def calculate(R, v, time_step, n_steps):
# G = 1
# M1 = 1
# M2 = 1
v_low = v / np.sqrt(2)
v_high = v * 2
v_third = v / 3
r1 = Vec3(-R, 0, 0)
r2 = Vec3(R, 0, 0)
v1 = Vec3(0, -v, 0)
v2 = Vec3(0, v, 0)
r1_data, r2_data = [], []
runge1, runge2 = [], []
eccentr1, eccentr2 = [], []
for i in range(n_steps + 1):
r1_data.append(r1)
r2_data.append(r2)
rlv1 = Vec3.cross(v1, Vec3.cross(r1, v1)) - r1
rlv2 = Vec3.cross(v2, Vec3.cross(r2, v2)) - r2
ecc1 = math.sqrt(rlv1.abs_sq())
ecc2 = math.sqrt(rlv2.abs_sq())
runge1.append(rlv1)
runge2.append(rlv2)
eccentr1.append(ecc1)
eccentr2.append(ecc2)
r1, r2, v1, v2 = step(r1, r2, v1, v2, time_step)
print("\rcalculation progress: t = {:.2f} / {:.2f} ({:.2f}%)".format(
i * time_step, n_steps * time_step, 100 * i / n_steps),
end="")
# return r1_data, r2_data, eccentr1, eccentr2
return r1, r2, v1, v2
def __init__(self,lookfrom,lookat,vup,vfov,aspect,aperture,focus_dist): self.lens_radius = aperture /2 theta = vfov * math.pi/180 half_height = math.tan(theta/2) half_width = aspect * half_height self.origin = lookfrom self.w = Vec3.unit_vector(lookfrom -lookat) self.u = Vec3.unit_vector(Vec3.cross(vup,self.w)) self.v = Vec3.cross(self.w,self.u) self.lower_left_corner = self.origin - half_width*focus_dist*self.u -half_height*focus_dist*self.v -focus_dist*self.w self.horizontal = 2*half_width*focus_dist*self.u self.vertical = 2*half_height*focus_dist*self.v
def __init__(self, lookfrom, lookat, vup, vfov, aspect, aperture,
focus_dist, t0, t1):
self.time0 = t0
self.time1 = t1
self.lens_radius = aperture / 2
theta = vfov * math.pi / 180
half_height = math.tan(theta / 2)
half_width = aspect * half_height
self.origin = lookfrom
self.w = Vec3.unit_vector(lookfrom - lookat)
self.u = Vec3.unit_vector(Vec3.cross(vup, self.w))
self.v = Vec3.cross(self.w, self.u)
self.lower_left_corner = self.origin - half_width * focus_dist * self.u - half_height * focus_dist * self.v - focus_dist * self.w
self.horizontal = 2 * half_width * focus_dist * self.u
self.vertical = 2 * half_height * focus_dist * self.v
def __init__(self,
look_from: Vec3 = Vec3(3.0, 3.0, 2.0),
look_at: Vec3 = Vec3(0.0, 0.0, -1.0),
vec_up: Vec3 = Vec3(0.0, 1.0, 0.0),
v_fov: float = 90.0,
aspect: float = 1.0,
aperture: float = 0.0,
focus_dist: float = 1.0):
self.lens_radius = aperture / 2.0
theta = v_fov * 3.14159 / 180.0
half_height = math.tan(theta / 2.0)
half_width = aspect * half_height
w = unit_vector(look_from - look_at)
self.u = unit_vector(vec_up.cross(w))
self.v = w.cross(self.u)
self.origin = look_from
self.upper_left_corner = look_from - \
half_width*self.u*focus_dist + \
half_height*self.v*focus_dist - w*focus_dist
self.horizontal = 2 * half_width * self.u * focus_dist
self.vertical = -2 * half_height * self.v * focus_dist
def createFromVectors(v1, v2):
""" Function createFromVectors expects two 3d vectors. Quat has the Sofa format i.e (x,y,z,w).
Examples:
>>> q = Quat.createFromVectors([1,0,0],[0,1,0])
>>> print(q)
[0.,0.,0.707,0.707]
"""
from quat import Quat
from vec3 import Vec3
from math import sqrt
q = Quat()
v = Vec3.cross(v1, v2)
q[0:3] = v
q[3] = sqrt((Vec3(v1).getNorm()**2) *
(Vec3(v2).getNorm()**2)) + Vec3.dot(v1, v2)
q.normalize()
return q
def get_normal(self):
return Vec3.cross(self.direction1, self.direction2).get_unit()
def leapfrog(R, v, time_step, n_steps):
r1 = Vec3(-R, 0, 0)
r2 = Vec3(R, 0, 0)
v1 = Vec3(0, -v, 0)
v2 = Vec3(0, v, 0)
r1_neu, r2_neu, v1, v2 = step(r1, r2, v1, v2, (time_step / 2))
r1_data, r2_data = [], []
runge1, runge2 = [], []
eccentr1, eccentr2 = [], []
r1_data.append(r1)
r2_data.append(r2)
rlv1 = Vec3.cross(v1, Vec3.cross(r1, v1)) - r1
rlv2 = Vec3.cross(v2, Vec3.cross(r2, v2)) - r2
ecc1 = math.sqrt(rlv1.abs_sq())
ecc2 = math.sqrt(rlv2.abs_sq())
runge1.append(rlv1)
runge2.append(rlv2)
eccentr1.append(ecc1)
eccentr2.append(ecc2)
for i in range(n_steps - 1):
r1, r2, v1, v2 = step1(r1, r2, v1, v2, time_step)
r1_data.append(r1)
r2_data.append(r2)
rlv1 = Vec3.cross(v1, Vec3.cross(r1, v1)) - r1
rlv2 = Vec3.cross(v2, Vec3.cross(r2, v2)) - r2
ecc1 = math.sqrt(rlv1.abs_sq())
ecc2 = math.sqrt(rlv2.abs_sq())
runge1.append(rlv1)
runge2.append(rlv2)
eccentr1.append(ecc1)
eccentr2.append(ecc2)
print("\rcalculation progress: t = {:.2f} / {:.2f} ({:.2f}%)".format(
i * time_step, n_steps * time_step, 100 * i / n_steps),
end="")
r1, r2, v1_neu, v2_neu = step(r1, r2, v1, v2, (time_step / 2))
r1_data.append(r1)
r2_data.append(r2)
rlv1 = Vec3.cross(v1, Vec3.cross(r1, v1)) - r1
rlv2 = Vec3.cross(v2, Vec3.cross(r2, v2)) - r2
ecc1 = math.sqrt(rlv1.abs_sq())
ecc2 = math.sqrt(rlv2.abs_sq())
runge1.append(rlv1)
runge2.append(rlv2)
eccentr1.append(ecc1)
eccentr2.append(ecc2)
return r1, r2, v1, v2
