def addVectors(a, b): # `a` and `b` must have the same lenght!
from vectormath import Vector3 as Vector3
return Vector3([a[i] + b[i] for i in range(len(a))])
import pyfabrik
from vectormath import Vector3
import numpy as np
import cv2
# Create a black image
img = np.zeros((500, 500, 3), np.uint8)
initial_joint_positions = [
Vector3(0, 0, 0),
Vector3(5, 2, 0),
Vector3(10, 2, 0),
Vector3(15, 0, 0)
]
tolerance = 0.01
# Initialize the Fabrik class (Fabrik, Fabrik2D or Fabrik3D)
fab = pyfabrik.Fabrik3D(initial_joint_positions, tolerance)
currentPosition = Vector3(15, 0, 0)
goalPosition = Vector3(10, 5, 0)
newGoalPosition = currentPosition
dx = (goalPosition[0] - currentPosition[0]) / 100
dy = (goalPosition[1] - currentPosition[1]) / 100
dz = (goalPosition[2] - currentPosition[2]) / 100
img_array = []
for i in range(1, 101):
img = np.zeros((500, 500, 3), np.uint8)
def getAtomsAtEquilibriumPositions():
import numpy as np
from math import sqrt, cos, sin, pi
import vectormath as vmath
from vectormath import Vector3 as Vector3
# BCC:
# A1 = Atom("Co", Vector3(1.0, 0.0, 0.0) )
# A2 = Atom("Co", Vector3(0.0, 1.0, 0.0) )
# A3 = Atom("Co", Vector3(0.0, 0.0, 1.0) )
# A4 = Atom("Co", Vector3(0.0, 0.0, 0.0) )
# A5 = Atom("Co", Vector3(1.0, 1.0, 0.0) )
# A6 = Atom("Co", Vector3(1.0, 0.0, 1.0) )
# A7 = Atom("Co", Vector3(0.0, 1.0, 1.0) )
# A8 = Atom("Co", Vector3(1.0, 1.0, 1.0) )
a = sqrt(2.0)
n = 3 # for a cuboid of n^3 atoms
ex = Vector3(1, 0, 0)
ey = Vector3(0, 1, 0)
ez = Vector3(0, 0, 1)
a1 = (a / 2) * (ex + ey)
a2 = (a / 2) * (ey + ez)
a3 = (a / 2) * (ex + ez)
lAtoms = []
for i in range(n):
for j in range(n):
for k in range(n):
vx = i * a1
vy = j * a2
vz = k * a3
lAtoms.append( Atom("H", vx + vy + vz, False, -1 ) )
# a = 0.978351 #0.982
# nMax = 5 #<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
#
# lAtoms = []
# for i in range(nMax):
# for j in range(nMax):
# # k = (i * nMax) + j
# x = i * a
# y = j * a
# lAtoms.append( Atom("H", Vector3(x, y, 0.0), False, -1 ) )
#
#
# A0 = Atom("Co", Vector3(0, 0, 0), False, -1 )
#
# # dist = a
# A1 = Atom("Co", Vector3(a, 0, 0), False, -1 )
# A2 = Atom("Co", Vector3(-a, 0, 0), False, -1 )
# A3 = Atom("Co", Vector3(0, a, 0), False, -1 )
# A4 = Atom("Co", Vector3(0, -a, 0), False, -1 )
#
# # dist = a*sqrt(2)
# lx = a
# ly = a
# A5 = Atom("Co", Vector3(lx, ly, 0), False, -1 )
# A6 = Atom("Co", Vector3(lx, -ly, 0), False, -1 )
# A7 = Atom("Co", Vector3(-lx, ly, 0), False, -1 )
# A8 = Atom("Co", Vector3(-lx, -ly,0), False, -1 )
#
# # dist = 2a
# l = 2 * a
# A9 = Atom("Co", Vector3( l, 0, 0), False, -1 ) #1
# A10 = Atom("Co", Vector3(-l, 0, 0), True, 9 ) #1
# A11 = Atom("Co", Vector3(0, l, 0), False, -1 ) #2
# A12 = Atom("Co", Vector3(0, -l, 0), True, 11 ) #2
#
# # dist = a*sqrt(5)
# lx = a
# ly = 2 * a
# A13 = Atom("Co", Vector3(lx, ly, 0), False, -1 ) #3
# A14 = Atom("Co", Vector3(lx, -ly, 0), True, 13 ) #3
# A15 = Atom("Co", Vector3(-lx, ly, 0), False, -1 ) #4
# A16 = Atom("Co", Vector3(-lx, -ly,0), True, 13 ) #4
#
# lx = 2 * a
# ly = a
# A17 = Atom("Co", Vector3(lx, ly, 0), False, -1 ) #5
# A18 = Atom("Co", Vector3(lx, -ly, 0), False, -1 ) #6
# A19 = Atom("Co", Vector3(-lx, ly, 0), True, 18 ) #5
# A20 = Atom("Co", Vector3(-lx, -ly,0), True, 17 ) #6
#
# lx = 2 * a
# ly = 2 * a
# A21 = Atom("Co", Vector3(lx, ly, 0), False, -1 ) #7
# A22 = Atom("Co", Vector3(lx, -ly, 0), True, 21 ) #7
# A23 = Atom("Co", Vector3(-lx, ly, 0), True, 21 ) #7
# A24 = Atom("Co", Vector3(-lx, -ly,0), True, 21 ) #7
#
#
# lAtoms = [A0, A1,A2,A3,A4, A5,A6,A7,A8,A9,A10,\
# A11,A12,A13,A14,A15,A16,A17,A18,A19,A20,\
# A21,A22,A23,A24]
#
#
#
# # lAtoms = [A1,A2,A3,A4,A5,A6,A7,A8]
# # lAtoms = [A1,A2,A3]
return lAtoms, a1, a2, a3
def facing(quat) -> Vector3:
"""Given a Unit Quaternion, return the Unit Vector of its direction."""
return rotate_vector(Vector3(0, 1, 0), quat)
def break_rotor(q: quaternion) -> Tuple[float, Vector3]:
"""Given a Unit Quaternion, break it into an angle and a Vector3."""
theta, v = 2 * np.arccos(q.w), []
axis = Vector3(*v)
return theta, axis
# Library imports
import argparse
import numpy as np
import vectormath as vm
from vectormath import Vector3
from pprint import pprint
from PIL import Image
import time
# Project imports
import raytracer as rt
m1 = rt.Material(diffuse=Vector3(0.7, 0.2, 0.5),
ambient=Vector3(0.3, 0.3, 0.3),
specular=Vector3(0.85, 0.85, 0.85),
reflective=Vector3(0.5, 0.2, 0.1),
phong_power=200)
m2 = rt.Material(diffuse=Vector3(0.5, 0.7, 0.4),
ambient=Vector3(0.3, 0.3, 0.3),
specular=Vector3(0.55, 0.55, 0.55),
reflective=Vector3(0.1, 0.3, 0.2),
phong_power=32)
m3 = rt.Material(diffuse=Vector3(0.1, 0.3, 0.7),
ambient=Vector3(0.3, 0.3, 0.3),
specular=Vector3(0.75, 0.75, 0.75),
reflective=Vector3(0.1, 0.2, 0.4),
phong_power=148)
m4 = rt.Material(diffuse=Vector3(0.4, 0.1, 0.6),
from math import degrees, radians
from typing import Tuple, Type, Union
from numba import jit
import numpy as np
from quaternion import quaternion
from vectormath import Vector3
NumpyVector: Type = Union[np.ndarray, Tuple[float, float, float]]
Quat: Type = Union[quaternion, Tuple[float, float, float, float]]
EAST = Vector3(1, 0, 0)
WEST = Vector3(-1, 0, 0)
NORTH = Vector3(0, 1, 0)
SOUTH = Vector3(0, -1, 0)
ZENITH = Vector3(0, 0, 1)
NADIR = Vector3(0, 0, -1)
###===---
# COORDINATE TRANSFORMATIONS
###===---
@jit(nopython=True)
def to_spherical(x: float, y: float, z: float) -> Tuple[float, float, float]:
"""Convert three-dimensional Cartesian Coordinates to Spherical."""
rho = np.sqrt(np.sum(np.square(np.array((x, y, z)))))
theta = 90 - degrees(np.arccos(z / rho)) if rho else 0
phi = (0 if theta == 90 or theta == -90 else
def velocity(self, value: np.ndarray):
self._vel: Vector3 = Vector3(value)
from raymarch import * from raymarch.shapes import Sphere from vectormath import Vector3 # create some spheres shapes = [Sphere(Vector3(0,0,0), 1), Sphere(Vector3(1,0,0), 0.5, [255, 100, 100]), Sphere(Vector3(-1,0,0), 0.5, [100,100,255])] # create the camera camera = Camera(1080, 720, 90, Vector3(0, 3, 0), Vector3(0, -1, 0)) # create the scene with a black background # if you want, you can specify a special norm by specifing p_norm=1 (or any other value > 0) scene = Scene(camera, shapes, [0,0,0]) # set the number of threads you want to spawn #scene.poolsize = 4 # draw the scene scene.draw()
def velocity(self) -> Vector3:
"""Go into the relevant Space structure and retrieve the Velocity that
is assigned to this FoR, and wrap it in a Vector3.
"""
return Vector3(self.domain.array_velocity[self.index])
def position(self, value: np.ndarray):
self._pos: Vector3 = Vector3(value)
def position(self) -> Vector3:
"""Go into the relevant Space structure and retrieve the Position that
is assigned to this FoR, and wrap it in a Vector3.
"""
return Vector3(self.domain.array_position[self.index])
def simplest_scene():
cam = default_camera()
lights = [rt.Light(cam.position, Vector3(.9, .9, .9))]
spheres = [rt.Sphere(Vector3(0.0, 0.0, 0.0), .5, m1)]
return rt.Scene(cam, lights, spheres, background=Vector3(0.3, 0.3, 0.3))
def default_camera():
return rt.Camera(position=Vector3(0., 0., 6.),
look_at=Vector3(0., 0., 0.),
up=Vector3(0.0, 1.0, 0.0),
right=Vector3(1.0, 0.0, 0.0))
# moves are performed... more info about how to do the last part.
# select a starting configuration:
#e, X = Emin, lAtomsEquilibrium
# e, X = Emin, [lAtomsEquilibrium[i].position for i in range(len(lAtomsEquilibrium))]
import copy
# structEq
# convert 'structX' to a simple array of coordinates `X`:
# Xeq = [list(structEq[i].coords) for i in range(structEq.num_sites)]
Xeq = [list(structEq[i].frac_coords) for i in range(structEq.num_sites)]
from vectormath import Vector3 as Vector3
Xeq = [
Vector3(list(structEq[i].frac_coords)) for i in range(structEq.num_sites)
]
# Xeq
X = copy.deepcopy(Xeq)
# X
# structEq[0]
# structEq[0].coords
# structEq[0].frac_coords
e = Emin
X = copy.deepcopy(Xeq)
# Main Reverse Energy Partitioning loop:
#L = 0.005 #0.05 #0.1 #0.01 #0.01 #0.2 #0.5 # 0.1# ~amplitud of random walk
def plot_spherical(
ax: Axes3D,
x: float,
y: float,
z: float,
*,
arcs_primary: bool = False,
label_primary: bool = False,
arcs_secondary: bool = False,
cartesian_trace: bool = False,
angle_square: bool = False,
mark_final: bool = True,
):
rho, theta, phi = to_spherical(x, y, z)
color_rho = "red"
color_theta = "green"
color_phi = "blue"
grey = "#777777"
seg = 15
w = 0.1
def mark(x_, y_, z_, label: str = None):
ax.text(
x_,
y_,
z_,
(label or " {}").format(point(x_, y_, z_)),
)
def plot(*points: Tuple[float, float, float], **kw):
points = np.array(points)
return ax.plot(points[..., 0], points[..., 1], points[..., 2], **kw)
arc_theta = lambda d=1: starmap(from_spherical, (
(rho * d, (theta / seg * i), phi) for i in range(seg + 1)))
arc_phi = lambda d=1: starmap(from_spherical, (
(rho * d, 0, (phi / seg * i)) for i in range(seg + 1)))
# Y-axis Line.
if arcs_primary:
plot((0, rho, 0), (0, 0, 0), c=grey)
elif arcs_secondary:
plot((0, rho * 0.5, 0), (0, 0, 0), c=grey)
# Coordinate Triangle.
if cartesian_trace:
plot(
(x, y, z), # Endpoint.
(x, y, 0), # Below Endpoint.
(x, 0, 0), # Endpoint on X-Axis.
(0, 0, 0), # Origin.
c=grey,
)
# Right Angle.
if angle_square:
angle_off = min(abs(x * w), abs(y * w), abs(z * w))
plot(
(x, y, angle_off),
(x, y - angle_off, angle_off),
(x, y - angle_off, 0),
c=grey,
)
# mark(x, 0, 0) # Endpoint on X-Axis.
# mark(x, y, 0) # Below Endpoint.
# SECONDARY Labels.
if arcs_secondary:
ax.text(0, rho * 0.52, 0, "ρ", c="black")
ax.text(*from_spherical(rho * 0.52, (theta / 2), phi), "θ", c="black")
ax.text(*from_spherical(rho * 0.52, 0, (phi / 2)), "φ", c="black")
plot(*arc_theta(0.5), c=grey) # GREY Theta Arc.
plot(*arc_phi(0.5), c=grey) # GREY Phi Arc.
if arcs_primary:
plot(*arc_theta(), c=color_theta) # Theta Arc.
plot(*arc_phi(), c=color_phi) # Phi Arc.
plot((0, 0, 0), (x, y, z), c=color_rho)
plot(
(0, 0, 0), # Origin.
Vector3(x, y, 0).normalize() * rho, # Point where Theta=0.
c=grey,
)
# PRIMARY Labels.
if label_primary:
ax.text(
x,
y,
z,
f"ρ ({np.round(rho, 2)})",
c=color_rho,
fontsize=12,
horizontalalignment="right",
verticalalignment="bottom",
)
ax.text(
*from_spherical(rho, (theta / 2), phi),
f"θ ({np.round(theta, 2)}°)",
c=color_theta,
fontsize=12,
horizontalalignment="left",
verticalalignment="bottom",
)
ax.text(
*from_spherical(rho, 0, (phi / 2)),
f"φ ({np.round(phi, 2)}°)",
c=color_phi,
fontsize=12,
horizontalalignment="left",
verticalalignment="bottom",
)
if mark_final:
mark(x, y, z, f"{{}}\n{point(rho, theta, phi)}") # Endpoint.
def test_value_error_raised_when_joints_overlap():
poss = [Vector3(0, 0, 0), Vector3(10, 0, 0), Vector3(10, 0, 0)]
with pytest.raises(ValueError) as exinfo:
fab = Fabrik3D(poss, 0.01)
assert str(exinfo.value) == "link lengths must be > 0"
def test_value_error_raised_when_tolerance_isnt_positive(tolerance):
poss = [Vector3(0, 0, 0), Vector3(10, 0, 0), Vector3(10, 0, 0)]
with pytest.raises(ValueError) as exinfo:
fab = Fabrik3D(poss, tolerance)
assert str(exinfo.value) == "tolerance must be > 0"