0, shaft_top), (rs * 0.95, shaft_top + 0.02), (rs * 1.15, shaft_top + cap_h * 0.45), (rs * 1.38, shaft_top + cap_h * 0.85), (rs * 1.42, shaft_top + cap_h), (0, shaft_top + cap_h)] lt = lathe(name + '_shaft', prof, material=material, seg=14) parts.append(lt) parts.append(box(name + '_abacus', (rs * 3.0, rs * 3.0, ab), loc=(0, 0, h - ab), material=material, base=True)) return join(parts, name) def place_ring(proto, count, radius, z=0.0, start=0.0, parent=None, name=None): obs = [] for i in range(count): a = start + 2 * math.pi * i / count ob = proto if i == 0 else duplicate(proto, name=f'{name or proto.name}.{i:02d}') ob.location = (radius * math.cos(a), radius * math.sin(a), z) ob.rotation_euler = (0, 0, a) own(ob, parent) obs.append(ob) return obs def place_rot(proto, count, start=0.0, parent=None, name=None): """원점 기준으로 이미 반경에 놓인 부품을 Z 축 회전으로 복제.""" for i in range(count): ob = proto if i == 0 else duplicate(proto, name=f'{name or proto.name}.{i:02d}') ob.rotation_euler = (0, 0, start + 2 * math.pi * i / count) own(ob, parent) # ── 치수 ───────────────────────────────────────────── Z_GROUND_TOP = 11.3 # 1층 처마(첫 돌림띠 윗면) H_FLOOR = 6.0 # 회랑층 층고 N_LOGGIA = 6 R_CORE = 5.5 # 회랑 안쪽 원통벽 R_COL = 7.15 # 회랑 기둥 중심 반경 R_CORN = 7.62 # 돌림띠 바깥 반경 CORN_DN, CORN_UP = 0.6, 0.15 # ── 기단 · 1층 ─────────────────────────────────────── base = ring_profile('Tower_BaseMoulding', [(0.0, 0.0), (7.95, 0.0), (7.95, 0.55), (7.85, 0.7), (7.75, 0.78), (7.75, 0.95), (7.6, 1.05), (0.0, 1.05)], M_MARBLE) own(base) wall0 = cylinder('GroundFloor_Wall', r=7.35, h=Z_GROUND_TOP - CORN_DN - 1.0 + 0.05, loc=(0, 0, 1.0), seg=96, material=M_MARBLE) own(wall0) for k, zb in enumerate((2.6, 4.4, 6.2, 8.0)): own(cylinder(f'GroundFloor_GreyCourse_{k}', r=7.37, h=0.22, loc=(0, 0, zb), seg=96, material=M_GREY)) N0 = 15 B0 = 2 * math.pi / N0 R0C = 7.47 col0 = column('GroundFloor_HalfColumn', 8.1, 0.3, M_COLUMN, cap_scale=1.4) place_ring(col0, N0, R0C, z=1.05, name='GroundFloor_HalfColumn') half0 = R0C * B0 / 2 bay0 = arch_bay('GroundFloor_BlindArch', R0C, 7.25, 7.72, half0, half0 - 0.36, 1.05 + 8.1, Z_GROUND_TOP - CORN_DN, material=M_MARBLE) bay0 = join([bay0, archivolt('GroundFloor_Archivolt', R0C, 7.70, 7.78, half0 - 0.36, half0 - 0.18, 1.05 + 8.1, material=M_MARBLE)], 'GroundFloor_BlindArch') place_rot(bay0, N0, start=B0 / 2, name='GroundFloor_BlindArch') # 블라인드 아치 안의 마름모 상감(로산게) loz = prism('GroundFloor_Lozenge', [(0, -0.42), (0.55, 0), (0, 0.42), (-0.55, 0)], 0.06, material=M_INLAY) loz.data.transform(Matrix.Rotation(math.pi / 2, 4, 'Y')) # 돌출 방향을 +X(반경 바깥)로 loz.data.transform(Matrix.Translation((7.33, 0, 0))) DOOR_BAY = 14 # 카메라 쪽(-12°) 아치에 정문 for i in range(N0): a = B0 / 2 + B0 * i if i == DOOR_BAY: continue ob = loz if i == 0 else duplicate(loz, name=f'GroundFloor_Lozenge.{i:02d}') ob.location = (0, 0, 9.75) ob.rotation_euler = (0, 0, a) own(ob) # 정문: 문틀(대리석) + 어두운 문 개구부 + 위쪽 반달 상인방 a_d = B0 / 2 + B0 * DOOR_BAY door = join([ sector('MainDoor_JambL', 7.33, 7.52, -0.13, -0.095, 1.05, 4.75, seg=1, material=M_MARBLE), sector('MainDoor_JambR', 7.33, 7.52, 0.095, 0.13, 1.05, 4.75, seg=1, material=M_MARBLE), sector('MainDoor_Lintel', 7.33, 7.56, -0.15, 0.15, 4.75, 5.25, seg=3, material=M_MARBLE), ], 'MainDoor_Frame') door.rotation_euler = (0, 0, a_d) own(door) door_open = sector('MainDoor_Opening', 7.34, 7.42, -0.095, 0.095, 1.05, 4.75, seg=3, material=M_DARK) door_open.rotation_euler = (0, 0, a_d) own(door_open) door_tymp = prism('MainDoor_Lunette', [(math.cos(t) * 0.8, math.sin(t) * 0.8) for t in [math.pi * i / 12 for i in range(13)]], 0.06, material=M_INLAY) door_tymp.data.transform(Matrix.Rotation(math.pi / 2, 4, 'X')) door_tymp.data.transform(Matrix.Rotation(math.pi / 2, 4, 'Z')) door_tymp.data.transform(Matrix.Translation((7.33, 0, 5.25))) door_tymp.rotation_euler = (0, 0, a_d) own(door_tymp) # ── 돌림띠(처마) — 층마다 하나, 회랑 바닥과 천장을 겸함 ── corn_prof = lambda zt: [(R_CORE - 0.2, zt - CORN_DN), (R_CORN - 0.2, zt - CORN_DN), (R_CORN - 0.05, zt - CORN_DN + 0.08), (R_CORN - 0.05, zt - 0.32), (R_CORN + 0.1, zt - 0.24), (R_CORN + 0.1, zt - 0.1), (R_CORN, zt), (R_CORN - 0.32, zt), (R_CORN - 0.36, zt + CORN_UP), (R_CORE - 0.2, zt + CORN_UP)] for k in range(N_LOGGIA + 1): zt = Z_GROUND_TOP + k * H_FLOOR own(ring_profile(f'Cornice_{k + 1}', corn_prof(zt), M_MARBLE)) # ── 회랑층 2~7 ─────────────────────────────────────── NL = 30 BL = 2 * math.pi / NL COL_H = 3.95 lcol = column('Loggia_Column', COL_H, 0.19, M_COLUMN) halfL = R_COL * BL / 2 lbay = arch_bay('Loggia_Arch', R_COL, 6.88, 7.42, halfL, halfL - 0.2, CORN_UP + COL_H, H_FLOOR - CORN_DN, material=M_MARBLE) lbay = join([lbay, archivolt('Loggia_Archivolt', R_COL, 7.40, 7.46, halfL - 0.2, halfL - 0.1, CORN_UP + COL_H, material=M_MARBLE)], 'Loggia_Arch') core_door = join([ sector('Loggia_CoreDoor', R_CORE - 0.05, R_CORE + 0.03, -0.09, 0.09, 0.0, 2.3, seg=2, material=M_DARK), ], 'Loggia_CoreDoor') for f in range(N_LOGGIA): z0 = Z_GROUND_TOP + f * H_FLOOR fl = f + 2 core = cylinder(f'Floor{fl}_GalleryWall', r=R_CORE, h=H_FLOOR, loc=(0, 0, z0), seg=64, material=M_WALL, cap=False) own(core) for b, zz in enumerate((1.6, 3.4)): own(cylinder(f'Floor{fl}_GreyCourse_{b}', r=R_CORE + 0.02, h=0.2, loc=(0, 0, z0 + CORN_UP + zz), seg=64, cap=False, material=M_GREY)) for c in range(NL): a = BL * c ob = lcol if (f == 0 and c == 0) else duplicate(lcol, name=f'Floor{fl}_Column.{c:02d}') ob.location = (R_COL * math.cos(a), R_COL * math.sin(a), z0 + CORN_UP) ob.rotation_euler = (0, 0, a) own(ob) ob = lbay if (f == 0 and c == 0) else duplicate(lbay, name=f'Floor{fl}_Arch.{c:02d}') ob.location = (0, 0, z0) ob.rotation_euler = (0, 0, a + BL / 2) own(ob) for d in range(5): ob = core_door if (f == 0 and d == 0) else duplicate(core_door, name=f'Floor{fl}_CoreDoor.{d}') ob.location = (0, 0, z0 + CORN_UP) ob.rotation_euler = (0, 0, BL / 2 + d * 2 * math.pi / 5 + f * 0.7) own(ob) # ── 7층 위 테라스 난간 ─────────────────────────────── Z_TERR = Z_GROUND_TOP + N_LOGGIA * H_FLOOR + CORN_UP post = box('Terrace_RailPost', (0.05, 0.05, 1.0), material=M_IRON, base=True) place_ring(post, 72, 7.12, z=Z_TERR, name='Terrace_RailPost') for k, zz in enumerate((0.45, 0.98)): own(torus(f'Terrace_Rail_{k}', R=7.12, r=0.03, loc=(0, 0, Z_TERR + zz), seg=96, rseg=6, material=M_IRON)) # ── 종루 ───────────────────────────────────────────── own(cylinder('Terrace_Floor', r=5.6, h=0.4, loc=(0, 0, Z_TERR - 0.41), seg=64, material=M_MARBLE)) belfry_pivot.location = (0, 0, Z_TERR) belfry_pivot.rotation_euler = (math.radians(-0.8), 0, 0) BP = belfry_pivot RB_O, RB_I = 4.55, 3.85 NB = 12 BB = 2 * math.pi / NB own(ring_profile('Belfry_Plinth', [(0.0, -0.25), (4.85, -0.25), (4.85, 0.35), (4.7, 0.45), (4.6, 0.6), (4.6, 1.1), (0.0, 1.1)], M_MARBLE), BP) own(cylinder('Belfry_Floor', r=RB_I + 0.05, h=0.02, loc=(0, 0, 1.1), seg=48, material=M_WALL), BP) Z_SPRING_B = 5.0 pier = sector('Belfry_Pier', RB_I, RB_O, -0.15, 0.15, 1.1, Z_SPRING_B, seg=2, material=M_MARBLE) place_rot(pier, NB, parent=BP, name='Belfry_Pier') bcol = column('Belfry_HalfColumn', Z_SPRING_B - 1.1, 0.17, M_COLUMN) place_ring(bcol, NB, RB_O + 0.02, z=1.1, parent=BP, name='Belfry_HalfColumn') halfB = (RB_O + 0.02) * BB / 2 bbay = arch_bay('Belfry_Arch', RB_O + 0.02, RB_I, RB_O, halfB, halfB - 0.62, Z_SPRING_B, 6.5, material=M_MARBLE) place_rot(bbay, NB, start=BB / 2, parent=BP, name='Belfry_Arch') own(ring_profile('Belfry_Cornice', [(RB_I - 0.3, 6.5), (RB_O + 0.05, 6.5), (RB_O + 0.25, 6.7), (RB_O + 0.25, 6.95), (RB_O + 0.05, 7.05), (RB_O, 7.05), (RB_O, 7.75), (RB_O + 0.15, 7.85), (RB_O + 0.15, 8.0), (RB_O - 0.35, 8.0), (RB_O - 0.35, 7.25), (RB_I - 0.3, 7.25)], M_MARBLE), BP) own(lathe('Belfry_Roof', [(RB_O - 0.35, 7.3), (2.0, 7.55), (0.9, 7.75), (0.9, 8.6), (0.0, 8.75)], material=M_ROOF, seg=48), BP) own(cylinder('Belfry_Ceiling', r=RB_I + 0.05, h=0.2, loc=(0, 0, 6.3), seg=48, material=M_WALL), BP) # 종(청동) — 아치 개구부 안쪽에 매달린 7개 bell = lathe('Bell', [(0.0, -0.95), (0.62, -0.95), (0.6, -0.86), (0.5, -0.75), (0.42, -0.45), (0.38, -0.1), (0.3, 0.05), (0.0, 0.1)], material=M_BRONZE, seg=28) yoke = box('Bell_Yoke', (0.25, 1.1, 0.25), loc=(0, 0, 0.12), material=M_WOOD, base=True) hang = box('Bell_Hanger', (0.12, 0.12, 6.3 - 3.9 - 0.37), material=M_WOOD, base=True) for i, k in enumerate((0, 2, 4, 6, 7, 9, 11)): a = BB / 2 + BB * k r = 2.9 loc = (r * math.cos(a), r * math.sin(a), 3.9) b = bell if i == 0 else duplicate(bell, name=f'Bell.{i}') b.location = loc own(b, BP) y = yoke if i == 0 else duplicate(yoke, name=f'Bell_Yoke.{i}') y.location = loc y.rotation_euler = (0, 0, a) own(y, BP) h = hang if i == 0 else duplicate(hang, name=f'Bell_Hanger.{i}') h.location = (loc[0], loc[1], 3.9 + 0.37) own(h, BP) # ── 바닥: 기단 계단 · 포석 · 잔디 (기울지 않음) ────── lawn = box('PiazzaDeiMiracoli_Lawn', (26, 26, 0.6), loc=(0, -0.8, -0.6), material=M_LAWN, base=True) pave = cylinder('Paving_Ring', r=11.5, h=0.64, loc=(0, -0.5, -0.6), seg=96, material=M_PAVE) step1 = cylinder('Tower_Step_1', r=9.4, h=0.35 + 0.6 - 0.02, loc=(0, 0, -0.58), seg=96, material=M_MARBLE) step2 = cylinder('Tower_Step_2', r=8.7, h=0.75 + 0.6 - 0.04, loc=(0, 0, -0.56), seg=96, material=M_MARBLE)