def radial_slice(points, center, start_angle, end_angle):
"""
>>> points = circle((0, 0), 2.3)
>>> print(format_points(offset_points(points)))
###
#####
#####
#####
###
>>> points = radial_slice(points, (0, 0), -90, 45)
>>> print(format_points(offset_points(points)))
##
###
###
##
>>> points = radial_slice(points, (0, 0), 0, 30)
>>> print(format_points(offset_points(points)))
#
###
"""
start_point = (1, 0)
start_point = vec.rotate(start_point, math.radians(start_angle))
start_point = vec.add(center, start_point)
start_line = (start_point, center) # Pointing inward, so partition goes counter-clockwise.
end_point = (1, 0)
end_point = vec.rotate(end_point, math.radians(end_angle))
end_point = vec.add(center, end_point)
end_line = (center, end_point) # Pointing outward, so partition goes clockwise.
return (
set(partition(points, *start_line)) &
set(partition(points, *end_line))
)
def arc_to(self, endpoint, center=None, start_slant=None, end_slant=None):
"""
Draw an arc ending at the specified point, starting tangent to the
current position and heading.
"""
if points_equal(self._position, endpoint):
return
# Handle unspecified center.
# We need to find the center of the arc, so we can find its radius. The
# center of this arc is uniquely defined by the intersection of two
# lines:
# 1. The first line is perpendicular to the pen heading, passing
# through the pen position.
# 2. The second line is the perpendicular bisector of the pen position
# and the target arc end point.
v_pen = self._vector()
v_perp = vec.perp(self._vector())
v_chord = vec.vfrom(self._position, endpoint)
if center is None:
midpoint = vec.div(vec.add(self._position, endpoint), 2)
v_bisector = vec.perp(v_chord)
center = intersect_lines(
self._position,
vec.add(self._position, v_perp),
midpoint,
vec.add(midpoint, v_bisector),
)
# Determine true start heading. This may not be the same as the
# original pen heading in some circumstances.
assert not points_equal(center, self._position)
v_radius_start = vec.vfrom(center, self._position)
v_radius_perp = vec.perp(v_radius_start)
if vec.dot(v_radius_perp, v_pen) < 0:
v_radius_perp = vec.neg(v_radius_perp)
start_heading = math.degrees(vec.heading(v_radius_perp))
self.turn_to(start_heading)
# Refresh v_pen and v_perp based on the new start heading.
v_pen = self._vector()
v_perp = vec.perp(self._vector())
# Calculate the arc angle.
# The arc angle is double the angle between the pen vector and the
# chord vector. Arcing to the left is a positive angle, and arcing to
# the right is a negative angle.
arc_angle = 2 * math.degrees(vec.angle(v_pen, v_chord))
radius = vec.mag(v_radius_start)
# Check which side of v_pen the goes toward.
if vec.dot(v_chord, v_perp) < 0:
arc_angle = -arc_angle
radius = -radius
self._arc(
center,
radius,
endpoint,
arc_angle,
start_slant,
end_slant,
)
def update_snowballs(lobby):
changed_healths = []
destroyed_snowballs = []
player_hit = False
ground_hit = False
for id, snowball in lobby.snowballs.items():
new_vel = vec.add(snowball.velocity, (0, GRAVITY_ACCELERATION))
new_pos = vec.add(snowball.position, new_vel)
new_x, new_y = new_pos
hit_object, can_move = level.can_move_to(SNOWBALL_SIZE, SNOWBALL_SIZE,
round(new_x), round(new_y),
all_players(lobby.clients))
if can_move:
snowball.velocity = new_vel
snowball.position = new_pos
else:
destroyed_snowballs.append(id)
if isinstance(hit_object, player.Player):
player_hit = True
speed = vec.length(snowball.velocity)
hit_object.health = max(
0, hit_object.health - speed * SNOWBALL_DAMAGE)
changed_healths.append(hit_object)
else:
ground_hit = True
lobby.snowballs = {
id: v
for id, v in lobby.snowballs.items() if id not in destroyed_snowballs
}
return changed_healths, destroyed_snowballs, player_hit, ground_hit
def arc_to(self, endpoint, center=None, start_slant=None, end_slant=None):
"""
Draw an arc ending at the specified point, starting tangent to the
current position and heading.
"""
if points_equal(self._position, endpoint):
return
# Handle unspecified center.
# We need to find the center of the arc, so we can find its radius. The
# center of this arc is uniquely defined by the intersection of two
# lines:
# 1. The first line is perpendicular to the pen heading, passing
# through the pen position.
# 2. The second line is the perpendicular bisector of the pen position
# and the target arc end point.
v_pen = self._vector()
v_perp = vec.perp(self._vector())
v_chord = vec.vfrom(self._position, endpoint)
if center is None:
midpoint = vec.div(vec.add(self._position, endpoint), 2)
v_bisector = vec.perp(v_chord)
center = intersect_lines(
self._position,
vec.add(self._position, v_perp),
midpoint,
vec.add(midpoint, v_bisector),
)
# Determine true start heading. This may not be the same as the
# original pen heading in some circumstances.
assert not points_equal(center, self._position)
v_radius_start = vec.vfrom(center, self._position)
v_radius_perp = vec.perp(v_radius_start)
if vec.dot(v_radius_perp, v_pen) < 0:
v_radius_perp = vec.neg(v_radius_perp)
start_heading = math.degrees(vec.heading(v_radius_perp))
self.turn_to(start_heading)
# Refresh v_pen and v_perp based on the new start heading.
v_pen = self._vector()
v_perp = vec.perp(self._vector())
# Calculate the arc angle.
# The arc angle is double the angle between the pen vector and the
# chord vector. Arcing to the left is a positive angle, and arcing to
# the right is a negative angle.
arc_angle = 2 * math.degrees(vec.angle(v_pen, v_chord))
radius = vec.mag(v_radius_start)
# Check which side of v_pen the goes toward.
if vec.dot(v_chord, v_perp) < 0:
arc_angle = -arc_angle
radius = -radius
self._arc(
center,
radius,
endpoint,
arc_angle,
start_slant,
end_slant,
)
def update(self, elapsed_seconds, force=None, extra_drag=0):
# Apply force if necessary.
if force is not None:
self.velocity = vec.add(
self.velocity,
vec.mul(force, (elapsed_seconds / self.mass)),
)
# Apply drag.
# Decrease the magnitude of the velocity vector by
# the amount of drag.
drag = (self.drag_rate + extra_drag) * elapsed_seconds
if drag > self.speed:
self.velocity = (0, 0)
elif drag != 0 and self.velocity != (0, 0):
drag_vector = vec.norm(self.velocity, -drag)
self.velocity = vec.add(
self.velocity,
drag_vector,
)
# Limit to maximum speed.
if self.speed > c.max_speed:
self.velocity = vec.norm(self.velocity, c.max_speed)
# Update position based on velocity.
self.last_pos = self.pos
self.pos = vec.add(
self.pos,
vec.mul(self.velocity, elapsed_seconds),
)
def collide_particles(p1, p2):
restitution = p1.restitution * p2.restitution
# Don't collide immovable particles.
if p1.immovable and p2.immovable:
return
# Test if p1 and p2 are actually intersecting.
if not intersect(p1, p2):
return
# If one particle is immovable, make it the first one.
if not p1.immovable and p2.immovable:
p1, p2 = p2, p1
# Vector spanning between the centers, normal to contact surface.
v_span = vec.vfrom(p1.pos, p2.pos)
# Split into normal and tangential components and calculate
# initial velocities.
normal = vec.norm(v_span)
tangent = vec.perp(normal)
v1_tangent = vec.proj(p1.velocity, tangent)
v2_tangent = vec.proj(p2.velocity, tangent)
p1_initial = vec.dot(p1.velocity, normal)
p2_initial = vec.dot(p2.velocity, normal)
# Don't collide if particles were actually moving away from each other, so
# they don't get stuck inside one another.
if p1_initial - p2_initial < 0:
return
# Handle immovable particles specially.
if p1.immovable:
p2_final = -p2_initial * restitution
p2.velocity = vec.add(
v2_tangent,
vec.mul(normal, p2_final),
)
return
# Elastic collision equations along normal component.
m1, m2 = p1.mass, p2.mass
m1plusm2 = (m1 + m2) / restitution
p1_final = (p1_initial * (m1 - m2) / m1plusm2 + p2_initial *
(2 * m2) / m1plusm2)
p2_final = (p2_initial * (m2 - m1) / m1plusm2 + p1_initial *
(2 * m1) / m1plusm2)
# Tangential component is unchanged, recombine.
p1.velocity = vec.add(
v1_tangent,
vec.mul(normal, p1_final),
)
p2.velocity = vec.add(
v2_tangent,
vec.mul(normal, p2_final),
)
def update_physics(self, elapsed_seconds):
# Handle turning.
if self.turning_time >= c.player_start_turn_time:
turn_rate = c.player_turn_rate_radians
else:
turn_rate = interpolate(
c.player_start_turn_rate_radians,
c.player_turn_rate_radians,
self.turning_time / c.player_start_turn_time,
)
self.heading += self.turn_direction * turn_rate * elapsed_seconds
self.direction = heading_to_vector(self.heading)
# Handle thrust.
force = (0, 0)
if self.do_thrust:
# We vary the thrust depending on how fast the player is
# already moving.
thrust = curve_value(self.speed, c.player_thrust_curve)
force = vec.add(
force,
vec.mul(self.direction, thrust),
)
# Handle braking.
extra_drag = 0
if self.do_brake:
extra_drag = c.player_braking_drag
# Handle boost.
if self.boost_time_remaining > 0.0:
force = vec.add(
force,
vec.mul(self.direction, c.player_boost_strength),
)
# Get heavy while boosting.
if self.boost_heavy_time_remaining > 0.0:
self.mass = self.original_mass * c.player_boost_heavy_multiplier
self.restitution = (
self.original_restitution *
c.player_boost_restitution_multiplier
)
else:
self.mass = self.original_mass
self.restitution = self.original_restitution
# Handle rudder.
self.rudder_force = (0, 0)
if self.velocity != (0, 0):
# Only use the rudder if the player is thrusting or turning.
if self.do_thrust or self.turn_direction != 0:
self.rudder_force = self.calc_rudder_force()
force = vec.add(force, self.rudder_force)
return force, extra_drag
def update_physics(self, elapsed_seconds):
# Handle turning.
if self.turning_time >= c.player_start_turn_time:
turn_rate = c.player_turn_rate_radians
else:
turn_rate = interpolate(
c.player_start_turn_rate_radians,
c.player_turn_rate_radians,
self.turning_time / c.player_start_turn_time,
)
self.heading += self.turn_direction * turn_rate * elapsed_seconds
self.direction = heading_to_vector(self.heading)
# Handle thrust.
force = (0, 0)
if self.do_thrust:
# We vary the thrust depending on how fast the player is
# already moving.
thrust = curve_value(self.speed, c.player_thrust_curve)
force = vec.add(
force,
vec.mul(self.direction, thrust),
)
# Handle braking.
extra_drag = 0
if self.do_brake:
extra_drag = c.player_braking_drag
# Handle boost.
if self.boost_time_remaining > 0.0:
force = vec.add(
force,
vec.mul(self.direction, c.player_boost_strength),
)
# Get heavy while boosting.
if self.boost_heavy_time_remaining > 0.0:
self.mass = self.original_mass * c.player_boost_heavy_multiplier
self.restitution = (self.original_restitution *
c.player_boost_restitution_multiplier)
else:
self.mass = self.original_mass
self.restitution = self.original_restitution
# Handle rudder.
self.rudder_force = (0, 0)
if self.velocity != (0, 0):
# Only use the rudder if the player is thrusting or turning.
if self.do_thrust or self.turn_direction != 0:
self.rudder_force = self.calc_rudder_force()
force = vec.add(force, self.rudder_force)
return force, extra_drag
def set_slants(self, start_slant, end_slant):
if start_slant is not None:
start_slant = Heading(start_slant)
if end_slant is not None:
end_slant = Heading(end_slant)
self.start_slant = start_slant
self.end_slant = end_slant
# Intersect the slant lines with the left and right offset circles
# to find the corners.
center_left, radius_left = self.offset_circle_left()
center_right, radius_right = self.offset_circle_right()
# Start corners.
if start_slant is None:
v_slant = vec.vfrom(self.center, self.a)
else:
v_slant = vec.from_heading(start_slant.rad)
a = self.a
b = vec.add(self.a, v_slant)
points_left = intersect_circle_line(center_left, radius_left, a, b)
points_right = intersect_circle_line(center_right, radius_right, a, b)
if len(points_left) == 0 or len(points_right) == 0:
self.start_joint_illegal = True
return
self.a_left = Point(*closest_point_to(self.a, points_left))
self.a_right = Point(*closest_point_to(self.a, points_right))
# End corners.
if end_slant is None:
v_slant = vec.vfrom(self.center, self.b)
else:
v_slant = vec.from_heading(end_slant.rad)
a = self.b
b = vec.add(self.b, v_slant)
points_left = intersect_circle_line(center_left, radius_left, a, b)
points_right = intersect_circle_line(center_right, radius_right, a, b)
if len(points_left) == 0 or len(points_right) == 0:
self.end_joint_illegal = True
return
self.b_left = Point(*closest_point_to(self.b, points_left))
self.b_right = Point(*closest_point_to(self.b, points_right))
self.check_degenerate_segment()
def set_slants(self, start_slant, end_slant):
if start_slant is not None:
start_slant = Heading(start_slant)
if end_slant is not None:
end_slant = Heading(end_slant)
self.start_slant = start_slant
self.end_slant = end_slant
# Intersect the slant lines with the left and right offset circles
# to find the corners.
center_left, radius_left = self.offset_circle_left()
center_right, radius_right = self.offset_circle_right()
# Start corners.
if start_slant is None:
v_slant = vec.vfrom(self.center, self.a)
else:
v_slant = vec.from_heading(start_slant.rad)
a = self.a
b = vec.add(self.a, v_slant)
points_left = intersect_circle_line(center_left, radius_left, a, b)
points_right = intersect_circle_line(center_right, radius_right, a, b)
if len(points_left) == 0 or len(points_right) == 0:
self.start_joint_illegal = True
return
self.a_left = Point(*closest_point_to(self.a, points_left))
self.a_right = Point(*closest_point_to(self.a, points_right))
# End corners.
if end_slant is None:
v_slant = vec.vfrom(self.center, self.b)
else:
v_slant = vec.from_heading(end_slant.rad)
a = self.b
b = vec.add(self.b, v_slant)
points_left = intersect_circle_line(center_left, radius_left, a, b)
points_right = intersect_circle_line(center_right, radius_right, a, b)
if len(points_left) == 0 or len(points_right) == 0:
self.end_joint_illegal = True
return
self.b_left = Point(*closest_point_to(self.b, points_left))
self.b_right = Point(*closest_point_to(self.b, points_right))
self.check_degenerate_segment()
def set_slants(self, start_slant, end_slant):
if start_slant is not None:
start_slant = Heading(start_slant)
if end_slant is not None:
end_slant = Heading(end_slant)
self.start_slant = start_slant
self.end_slant = end_slant
# Intersect the slant lines with the left and right offset lines
# to find the corners.
line_left = self.offset_line_left()
line_right = self.offset_line_right()
# Start corners.
if start_slant is None:
v_slant = vec.perp(self._vector())
else:
v_slant = vec.from_heading(start_slant.rad)
a = self.a
b = vec.add(self.a, v_slant)
left = intersect_lines(a, b, line_left[0], line_left[1])
right = intersect_lines(a, b, line_right[0], line_right[1])
if left is None or right is None:
self.start_joint_illegal = True
else:
self.a_left = Point(*left)
self.a_right = Point(*right)
# End corners.
if end_slant is None:
v_slant = vec.perp(self._vector())
else:
v_slant = vec.from_heading(end_slant.rad)
a = self.b
b = vec.add(self.b, v_slant)
left = intersect_lines(a, b, line_left[0], line_left[1])
right = intersect_lines(a, b, line_right[0], line_right[1])
if left is None or right is None:
self.end_joint_illegal = True
else:
self.b_left = Point(*left)
self.b_right = Point(*right)
# Done, make sure we didn't cross
self.check_degenerate_segment()
def intersect_circles(center1, radius1, center2, radius2):
radius1 = abs(radius1)
radius2 = abs(radius2)
if radius2 > radius1:
return intersect_circles(center2, radius2, center1, radius1)
transverse = vec.vfrom(center1, center2)
dist = vec.mag(transverse)
# Check for identical or concentric circles. These will have either
# no points in common or all points in common, and in either case, we
# return an empty list.
if points_equal(center1, center2):
return []
# Check for exterior or interior tangent.
radius_sum = radius1 + radius2
radius_difference = abs(radius1 - radius2)
if (float_equal(dist, radius_sum) or float_equal(dist, radius_difference)):
return [
vec.add(center1, vec.norm(transverse, radius1)),
]
# Check for non intersecting circles.
if dist > radius_sum or dist < radius_difference:
return []
# If we've reached this point, we know that the two circles intersect
# in two distinct points.
# Reference:
# http://mathworld.wolfram.com/Circle-CircleIntersection.html
# Pretend that the circles are arranged along the x-axis.
# Find the x-value of the intersection points, which is the same for both
# points. Then find the chord length "a" between the two intersection
# points, and use vector math to find the points.
dist2 = vec.mag2(transverse)
x = (dist2 - radius2**2 + radius1**2) / (2 * dist)
a = ((1 / dist) * sqrt(
(-dist + radius1 - radius2) * (-dist - radius1 + radius2) *
(-dist + radius1 + radius2) * (dist + radius1 + radius2)))
chord_middle = vec.add(
center1,
vec.norm(transverse, x),
)
perp = vec.perp(transverse)
return [
vec.add(chord_middle, vec.norm(perp, a / 2)),
vec.add(chord_middle, vec.norm(perp, -a / 2)),
]
def set_slants(self, start_slant, end_slant):
if start_slant is not None:
start_slant = Heading(start_slant)
if end_slant is not None:
end_slant = Heading(end_slant)
self.start_slant = start_slant
self.end_slant = end_slant
# Intersect the slant lines with the left and right offset lines
# to find the corners.
line_left = self.offset_line_left()
line_right = self.offset_line_right()
# Start corners.
if start_slant is None:
v_slant = vec.perp(self._vector())
else:
v_slant = vec.from_heading(start_slant.rad)
a = self.a
b = vec.add(self.a, v_slant)
left = intersect_lines(a, b, line_left[0], line_left[1])
right = intersect_lines(a, b, line_right[0], line_right[1])
if left is None or right is None:
self.start_joint_illegal = True
else:
self.a_left = Point(*left)
self.a_right = Point(*right)
# End corners.
if end_slant is None:
v_slant = vec.perp(self._vector())
else:
v_slant = vec.from_heading(end_slant.rad)
a = self.b
b = vec.add(self.b, v_slant)
left = intersect_lines(a, b, line_left[0], line_left[1])
right = intersect_lines(a, b, line_right[0], line_right[1])
if left is None or right is None:
self.end_joint_illegal = True
else:
self.b_left = Point(*left)
self.b_right = Point(*right)
# Done, make sure we didn't cross
self.check_degenerate_segment()
def rebound(self, normal, point=None, restitution=1):
# Split into normal and tangential components.
tangent = vec.perp(normal)
v_tangent = vec.proj(self.velocity, tangent)
v_normal = vec.proj(self.velocity, normal)
# Invert normal component and recombine, with restitution.
v_normal = vec.neg(v_normal)
self.velocity = vec.add(v_tangent, vec.mul(v_normal, restitution))
# If the particle is partially inside the wall, move it out.
if point is not None:
v = vec.vfrom(point, self.pos)
if vec.mag2(v) < self.radius ** 2:
v = vec.norm(v, self.radius)
self.pos = vec.add(point, v)
def intersect_lines(a, b, c, d, segment=False):
"""
Find the intersection of lines a-b and c-d.
If the "segment" argument is true, treat the lines as segments, and check
whether the intersection point is off the end of either segment.
"""
# Reference:
# http://geomalgorithms.com/a05-_intersect-1.html
u = vec.vfrom(a, b)
v = vec.vfrom(c, d)
w = vec.vfrom(c, a)
u_perp_dot_v = vec.dot(vec.perp(u), v)
if float_equal(u_perp_dot_v, 0):
return None # We have collinear segments, no single intersection.
v_perp_dot_w = vec.dot(vec.perp(v), w)
s = v_perp_dot_w / u_perp_dot_v
if segment and (s < 0 or s > 1):
return None
u_perp_dot_w = vec.dot(vec.perp(u), w)
t = u_perp_dot_w / u_perp_dot_v
if segment and (t < 0 or t > 1):
return None
return vec.add(a, vec.mul(u, s))
def intersect_lines(a, b, c, d, segment=False):
"""
Find the intersection of lines a-b and c-d.
If the "segment" argument is true, treat the lines as segments, and check
whether the intersection point is off the end of either segment.
"""
# Reference:
# http://geomalgorithms.com/a05-_intersect-1.html
u = vec.vfrom(a, b)
v = vec.vfrom(c, d)
w = vec.vfrom(c, a)
u_perp_dot_v = vec.dot(vec.perp(u), v)
if float_equal(u_perp_dot_v, 0):
return None # We have collinear segments, no single intersection.
v_perp_dot_w = vec.dot(vec.perp(v), w)
s = v_perp_dot_w / u_perp_dot_v
if segment and (s < 0 or s > 1):
return None
u_perp_dot_w = vec.dot(vec.perp(u), w)
t = u_perp_dot_w / u_perp_dot_v
if segment and (t < 0 or t > 1):
return None
return vec.add(a, vec.mul(u, s))
def put(position, velocity, storage_offset, stack, stack_of_stacks, push_mode, program):
y = stack_pop(stack)
x = stack_pop(stack)
v = stack_pop(stack)
location = vec.add((x, y), storage_offset)
program.set(location, chr(v))
return position, velocity, storage_offset, stack, stack_of_stacks, push_mode, program, True
def arc_left(
self, arc_angle, radius=None, center=None, start_slant=None, end_slant=None,
):
if (
(radius is None and center is None)
or (radius is not None and center is not None)
):
raise TypeError('You must specify exactly one of center or radius.')
arc_angle = Angle(arc_angle)
# Create a radius vector, which is a vector from the arc center to the
# current position. Subtract to find the center, then rotate the radius
# vector to find the arc end point.
if center is None:
if arc_angle < 0:
radius = -abs(radius)
v_radius = vec.neg(vec.perp(self._vector(radius)))
center = vec.sub(self._position, v_radius)
elif radius is None:
v_radius = vec.vfrom(center, self._position)
radius = vec.mag(v_radius)
if arc_angle < 0:
radius = -radius
endpoint = vec.add(center, vec.rotate(v_radius, arc_angle.rad))
self._arc(
center,
radius,
endpoint,
arc_angle,
start_slant=start_slant,
end_slant=end_slant,
)
def update(s, gs, dt):
#print(s.vel)
if s.thrusting:
force = s.thrustForce * dt
facing = vec.fromAngle(s.facing + 180)
f = vec.mul(facing, force)
s.applyForce(f)
offset = vec.fromAngle(s.facing)
offset = vec.mul(offset, s.radius)
loc = vec.add(s.loc, offset)
# v = vec.invert(s.vel)
s.driveEmitter.emit(gs, dt, loc, s.facing, vel=s.vel)
if not s.engineSoundPlayer.playing:
s.engineSoundPlayer.seek(0.0)
s.engineSoundPlayer.eos_action = s.engineSoundPlayer.EOS_LOOP
s.engineSoundPlayer.play()
else:
s.engineSoundPlayer.eos_action = s.engineSoundPlayer.EOS_PAUSE
# Turning should be either 0, -1 or +1
if s.turning != 0:
force = s.turnForce * dt * s.turning
s.applyRforce(force)
Planet.update(s, gs, dt)
def GF2_span(D, L):
'''
>>> from GF2 import one
>>> D = {'a', 'b', 'c'}
>>> L = [Vec(D, {'a': one, 'c': one}), Vec(D, {'b': one})]
>>> len(GF2_span(D, L))
4
>>> Vec(D, {}) in GF2_span(D, L)
True
>>> Vec(D, {'b': one}) in GF2_span(D, L)
True
>>> Vec(D, {'a':one, 'c':one}) in GF2_span(D, L)
True
>>> Vec(D, {x:one for x in D}) in GF2_span(D, L)
True
'''
l = []
multiplied =[]
for e in L:
a= scalar_mul(e, 0)
multiplied.append(a)
b = scalar_mul(e, 1)
multiplied.append(b)
for i in multiplied:
for j in multiplied:
final = add(i,j)
if final not in l:
l.append(final)
return l
def draw(self, screen):
self.surface.lock()
self.surface.fill(self.clear)
pg.draw.line(
self.surface,
self.green,
(14-10, 14),
(14+10, 14),
2,
)
pg.draw.line(
self.surface,
self.green,
(14, 14-10),
(14, 15+10),
2,
)
joypos = vec.mul((self.input.x_axis, -self.input.y_axis), 8)
pg.draw.circle(
self.surface,
self.red,
vec.add(joypos, (15,15)),
4,
)
self.surface.unlock()
_width, height = self.display.screen_size
x = 10 + 30 * self.number
y = height - self.surface.get_height() - 10
screen.blit(self.surface, (x, y))
def arc_left(
self, arc_angle, radius=None, center=None, start_slant=None, end_slant=None,
):
if (
(radius is None and center is None) or
(radius is not None and center is not None)
):
raise TypeError('You must specify exactly one of center or radius.')
arc_angle = Angle(arc_angle)
# Create a radius vector, which is a vector from the arc center to the
# current position. Subtract to find the center, then rotate the radius
# vector to find the arc end point.
if center is None:
if arc_angle < 0:
radius = -abs(radius)
v_radius = vec.neg(vec.perp(self._vector(radius)))
center = vec.sub(self._position, v_radius)
elif radius is None:
v_radius = vec.vfrom(center, self._position)
radius = vec.mag(v_radius)
if arc_angle < 0:
radius = -radius
endpoint = vec.add(center, vec.rotate(v_radius, arc_angle.rad))
self._arc(
center,
radius,
endpoint,
arc_angle,
start_slant=start_slant,
end_slant=end_slant,
)
def draw(self, screen):
self.surface.lock()
self.surface.fill(self.clear)
pg.draw.line(
self.surface,
self.green,
(14 - 10, 14),
(14 + 10, 14),
2,
)
pg.draw.line(
self.surface,
self.green,
(14, 14 - 10),
(14, 15 + 10),
2,
)
joypos = vec.mul((self.input.x_axis, -self.input.y_axis), 8)
pg.draw.circle(
self.surface,
self.red,
vec.add(joypos, (15, 15)),
4,
)
self.surface.unlock()
_width, height = self.display.screen_size
x = 10 + 30 * self.number
y = height - self.surface.get_height() - 10
screen.blit(self.surface, (x, y))
def collide_particles(p1, p2):
restitution = p1.restitution * p2.restitution
# Don't collide immovable particles.
if p1.immovable and p2.immovable:
return
# Test if p1 and p2 are actually intersecting.
if not intersect(p1, p2):
return
# If one particle is immovable, make it the first one.
if not p1.immovable and p2.immovable:
p1, p2 = p2, p1
# Vector spanning between the centers, normal to contact surface.
v_span = vec.vfrom(p1.pos, p2.pos)
# Split into normal and tangential components and calculate
# initial velocities.
normal = vec.norm(v_span)
tangent = vec.perp(normal)
v1_tangent = vec.proj(p1.velocity, tangent)
v2_tangent = vec.proj(p2.velocity, tangent)
p1_initial = vec.dot(p1.velocity, normal)
p2_initial = vec.dot(p2.velocity, normal)
# Don't collide if particles were actually moving away from each other, so
# they don't get stuck inside one another.
if p1_initial - p2_initial < 0:
return
# Handle immovable particles specially.
if p1.immovable:
p2_final = -p2_initial * restitution
p2.velocity = vec.add(v2_tangent, vec.mul(normal, p2_final))
return
# Elastic collision equations along normal component.
m1, m2 = p1.mass, p2.mass
m1plusm2 = (m1 + m2) / restitution
p1_final = p1_initial * (m1 - m2) / m1plusm2 + p2_initial * (2 * m2) / m1plusm2
p2_final = p2_initial * (m2 - m1) / m1plusm2 + p1_initial * (2 * m1) / m1plusm2
# Tangential component is unchanged, recombine.
p1.velocity = vec.add(v1_tangent, vec.mul(normal, p1_final))
p2.velocity = vec.add(v2_tangent, vec.mul(normal, p2_final))
def rebound(self, normal, point=None, restitution=1):
# Split into normal and tangential components.
tangent = vec.perp(normal)
v_tangent = vec.proj(self.velocity, tangent)
v_normal = vec.proj(self.velocity, normal)
# Invert normal component and recombine, with restitution.
v_normal = vec.neg(v_normal)
self.velocity = vec.add(
v_tangent,
vec.mul(v_normal, restitution),
)
# If the particle is partially inside the wall, move it out.
if point is not None:
v = vec.vfrom(point, self.pos)
if vec.mag2(v) < self.radius**2:
v = vec.norm(v, self.radius)
self.pos = vec.add(point, v)
def create_snowball(lobby, pos, angle, force):
ball_id = create_snowball_id(lobby)
snowball = player.Snowball(ball_id)
direction = vec.from_direction(angle, 1)
velocity = vec.mul(direction, force * MAX_THROWING_FORCE)
snowball.position = vec.add(pos, vec.mul(direction,
SNOWBALL_SPAWN_DISTANCE))
snowball.velocity = velocity
lobby.snowballs[ball_id] = snowball
def canCapture(s, point, distance, targetPlanet):
if s.isParent(targetPlanet):
#print "Nope, is parent"
return False
if targetPlanet.parent != None:
#print "Nope, has parent"
return False
if targetPlanet == s:
#print "Nope, self"
return False
if s in targetPlanet.children:
#print "Nope, is a child already"
return False
vecBetweenPlanets = vec.sub(targetPlanet.loc, s.loc)
# Adjust distance to measure from surface to surface, not center
# to center
distance += s.radius + targetPlanet.radius
if vec.magSquared(vecBetweenPlanets) > (distance * distance):
#print "Nope, out of range"
return False
# Okay we are close enough to an eligible planet, are we facing it?
angleBetweenPlanets = vec.toAngle(vecBetweenPlanets)
# Urrrrrg I hate this, -180 to 180 and 0-360 behave differently and both are
# awful in different situations so neither one is really correct.
point = (point + 360) % 360
angleBetweenPlanets = (angleBetweenPlanets + 360) % 360
#print "Point and angle:", point, angleBetweenPlanets
if abs(angleBetweenPlanets - point) < 10:
#print "Yep!"
return True
#print "Nope, angle too great", angleBetweenPlanets, point, abs(angleBetweenPlanets - point)
return False
vecBetweenPlanets = vec.sub(targetPlanet.loc, s.loc)
vecBPU = vec.unit(vecBetweenPlanets)
vecToPlanetEdge = vec.mul(vec.perpendicular(vecBPU),
targetPlanet.radius)
#print("Vec between planets: {0}, vec to planet edge: {1}".format(vecBPU, vec.unit(vecToPlanetEdge)))
angularSize = vec.angleBetween(
vecBetweenPlanets, vec.add(vecBetweenPlanets, vecToPlanetEdge))
vecToPoint = vec.mul(vec.fromAngle(point), s.radius)
angularDistance = vec.angleBetween(vecBetweenPlanets, vecToPoint)
#print("Angular size: {0}, angular distance: {1}".format(angularSize, angularDistance))
if angularDistance > abs(angularSize):
return False
else:
# Check distance between planets surfaces
distance = distance + (s.radius + targetPlanet.radius)
# Can't capture a planet if you're overlapping it
# XXX: Doesn't seem to work, but...
if distance < 0:
return False
return vec.within(s.loc, targetPlanet.loc, distance)
def repeat(position, velocity, storage_offset, stack, stack_of_stacks, push_mode, program):
instruction = program.get(vec.add(position, velocity))
if instruction in INSTRUCTIONS:
operation = INSTRUCTIONS[instruction]
else:
operation = DEFAULT_INSTRUCTION
result = position, velocity, storage_offset, stack, stack_of_stacks, push_mode, program, True
for _ in xrange(stack_pop(stack)):
result = operation(position, velocity, storage_offset, stack, stack_of_stacks, push_mode, program)
return result
def to_screen(self, pos):
"""Convert pos to screen coordinates.
Takes a tuple a world position, and returns a tuple for the
screen position.
"""
x, y = vec.add(
self.screen_origin,
vec.mul(pos, self.pixels_per_unit),
)
return (int(x), int(y))
def emit(s, gs, dt, loc, facing, vel=vec.ZERO):
s.timer += dt
while s.timer > s.interval:
s.timer -= s.interval
for i in range(s.count):
variance = + (s.angle * random.random()) - (s.angle / 2.0)
angle = facing + variance
v = vec.mul(vec.fromAngle(angle), s.speed)
v = vec.add(vel, v)
part = s.particleType(loc, v)
gs.addParticle(part)
def draw_graph(graph):
gap_size = 0.25
p = canoepaddle.Pen()
p.stroke_mode(0.1, 'black')
for a, b in graph_edges(graph):
gap = vec.norm(vec.vfrom(a, b), gap_size)
p.move_to(vec.add(a, gap))
p.line_to(vec.sub(b, gap))
return p.paper
def to_screen(self, pos):
"""Convert pos to screen coordinates.
Takes a tuple a world position, and returns a tuple for the
screen position.
"""
x, y = vec.add(
self.screen_origin,
vec.mul(pos, self.pixels_per_unit),
)
return (int(x), int(y))
def create_shield(self):
self.shield_pieces = []
for i in range(8):
d = DIRECTIONS[i]
pos = vec.add(self.pos, d)
piece = HeroPiece()
piece.pos = pos
piece.display_character = '-\|/'[i % 4]
self.world.register_entity(piece)
self.shield_pieces.append(piece)
Polyomino([self] + self.shield_pieces)
self.shield((0, 0))
def project(self, points, reverse=False):
if reverse:
if self.H_ is None:
self.H_ = mtx.lu([r[:] for r in self.H])
qs = [
mtx.solve(self.H_,
vec.sub(p, self.offset) + [1]) for p in points
]
return [vec.div(q[:-1], q[-1]) for q in qs]
else:
qs = [mtx.mul(self.H, p + [1]) for p in points]
return [vec.add(self.offset, vec.div(q[:-1], q[-1])) for q in qs]
def balls_collisions(balls):
collided = False
for b1 in balls:
for b2 in balls:
if b1 is b2:
continue
d = vec.sub(b1.pos, b2.pos)
penetration = (b1.radius + b2.radius) - vec.len(d)
if penetration < 0:
continue
collided = True
n = vec.unit(d)
b1.pos = vec.add(b1.pos, vec.scale(n, penetration / 2 + 1))
b2.pos = vec.add(b2.pos, vec.scale(n, -penetration / 2 - 1))
j = vec.dot(vec.sub(b2.speed, b1.speed), n)
b1.speed = vec.add(b1.speed, vec.scale(n, j))
b2.speed = vec.add(b2.speed, vec.scale(n, -j))
return collided
def update(self, elapsed_seconds, force=None, extra_drag=0):
# Apply force if necessary.
if force is not None:
self.velocity = vec.add(self.velocity, vec.mul(force, (elapsed_seconds / self.mass)))
# Apply drag.
# Decrease the magnitude of the velocity vector by
# the amount of drag.
drag = (self.drag_rate + extra_drag) * elapsed_seconds
if drag > self.speed:
self.velocity = (0, 0)
elif drag != 0 and self.velocity != (0, 0):
drag_vector = vec.norm(self.velocity, -drag)
self.velocity = vec.add(self.velocity, drag_vector)
# Limit to maximum speed.
if self.speed > c.max_speed:
self.velocity = vec.norm(self.velocity, c.max_speed)
# Update position based on velocity.
self.last_pos = self.pos
self.pos = vec.add(self.pos, vec.mul(self.velocity, elapsed_seconds))
def draw(s, gs):
rot = s.parent.facing + s.loc
totalAngle = vec.fromAngle(rot)
offsetVec = vec.mul(totalAngle, s.radius)
location = vec.add(s.parent.loc, offsetVec)
(scx, scy) = gs.screenCoords(location)
#print "rot: %s, totalAngle: %s, offsetVec: %s, location: %s, sc: %s" % (rot, totalAngle, offsetVec, location, (scx, scy))
# Add a slight offset to center the image rather than drawing
# it from the lower-left corner...
# Also add oregano.
s.sprite.rotation = s.loc + s.parent.facing
#print s.sprite.rotation, s.loc, s.parent.facing
s.sprite.position = (scx, scy)
s.sprite.draw()
def join_with_arc(self, other):
# Special case coincident arcs.
if points_equal(self.center, other.center):
if not (
float_equal(self.radius, other.radius) and
float_equal(self.width, other.width)
):
self.end_joint_illegal = True
other.start_joint_illegal = True
return
r = vec.vfrom(self.center, self.b)
if self.radius < 0:
r = vec.neg(r)
v_left = vec.norm(r, self.radius - self.width / 2)
self.b_left = other.a_left = Point(*vec.add(self.center, v_left))
v_right = vec.norm(r, self.radius + self.width / 2)
self.b_right = other.a_right = Point(*vec.add(self.center, v_right))
return
c1, r1 = self.offset_circle_left()
c2, r2 = other.offset_circle_left()
points_left = intersect_circles(c1, r1, c2, r2)
if len(points_left) > 0:
p = Point(*closest_point_to(self.b, points_left))
self.b_left = other.a_left = p
c1, r1 = self.offset_circle_right()
c2, r2 = other.offset_circle_right()
points_right = intersect_circles(c1, r1, c2, r2)
if len(points_right) > 0:
p = Point(*closest_point_to(self.b, points_right))
self.b_right = other.a_right = p
if len(points_left) == 0 or len(points_right) == 0:
self.end_joint_illegal = True
other.start_joint_illegal = True
def join_with_arc(self, other):
# Special case coincident arcs.
if points_equal(self.center, other.center):
if not (
float_equal(self.radius, other.radius)
and float_equal(self.width, other.width)
):
self.end_joint_illegal = True
other.start_joint_illegal = True
return
r = vec.vfrom(self.center, self.b)
if self.radius < 0:
r = vec.neg(r)
v_left = vec.norm(r, self.radius - self.width / 2)
self.b_left = other.a_left = Point(*vec.add(self.center, v_left))
v_right = vec.norm(r, self.radius + self.width / 2)
self.b_right = other.a_right = Point(*vec.add(self.center, v_right))
return
c1, r1 = self.offset_circle_left()
c2, r2 = other.offset_circle_left()
points_left = intersect_circles(c1, r1, c2, r2)
if len(points_left) > 0:
p = Point(*closest_point_to(self.b, points_left))
self.b_left = other.a_left = p
c1, r1 = self.offset_circle_right()
c2, r2 = other.offset_circle_right()
points_right = intersect_circles(c1, r1, c2, r2)
if len(points_right) > 0:
p = Point(*closest_point_to(self.b, points_right))
self.b_right = other.a_right = p
if len(points_left) == 0 or len(points_right) == 0:
self.end_joint_illegal = True
other.start_joint_illegal = True
def generate_castle_position():
if not castles:
return (0, 0)
it = 0
while True:
r1 = random.randint(-1 - it, 1 + it)
r2 = random.randint(-1 - it, 1 + it)
direction = (r1 * SPAWN_DISTANCE, r2 * SPAWN_DISTANCE)
for castle in castles.values():
pos = castle.position_tuple()
new_pos = vec.add(direction, pos)
if is_castle_position_free(new_pos):
# print('FOUND!')
return new_pos
it += 1
def update(s, gs, dt):
if s.parent == None:
PhysicsObj.update(s, gs, dt)
else:
#print("parent offset: {0}, parent direction {1}, parent distance {2}, parent facing {3}".format(s.parentVec, vec.toAngle(p), vec.mag(p), s.parent.facing))
# To figure out the current facing we must know what our parent's facing is,
# where we were facing when captured, and where the parent was facing when captured.
s.facing = s.capturedFacing + (s.parent.facing -
s.capturedParentFacing)
rotation = s.parent.facing - s.capturedParentFacing + 180
p = vec.rotate(s.parentVec, -rotation)
# THAT F*****G SIMPLE AAAAAAAAAAH
relativePosition = vec.add(s.parent.loc, p)
s.loc = relativePosition
def draw(s, gs):
sx, sy = gs.screenCoords(s.loc)
s.sprite.x = sx
s.sprite.y = sy
s.sprite.rotation = s.facing
s.sprite.draw()
if s.parent != None:
#parentSloc = gs.screenCoords(s.parent.loc)
vecToParent = vec.sub(s.parent.loc, s.loc)
angle = vec.toAngle(vecToParent)
centerPointVec = vec.div(vecToParent, 2)
actualVec = vec.add(s.loc, centerPointVec)
s.captureSprite.position = gs.screenCoords(actualVec)
s.captureSprite.rotation = angle
s.captureSprite.draw()
def draw(s, gs):
swingSpeed = 190.0 # Degrees per second
startingFacing = 90.0
if s.direction > 0:
swing = startingFacing + -(s.lifetime * swingSpeed)
else:
swing = (s.lifetime * swingSpeed) - startingFacing
rot = s.parent.facing + s.loc
totalAngle = vec.fromAngle(rot)
offset = vec.mul(totalAngle, s.radius)
location = vec.add(s.parent.loc, offset)
s.sprite.position = gs.screenCoords(location)
#print location
s.sprite.rotation = rot + swing
s.sprite.draw()
def draw_player(self, player):
# Show whether or not the player is thrusting.
if player.do_thrust:
trailing_point = vec.add(
player.pos,
vec.norm(player.direction, -1.5 * player.radius),
)
self.line(THRUST_COLOR, player.pos, trailing_point,
.5 * player.radius)
if player.boost_heavy_time_remaining > 0.0:
trailing_point = vec.add(
player.pos,
vec.norm(player.direction, -2.0 * player.radius),
)
self.line(THRUST_COLOR, player.pos, trailing_point,
1.5 * player.radius)
# Show braking and boosting charge up.
if player.do_brake:
# Redden the brake color as we charge.
color = vec.add(
BRAKE_COLOR,
vec.mul(THRUST_COLOR,
player.boost_charge_time / c.player_boost_ready_time))
# Vibrate if we are fully charged.
r = 1.2
if player.boost_charge_time == c.player_boost_ready_time:
r += 0.1 * math.sin(6 *
(2 * math.pi) * pg.time.get_ticks() / 1000)
self.circle(color, player.pos, r)
# Body.
self.circle(PLAYER_COLORS[player.number], player.pos, player.radius)
# Show the player pointing towards a direction.
leading_point = vec.add(
player.pos,
vec.norm(player.direction, player.radius),
)
self.line(DIRECTION_COLOR, player.pos, leading_point,
.2 * player.radius)
if SHOW_RUDDER_FORCE:
point = vec.add(
player.pos,
vec.mul(player.rudder_force, .1),
)
self.line(THRUST_COLOR, player.pos, point, .1 * player.radius)
if SHOW_INTENDED_DIRECTION and hasattr(player, 'intended_direction'):
point = vec.add(
player.pos,
player.intended_direction,
)
self.line(THRUST_COLOR, player.pos, point, .1 * player.radius)
def bounds(self):
# We use the outside radius, because the inside of the arc cannot be
# tangent to the boundary. This is not a perfect approximation, as
# setting end slants could fail to shrink the bounding box as
# they should.
r = abs(self.radius)
if self.width is not None:
r += self.width / 2
# Find the four "compass points" around the center.
compass_points = [
vec.add(self.center, direction)
for direction in [
(r, 0), # East, heading = 0.
(0, r), # North, heading = 90.
(-r, 0), # West, heading = 180.
(0, -r), # South, heading = 270.
]
]
# Check which compass points are in the body of the circle.
if self.arc_angle < 0:
start = self.end_heading + 90
end = self.start_heading + 90
else:
start = self.start_heading - 90
end = self.end_heading - 90
occupied_points = []
for i, h in enumerate([0, 90, 180, 270]):
h = Heading(h)
if h == start or h == end or h.between(start, end):
occupied_points.append(compass_points[i])
# The bounding box of the arc is the combined bounding box of the start
# point, the end point, and the compass points occupied by the body of
# the arc. If the arc is a thick arc, then the edge points also can
# push the boundary.
if self.width is None:
endpoints = [self.a, self.b]
else:
endpoints = [self.a_left, self.a_right, self.b_left, self.b_right]
return Bounds.union_all([
Bounds.from_point(p) for p in
endpoints + occupied_points
])
def bounds(self):
# We use the outside radius, because the inside of the arc cannot be
# tangent to the boundary. This is not a perfect approximation, as
# setting end slants could fail to shrink the bounding box as
# they should.
r = abs(self.radius)
if self.width is not None:
r += self.width / 2
# Find the four "compass points" around the center.
compass_points = [
vec.add(self.center, direction)
for direction in [
(r, 0), # East, heading = 0.
(0, r), # North, heading = 90.
(-r, 0), # West, heading = 180.
(0, -r), # South, heading = 270.
]
]
# Check which compass points are in the body of the circle.
if self.arc_angle < 0:
start = self.end_heading + 90
end = self.start_heading + 90
else:
start = self.start_heading - 90
end = self.end_heading - 90
occupied_points = []
for i, h in enumerate([0, 90, 180, 270]):
h = Heading(h)
if h == start or h == end or h.between(start, end):
occupied_points.append(compass_points[i])
# The bounding box of the arc is the combined bounding box of the start
# point, the end point, and the compass points occupied by the body of
# the arc. If the arc is a thick arc, then the edge points also can
# push the boundary.
if self.width is None:
endpoints = [self.a, self.b]
else:
endpoints = [self.a_left, self.a_right, self.b_left, self.b_right]
return Bounds.union_all([
Bounds.from_point(p) for p in
endpoints + occupied_points
])
def intersect_circle_line(center, radius, line_start, line_end):
"""
Find the intersection of a circle with a line.
"""
radius = abs(radius)
# First check whether the line is too far away, or if we have a
# single point of contact.
# Reference:
# http://mathworld.wolfram.com/Point-LineDistance2-Dimensional.html
r = vec.vfrom(center, line_start)
v = vec.perp(vec.vfrom(line_start, line_end))
d = vec.proj(r, v)
dist = vec.mag(d)
if float_equal(dist, radius):
# Single intersection point, because the circle and line are tangent.
point = vec.add(center, d)
return [point]
elif dist > radius:
return []
# Set up parametric equations for the line and the circle, and solve them.
# Reference:
# http://www.cs.cf.ac.uk/Dave/CM0268/PDF/circle_line_intersect_proof.pdf
xc, yc = center
x0, y0 = line_start
x1, y1 = line_end
line_x, line_y = (x1 - x0), (y1 - y0) # f, g
dx, dy = (x0 - xc), (y0 - yc)
a = line_x**2 + line_y**2
b = 2 * (line_x * dx + line_y * dy)
c = dx**2 + dy**2 - radius**2
t0, t1 = quadratic_formula(a, b, c)
return [
(
x0 + line_x * t0,
y0 + line_y * t0,
),
(
x0 + line_x * t1,
y0 + line_y * t1,
),
]
def intersect_circle_line(center, radius, line_start, line_end):
"""
Find the intersection of a circle with a line.
"""
radius = abs(radius)
# First check whether the line is too far away, or if we have a
# single point of contact.
# Reference:
# http://mathworld.wolfram.com/Point-LineDistance2-Dimensional.html
r = vec.vfrom(center, line_start)
v = vec.perp(vec.vfrom(line_start, line_end))
d = vec.proj(r, v)
dist = vec.mag(d)
if float_equal(dist, radius):
# Single intersection point, because the circle and line are tangent.
point = vec.add(center, d)
return [point]
elif dist > radius:
return []
# Set up parametric equations for the line and the circle, and solve them.
# Reference:
# http://www.cs.cf.ac.uk/Dave/CM0268/PDF/circle_line_intersect_proof.pdf
xc, yc = center
x0, y0 = line_start
x1, y1 = line_end
line_x, line_y = (x1 - x0), (y1 - y0) # f, g
dx, dy = (x0 - xc), (y0 - yc)
a = line_x**2 + line_y**2
b = 2 * (line_x * dx + line_y * dy)
c = dx**2 + dy**2 - radius**2
t0, t1 = quadratic_formula(a, b, c)
return [
(
x0 + line_x * t0,
y0 + line_y * t0,
),
(
x0 + line_x * t1,
y0 + line_y * t1,
),
]
def draw_player(self, player):
# Show whether or not the player is thrusting.
if player.do_thrust:
trailing_point = vec.add(
player.pos,
vec.norm(player.direction, -1.5 * player.radius),
)
self.line(THRUST_COLOR, player.pos, trailing_point, .5 * player.radius)
if player.boost_heavy_time_remaining > 0.0:
trailing_point = vec.add(
player.pos,
vec.norm(player.direction, -2.0 * player.radius),
)
self.line(THRUST_COLOR, player.pos, trailing_point, 1.5 * player.radius)
# Show braking and boosting charge up.
if player.do_brake:
# Redden the brake color as we charge.
color = vec.add(
BRAKE_COLOR,
vec.mul(THRUST_COLOR, player.boost_charge_time / c.player_boost_ready_time)
)
# Vibrate if we are fully charged.
r = 1.2
if player.boost_charge_time == c.player_boost_ready_time:
r += 0.1 * math.sin(6 * (2*math.pi) * pg.time.get_ticks() / 1000)
self.circle(color, player.pos, r)
# Body.
self.circle(PLAYER_COLORS[player.number], player.pos, player.radius)
# Show the player pointing towards a direction.
leading_point = vec.add(
player.pos,
vec.norm(player.direction, player.radius),
)
self.line(DIRECTION_COLOR, player.pos, leading_point, .2 * player.radius)
if SHOW_RUDDER_FORCE:
point = vec.add(
player.pos,
vec.mul(player.rudder_force, .1),
)
self.line(THRUST_COLOR, player.pos, point, .1 * player.radius)
if SHOW_INTENDED_DIRECTION and hasattr(player, 'intended_direction'):
point = vec.add(
player.pos,
player.intended_direction,
)
self.line(THRUST_COLOR, player.pos, point, .1 * player.radius)
def start_block(position, velocity, storage_offset, stack, stack_of_stacks, push_mode, program):
n = stack_pop(stack)
soss = stack
if n < 0:
toss = [0] * (n * -1)
elif n > len(soss):
i = n - len(soss)
toss = [0] * i + soss
soss = []
else:
s = len(soss) - n
assert s >= 0
toss = soss[s:]
soss = soss[:s]
sx, sy = storage_offset
soss += [sx, sy]
storage_offset = vec.add(position, velocity)
stack_of_stacks.append(soss)
stack = toss
return position, velocity, storage_offset, stack, stack_of_stacks, push_mode, program, True
def partition(points, l1, l2, s=None):
"""
Partition a set of points by a line.
The line is defined by l1, l2. The desired side of the line is given by the
point s.
If s is not given, return points to the right of the line.
If eq is True, also include points on the line.
>>> sorted(partition([(-1,0), (0,0), (1,0)], (0,1), (0,-1), (2,0)))
[(0, 0), (1, 0)]
>>> sorted(partition([(-1,0), (0,0), (1,0)], (0,1), (0,-1), (-2,0)))
[(-1, 0), (0, 0)]
>>> points = [(-2,2), (-1,0), (0,0), (1,0)]
>>> sorted(partition(points, (-1,0), (0,1), (3,0)))
[(-1, 0), (0, 0), (1, 0)]
>>> sorted(partition(points, (-1,0), (0,1), (-3,0)))
[(-2, 2), (-1, 0)]
You can omit the argument "s" if you don't care.
>>> sorted(partition([(-1,0), (0,0), (1,0)], (0,1), (0,-1)))
[(-1, 0), (0, 0)]
"""
if s is None:
s = vec.add(l1, vec.perp(vec.vfrom(l1, l2)))
if l1 == l2:
raise ValueError('l1 equals l2')
sign = sign_of(cmp_line(l1, l2, s))
if sign == 0:
raise ValueError('s is on the line l1 l2')
for p in points:
c = cmp_line(l1, l2, p)
if c == sign:
yield p
elif c == 0:
yield p
def partition(points, l1, l2, s=None):
"""
Partition a set of points by a line.
The line is defined by l1, l2. The desired side of the line is given by the
point s.
>>> partition([(-1,0), (0,0), (1,0)], (0,1), (0,-1), (2,0))[0]
{(1, 0)}
>>> partition([(-1,0), (0,0), (1,0)], (0,1), (0,-1), (-2,0))[0]
{(-1, 0)}
>>> points = [(-2,2), (-1,0), (0,0), (1,0)]
>>> sorted(partition(points, (-1,0), (0,1), (3,0))[0])
[(0, 0), (1, 0)]
>>> sorted(partition(points, (-1,0), (0,1), (-3,0))[0])
[(-2, 2)]
You can omit the argument "s" if you don't care.
>>> partition([(-1,0), (0,0), (1,0)], (0,1), (0,-1))
({(-1, 0)}, {(1, 0)})
"""
if s is None:
s = vec.add(l1, vec.perp(vec.vfrom(l1, l2)))
if l1 == l2:
raise ValueError('l1 equals l2')
sign = cmp_line(l1, l2, s)
if sign == 0:
raise ValueError('s is on the line l1 l2')
forward = set()
reverse = set()
for p in points:
c = cmp_line(l1, l2, p)
if c == sign:
forward.add(p)
elif c == -sign:
reverse.add(p)
return forward, reverse
[0, 0],
[2, -2],
[4, -6],
[2, 2],
[6, 4],
[16, 10],
[14, -10],
[10, 8],
[12, -8],
]
# 290 mm / 15 sqaures
paper_points = [vec.mul(q, 290 / 15) for q in paper_squares]
offset = [305, 0] # floor origin is 305 mm in front
world_points = [vec.add(p, offset) for p in paper_points]
p = Planar(H, offset=offset)
# Should be equal
print(world_points)
print(p.project(image_points))
# Should be equal
print(image_points)
print(p.project(world_points, reverse=True))
# Make sure H did not get changed
print(world_points)
print(p.project(image_points))
def _calc_forward_to_x(self, x_target):
x, y = self.position
x_diff = x_target - x
y_diff = x_diff * math.tan(self._heading.rad)
return vec.add(self.position, (x_diff, y_diff))
def _calc_forward_to_y(self, y_target):
x, y = self.position
y_diff = y_target - y
x_diff = y_diff / math.tan(self._heading.rad)
return vec.add(self.position, (x_diff, y_diff))
def _calc_forward_position(self, distance):
return vec.add(
self.position,
self._vector(distance),
)
def to_screen(self, pos):
return vec.add(pos, self.origin)
def move_relative(self, offset):
self.move_to(vec.add(self.position, offset))
def start_move(self, direction):
self.pos = vec.add(self.pos, direction)