/
LaserGeometry.py
346 lines (332 loc) · 12.7 KB
/
LaserGeometry.py
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import turtle,math,random,pdb
TAU = 2 * math.pi
def equals(a, b, epsilon = 10 ** -2):
return abs(a - b) < epsilon
class Vector:
def __init__(self, *components):
self.components = components
def from_angle(theta, magnitude = 1):
return Vector(math.cos(theta) * magnitude, math.sin(theta) * magnitude)
def draw(self):
turtle.penup()
turtle.goto(self.components)
turtle.dot(3)
def indices(self):
return range(len(self))
def zip_map(self, other, func):
return [func(self[i], other[i]) for i in self.indices()]
def __str__(self):
if len(self) == 2:
return "{}i + {}j".format(*self.components)
else:
return str(self.components)
def __getitem__(self, index):
return self.components[index]
def __iter__(self):
return iter(self.components)
def __len__(self):
return len(self.components)
def __add__(self, other):
return Vector(*[self[i] + other[i] for i in self.indices()])
def __sub__(self, other):
return Vector(*[self[i] - other[i] for i in self.indices()])
def __neg__(self):
return self.mul(-1)
def mul(self, scalar):
return Vector(*map(lambda x: x*scalar, self.components))
def div(self, scalar):
return Vector(*map(lambda x: x/scalar, self.components))
def to_theta(self):
return math.atan2(self[1], self[0])
def magnitude(self):
return math.sqrt(sum([a * a for a in self]))
def dot(self, other):
return sum([self[i] * other[i] for i in self.indices()])
class Ray:
def __init__(self, start, direc):
self.start = start
self.direc = direc
def __str__(self):
return "Start: {}, Direction: {}".format(self.start, self.direc)
def point_on(self, u):
return Vector(self.start[0] + self.direc[0] * u, self.start[1] + self.direc[1] * u)
def intersect(self, other):
det = other.direc[0] * self.direc[1] - other.direc[1] * self.direc[0]
if det == 0: return None
dx = other.start[0] - self.start[0]
dy = other.start[1] - self.start[1]
u = (dy * other.direc[0] - dx * other.direc[1]) / det
v = (dy * self.direc[0] - dx * self.direc[1]) / det
if u < 0 or v < 0: return None
# pdb.set_trace()
return (self.start[0] + self.direc[0] * u, self.start[1] + self.direc[1] * u)
def reflect(self, normal, point):
direc = self.direc - normal.mul(2 * self.direc.dot(normal))
return Ray(point, direc)
def draw(self, limit = None):
if limit == None: limit = Vector(*turtle.screensize()).magnitude()
turtle.goto(self.start)
turtle.dot(4)
turtle.pendown()
turtle.radians()
turtle.setheading(self.direc.to_theta())
turtle.fd(limit)
class Segment:
def __init__(self, start, end):
self.start = start
self.end = end
def __str__(self):
return "{} to {}".format(self.start, self.end)
def intersect(self, ray):
# pdb.set_trace()
dx = self.end[0] - self.start[0]
dy = self.end[1] - self.start[1]
det = ray.direc[1]*dx - ray.direc[0]*dy
if det == 0: return None
v = (ray.direc[1] * (ray.start[0] - self.start[0]) - ray.direc[0] * (ray.start[1] - self.start[1])) / det
if 0 > v or v > 1: return None
u = None
try:
u = (self.start[0] + dx * v - ray.start[0]) / ray.direc[0]
except ZeroDivisionError:
try:
u = (self.start[1] + dy * v - ray.start[1]) / ray.direc[1]
except ZeroDivisionError:
raise ValueError("invalid ray direction vector: {}".format(ray))
if u < 0 or equals(u, 0): return None
return (self.start[0] + dx * v, self.start[1] + dy * v)
def pos_vec(self):
return Vector(*self.end) - Vector(*self.start)
def normal(self):
return Vector.from_angle(self.pos_vec().to_theta() + TAU / 4)
def draw(self):
turtle.goto(self.start)
turtle.pendown()
turtle.goto(self.end)
class Rect:
def __init__(self, x0, x1, y0, y1):
self.x0 = x0
self.x1 = x1
self.y0 = y0
self.y1 = y1
def all_corners(self):
yield (self.x0,self.y0)
yield (self.x1,self.y0)
yield (self.x1,self.y1)
yield (self.x0,self.y1)
def all_sides(self):
point = self.all_corners()
p_start = next(point)
p_prev = p_start
for p_next in point:
yield Segment(p_prev, p_next)
p_prev = p_next
yield Segment(p_prev, p_start)
def intersect(self, ray):
min_dist = None
point = None
for side in self.all_sides():
# pdb.set_trace()
p = side.intersect(ray)
if p == None: continue
dist = (Vector(*p) - ray.start).magnitude()
if min_dist == None or dist < min_dist:
min_dist = dist
point = p
return point
def get_side(self, point):
for side in self.all_sides:
if side.contains(point):
yield side
def normal_at_corner(self, point):
# the bottom left and upper right corners have normals at 45 degrees
if (equals(point[0], self.x0) and equals(point[1], self.y0)) or (equals(point[0], self.x1) and equals(point[1], self.y1)):
return Vector.from_angle(TAU/8)
# the bottom right and upper left corners have normals at 135 degrees
if (equals(point[0], self.x1) and equals(point[1], self.y0)) or (equals(point[0], self.x0) and equals(point[1], self.y1)):
return Vector.from_angle(3*TAU/8)
return None
def reflect_ray(self, ray):
# return the ray's reflection on this object, the point of reflection, and the distance of the point to the start of the ray
temp = []
for side in self.all_sides():
pnt = side.intersect(ray)
if pnt == None: continue
dist = (Vector(*pnt) - ray.start).magnitude()
if equals(0, dist): continue
temp.append((pnt,side,dist))
if len(temp) == 0: return None, None, None
pnt, side, dist = min(temp, key = lambda pnt_side_dist: pnt_side_dist[2])
# normals have slightly different behavior at the side
normal = self.normal_at_corner(pnt)
if normal == None:
normal = side.normal()
reflect = ray.reflect(normal, pnt)
return reflect, pnt, dist
def draw(self):
turtle.goto(self.x0,self.y1)
turtle.pendown()
for point in self.all_corners():
turtle.goto(point)
class Circle:
def __init__(self, center, radius):
self.center = center
self.radius = radius
def intersect(self, ray, epsilon = 2):
# return where the ray intersects this
dx = ray.start[0] - self.center[0]
dy = ray.start[1] - self.center[1]
# use quadratic formula
A = ray.direc[0]**2 + ray.direc[1]**2
B = 2*dx*ray.direc[0] + 2*dy*ray.direc[1]
C = dx*dx + dy*dy - self.radius*self.radius
discr = B*B - 4 * A * C
if discr < 0: return None # no solutions
if discr == 0:
u = -B / 2 / A # exactly one solution
else:
# 2 possible candidates
u1 = (-B + math.sqrt(discr)) / 2 / A
u2 = (-B - math.sqrt(discr)) / 2 / A
# negative or below a certain threshold are rejected
# otherwise choose the smallest one
if u1 < epsilon: u = u2
elif u2 < epsilon: u = u1
else: u = min(u1,u2)
if u < epsilon: return None
return ray.point_on(u)
def reflect_ray(self, ray):
# return the ray's reflection on this object, the point of reflection, and the distance of the point to the start of the ray
pnt = self.intersect(ray)
if pnt == None: return None, None, None
normal = Vector(*pnt) - self.center
normal = normal.div(normal.magnitude())
reflect = ray.reflect(normal, pnt)
dist = (Vector(*pnt) - ray.start).magnitude()
return reflect, pnt, dist
def draw(self):
turtle.setheading(0)
turtle.goto(self.center[0], self.center[1] - self.radius)
turtle.pendown()
turtle.circle(self.radius)
class MultiLine:
def __init__(self, points, step = None):
self.points = points
self.step = step
self.look_up = {}
for index, point in enumerate(points):
key = self.get_key(point)
try:
self.look_up[key].append(index)
except KeyError:
self.look_up[key] = [index]
def get_key(self, point):
return ((point[0] // self.step) * self.step, (point[1] // self.step) * self.step)
def get_nearest_point(self, point):
index = None
min_dist = None
key = self.get_key(point)
for dx in [-self.step, 0, self.step]:
for dy in [-self.step, 0, self.step]:
nkey = (key[0] + dx, key[1] + dy)
for candidate_index in self.look_up[nkey]:
dist = (point - self.points[candidate_index]).magnitude()
if min_dist == None or dist < min_dist:
min_dist = dist
ans_point = candidate_index
return candidate
def intersect(self, ray):
prev = self.points[0]
for point in self.points:
pass
def reflect_ray(self, ray):
pass
def draw(self):
turtle.penup()
turtle.goto(self.points[0])
turtle.pendown()
for point in self.points:
turtle.goto(point)
def rand_point(dampen = 1):
w,h = turtle.screensize()
x = w//2
y = h//2
return (random.randint(-x, x) * dampen, random.randint(-y,y) * dampen)
def rand_dir():
return Vector.from_angle(TAU * random.random())
def rand_ray():
return Ray(rand_point(dampen = 0.333), rand_dir())
def rand_rect():
x0,y0 = rand_point()
x1,y1 = rand_point()
if x0 > x1: x1,x0 = x0,x1
if y0 > y1: y1,y0 = y0,y1
return Rect(x0,x1,y0,y1)
def border_rect():
w,h = turtle.screensize()
x = w
y = h
return Rect(-x, x, -y, y)
def rand_circ():
return Circle(rand_point(), random.randint(10,100))
def rand_obj():
if random.randint(0,1) == 0:
return rand_rect()
else:
return rand_circ()
def draw_all(*drawables, colors = None):
for drawable in drawables:
turtle.penup()
if colors != None:
turtle.pencolor(*next(colors))
drawable.draw()
class World:
def create_random(obj_count = 3):
objs = [rand_obj() for i in range(obj_count)]
objs.append(border_rect())
return World(rand_ray(), objs)
def __init__(self, laser_ray_initial, objects, calculate = True):
self.objects = objects
self.laser_ray = laser_ray_initial
self.points = [laser_ray_initial.start]
self.calculated = False
self.calculate()
def bounce(self):
min_dist, new_ray, new_pnt = None, None, None
# for low numbers of points, it's fine to iterate over them
# instead implemented some hash-map like data structure
for thing in self.objects:
reflect, pnt, dist = thing.reflect_ray(self.laser_ray)
if reflect != None and (min_dist == None or dist < min_dist):
new_ray = reflect
min_dist = dist
new_pnt = pnt
return new_ray, new_pnt
def calculate(self, limit = 1000):
if self.calculated: return None
i = 0
self.free_end = True
new_ray, new_pnt = self.bounce()
while new_ray != None and new_pnt != None:
self.points.append(new_pnt)
self.laser_ray = new_ray
new_ray, new_pnt = self.bounce()
i += 1
if i >= limit:
self.free_end = False
break
self.calculated = True
def draw(self):
self.calculate()
turtle.pensize(width = 3)
draw_all(*self.objects)
turtle.penup()
turtle.pensize(width = 1)
for pnt in self.points:
turtle.goto(pnt)
turtle.pendown()
if self.free_end:
draw_all(self.laser_ray)
w = World.create_random()
w.draw()
#reflect, pnt, dist = rect.reflect_ray(ray)