def __init__(self): # POV-Ray self.edge_color = "rgb <{}, {}, {}>".format(1, 165 / 255, 0) # orange self.edge_radius = 0.03 self.vert_color = "rgb <{}, {}, {}>".format(1, 165 / 255, 0) # orange self.vert_radius = 0.03 self.face_color = "rgb <0, 0, 0>" # not used verts = dict( a=Qvector((1, 0, 0, 0)), #A b=Qvector((0, 1, 0, 0)), #B c=Qvector((0, 0, 1, 0)), #C d=Qvector((0, 0, 0, 1))) #D self.name = "Tetrahedron" self.volume = 1 # per Concentric Hierarchy self.center = ORIGIN # 4 vertices self.vertexes = verts # 4 faces self.faces = (('a', 'b', 'c'), ('a', 'c', 'd'), ('a', 'd', 'b'), ('b', 'd', 'c')) self.edges = self._distill()
def __init__(self): # POV-Ray self.edge_color = "rgb <{}, {}, {}>".format(0, 0, 0) # black self.edge_radius = 0.03 self.vert_color = "rgb <{}, {}, {}>".format(0, 0, 0) # black self.vert_radius = 0.03 self.face_color = "rgb <0, 0, 0>" # not used verts = dict( e=-Qvector((1, 0, 0, 0)), #E f=-Qvector((0, 1, 0, 0)), #F g=-Qvector((0, 0, 1, 0)), #G h=-Qvector((0, 0, 0, 1))) #H self.name = "InvTetrahedron" self.volume = 1 # per Concentric Hierarchy self.center = ORIGIN # 4 vertices self.vertexes = verts # 4 faces self.faces = (('e', 'f', 'g'), ('e', 'g', 'h'), ('e', 'h', 'f'), ('f', 'h', 'g')) self.edges = self._distill()
def test_quadrant(self): qA = Qvector((1, 0, 0, 0)) qB = Qvector((0, 1, 0, 0)) qC = Qvector((0, 0, 1, 0)) tet = Tetrahedron(qA.length(), qB.length(), qC.length(), (qA - qB).length(), (qA - qC).length(), (qB - qC).length()) self.assertAlmostEqual(tet.ivm_volume(), Decimal(0.25))
def animation2(targdir="anim2"): path = os.path.join(".",targdir) if not os.path.isdir(targdir): os.mkdir(targdir) radii = np.linspace(0, 0.5, 8).tolist() radii += reversed(radii[1:-1]) for frame_id, radius in enumerate(radii, start=1): filename = f"balls{frame_id:03}.pov" with open(os.path.join(path,filename), "w") as target: target.write(pov_header) cubocta = Cuboctahedron() cubocta.vert_radius = radius cubocta.vert_color = "rgb <1,0,0>" draw_poly(cubocta, target, v=True, e=False) draw_vert(Qvector((0,0,0,0)), c=cubocta.vert_color, r=cubocta.vert_radius, t=target) if frame_id < 9: rd = RD() draw_poly(rd, target) for p in twelve_around_one(rd): draw_poly(p, target) draw_poly(Cuboctahedron(), target, v=True, e=True)
def animation11(targdir="anim11"): targdir = os.path.join(".",targdir) if not os.path.isdir(targdir): os.mkdir(targdir) thirteen_balls = [Qvector((0,0,0,0))] + list(IVM_DIRS) neighbors = one_hop_away(thirteen_balls) colors = cycle(["rgb <1,0,0>", "rgb <.8,0,.2>", "rgb <.6,0,.4>", "rgb <.4,0,.6>", "rgb <.2,0,.8>", "rgb <0,.5,.2>", "rgb <0,.7,.2>"]) rainbow = [next(colors) for _ in range(13)] for frame_id in range(13): filename = f"balls{frame_id:03}.pov" with open(os.path.join(targdir,filename), "w") as target: target.write(pov_header) rd = RD() draw_poly(rd, target) for idx, p in enumerate(twelve_around_one(rd)): if idx <= frame_id: draw_vert(neighbors[idx], rainbow[idx], r=0.4, t=target) draw_poly(p, target) if 12 == frame_id: draw_vert(neighbors[12], rainbow[12], r=0.4, t=target)
def animation10(targdir="anim10"): targdir = os.path.join(".",targdir) if not os.path.isdir(targdir): os.mkdir(targdir) thirteen_balls = [Qvector((0,0,0,0))] + list(IVM_DIRS) neighbors = one_hop_away(thirteen_balls) for frame_id in range(13): filename = f"balls{frame_id:03}.pov" with open(os.path.join(targdir,filename), "w") as target: target.write(pov_header) rd = RD() draw_poly(rd, target) for idx, p in enumerate(twelve_around_one(rd)): if idx <= frame_id: draw_vert(neighbors[idx], c="rgb <1,0,0>", r=0.5, t=target) draw_poly(p, target) if 12 == frame_id: draw_vert(neighbors[12], c="rgb <1,0,0>", r=0.5, t=target)
def animation3(targdir="anim3"): targdir = os.path.join(".",targdir) if not os.path.isdir(targdir): os.mkdir(targdir) radii = np.linspace(0, 0.5, 8).tolist() radii += reversed(radii[1:-1]) for frame_id, radius in enumerate(radii, start=1): filename = f"balls{frame_id:03}.pov" with open(os.path.join(targdir,filename), "w") as target: target.write(pov_header) cubocta = Cuboctahedron() cubocta.vert_radius = radius cubocta.vert_color = "rgb <1,0,0>" if frame_id <= 9: draw_poly(cubocta, target, v=True, e=False) draw_vert(Qvector((0,0,0,0)), c=cubocta.vert_color, r=cubocta.vert_radius, t=target) if frame_id > 9: cube = Cube() ico = Icosahedron() * (1/PHI * math.sqrt(2)/2) * 1.2 * radius st = Struts(cube, ico) draw_poly(ico, target) draw_poly(st, target) # draw_poly(cube, target) for ik in twelve_around_one(ico): draw_poly(ik, target) # for c in twelve_around_one(cube): # draw_poly(c, target) for s in twelve_around_one(st): draw_poly(s, target)
def sphere_packing(): cube = Cube() rd = RD() octa = Octahedron() cubocta = Cuboctahedron() draw_poly(cube) draw_poly(octa) draw_poly(rd) for p in twelve_around_one(cube): draw_poly(p) for p in twelve_around_one(rd): draw_poly(p) for p in twelve_around_one(octa): draw_poly(p) cubocta.vert_radius = Qvector((2, 1, 1, 0)).length() / 2 # grow the balls cubocta.vert_color = (1, 0, 0) draw_poly(cubocta, v=True, e=False) draw_vert(Qvector((0, 0, 0, 0)), c=cubocta.vert_color, r=cubocta.vert_radius)
def spheres_bulging(): with open("sphere_pack2.pov", "w") as target: target.write(pov_header) cube = Cube() rd = RD() octa = Octahedron() cubocta = Cuboctahedron() draw_poly(cube, target) draw_poly(octa, target) draw_poly(rd, target) for p in twelve_around_one(cube): draw_poly(p, target) for p in twelve_around_one(rd): draw_poly(p, target) for p in twelve_around_one(octa): draw_poly(p, target) cubocta.vert_radius = Qvector((2,1,1,0)).length()/2 # grow the balls cubocta.vert_color = "rgb <1,0,0>" draw_poly(cubocta, target, v=True, e=False) draw_vert(Qvector((0,0,0,0)), c=cubocta.vert_color, r=cubocta.vert_radius, t=target)
def struts(): IVM = {} IVM[0] = [Qvector((0, 0, 0, 0))] IVM[1] = list(IVM_DIRS) print(IVM) polys_blender.IVM = IVM radius = 0.5 cube = Cube() ico = Icosahedron() * (1 / PHI * math.sqrt(2) / 2) * 1.2 * radius st = Struts(cube, ico, True) draw_poly(ico) draw_poly(st) # draw_poly(cube, target) for ik in twelve_around_one(ico): draw_poly(ik) # for c in twelve_around_one(cube): # draw_poly(c, target) for s in twelve_around_one(st): draw_poly(s, v=False)
if f: for f in p.faces: draw_face(f, fc, the_file) if e: for e in p.edges: draw_edge(e, ec, er, the_file) import math from qrays import Qvector PHI = (1 + math.sqrt(5)) / 2.0 ORIGIN = Qvector((0, 0, 0, 0)) A = Qvector((1, 0, 0, 0)) B = Qvector((0, 1, 0, 0)) C = Qvector((0, 0, 1, 0)) D = Qvector((0, 0, 0, 1)) E, F, G, H = B + C + D, A + C + D, A + B + D, A + B + C I, J, K, L, M, N = A + B, A + C, A + D, B + C, B + D, C + D O, P, Q, R, S, T = I + J, I + K, I + L, I + M, N + J, N + K U, V, W, X, Y, Z = N + L, N + M, J + L, L + M, M + K, K + J # OPPOSITE DIAGONALS # ZY WX # RV OS # TU PQ control = (Z - T).length()
def test_martian(self): p = Qvector((2, 1, 0, 1)) q = Qvector((2, 1, 1, 0)) r = Qvector((2, 0, 1, 1)) result = make_tet(5 * q, 2 * p, 2 * r) self.assertAlmostEqual(result[0], 20, 7)
def test_phi_tet_2(self): p = Qvector((2, 1, 0, 1)) q = Qvector((2, 1, 1, 0)) r = Qvector((2, 0, 1, 1)) result = make_tet(PHI * q, (1 / PHI) * p, r) self.assertAlmostEqual(result[0], 1, 7)
#!/usr/bin/env python3 # -*- coding: utf-8 -*- """ Created on Fri Sep 4 09:56:18 2020 @author: mac """ import tetravolume as tv from itertools import permutations from qrays import Qvector from random import choice from gmpy2 import mpfr, get_context ccp_spokes = [Qvector(p) for p in set(permutations((0,1,1,2)))] get_context().precision=1000 zero = mpfr('0.0') def rand_vert(): vert = Qvector((zero, zero, zero, zero)) for _ in range(1000): vert += choice(ccp_spokes) return vert # vertexes A = rand_vert() B = rand_vert() C = rand_vert() D = rand_vert()
def test_area_martian2(self): p = 3 * Qvector((2,1,0,1)) q = 4 * Qvector((2,1,1,0)) result = p.area(q) self.assertAlmostEqual(result, 12)
def rand_vert(): vert = Qvector((zero, zero, zero, zero)) for _ in range(1000): vert += choice(ccp_spokes) return vert
def twelve_around_one(p): twelve = [] for v in unique: trans_vector = Qvector(v) twelve.append(p + trans_vector) return twelve
""" import sqlite3 as sql from flextegrity import Cuboctahedron, Cube, Octahedron from flextegrity import Tetrahedron, InvTetrahedron, RD, Icosahedron import sys sys.path.append("/Users/kurner/Documents/Python5") from string import ascii_uppercase as AtoZ from qrays import Qvector import time, os # four spokes of a caltrop A = Qvector((1, 0, 0, 0)) B = Qvector((0, 1, 0, 0)) C = Qvector((0, 0, 1, 0)) D = Qvector((0, 0, 0, 1)) E, F, G, H = B + C + D, A + C + D, A + B + D, A + B + C # inverse tet I, J, K, L, M, N = A + B, A + C, A + D, B + C, B + D, C + D # octahedron O, P, Q, R, S, T = I + J, I + K, I + L, I + M, N + J, N + K # cuboctahedron U, V, W, X, Y, Z = N + L, N + M, J + L, L + M, M + K, K + J # ... class DB: backend = 'sqlite3' # default timezone = int(time.strftime("%z", time.localtime())) target_path = os.getcwd() # current directory db_name = ":file:" db_name = os.path.join(target_path, 'shapes_lib.db')
def test_quadrant(self): qA = Qvector((1, 0, 0, 0)) qB = Qvector((0, 1, 0, 0)) qC = Qvector((0, 0, 1, 0)) tet = make_tet(qA, qB, qC) self.assertAlmostEqual(tet[0], 0.25)
from polys_blender import Cuboctahedron, Cube, Octahedron from polys_blender import Tetrahedron, InvTetrahedron, RD, Icosahedron, Struts from polys_blender import twelve_around_one, draw_poly, draw_vert from qrays import Qvector from itertools import cycle import os import numpy as np import math from itertools import permutations g = permutations((2, 1, 1, 0)) UNIQUE = {p for p in g} # set comprehension IVM_DIRS = {Qvector(x) for x in UNIQUE} PHI = (1 + math.sqrt(5)) / 2 def ch(): ico = Icosahedron() * 2 cubo = Cuboctahedron() * 2 cub = Cube() * 2 rd = RD() * 2 tet = Tetrahedron() * 2 octa = Octahedron() * 2 draw_poly(ico) draw_poly(cubo) draw_poly(rd) draw_poly(cub) draw_poly(tet)
import bpy import sys sys.path.append("C:\\Users\\Kirby\\School_of_Tomorrow") from qrays import Qvector from functools import partial from itertools import permutations g = permutations((2, 1, 1, 0)) ORIGIN_IVM = Qvector((0, 0, 0, 0)) # set comprehension in list comprehension SPOKES_IVM = [Qvector(v) for v in {p for p in g}] nucleus = tuple([ORIGIN_IVM]) def next_layer(curr_layer, prev_layer): """ generates a next layer of FCC spheres by trying 12-around-1 for each in the current layer (curr_layer) but without keeping any duplicates i.e. discarding redundant sphere centers. """ next_layer = set() for qv in curr_layer: for bv in SPOKES_IVM: v_sum = qv + bv if (not v_sum in curr_layer and not v_sum in prev_layer): next_layer.add(v_sum) return sorted(list(next_layer))
def setUp(self): q1 = Qvector((1,0,0,0)) q2 = Qvector((0,1,0,0)) q3 = Qvector((0,0,1,0)) q4 = Qvector((0,0,0,1)) self.the_tet = Tetrahedron(q1,q2,q3,q4)