def test_straight_joint_headings():
# The math in calculating joint geometry can get numerically unstable
# very close to straight joints at various headings.
for heading_angle in range(0, 45):
p = Pen()
p.stroke_mode(1.0)
p.move_to((0, 0))
p.turn_to(heading_angle)
p.line_forward(10)
p.line_forward(10)
path = p.paper.paths[0]
path.render_path(2) # Doesn't crash.
# Check that the joint angle is 90 degrees from the heading.
assert_equal(len(p.paper.paths), 1)
segments = p.paper.paths[0].segments
assert_equal(len(segments), 2)
s0, s1 = segments
target_angle = (heading_angle + 90) % 180
joint_angle = math.degrees(vec.heading(vec.vfrom(s0.b_right, s0.b_left)))
assert_almost_equal(joint_angle % 180, target_angle)
joint_angle = math.degrees(vec.heading(vec.vfrom(s1.a_right, s1.a_left)))
assert_almost_equal(joint_angle % 180, target_angle)
def test_straight_joint_headings():
# The math in calculating joint geometry can get numerically unstable
# very close to straight joints at various headings.
for heading_angle in range(0, 45):
p = Pen()
p.stroke_mode(1.0)
p.move_to((0, 0))
p.turn_to(heading_angle)
p.line_forward(10)
p.line_forward(10)
path = p.paper.paths[0]
path.render_path(2) # Doesn't crash.
# Check that the joint angle is 90 degrees from the heading.
assert_equal(len(p.paper.paths), 1)
segments = p.paper.paths[0].segments
assert_equal(len(segments), 2)
s0, s1 = segments
target_angle = (heading_angle + 90) % 180
joint_angle = math.degrees(vec.heading(vec.vfrom(s0.b_right, s0.b_left)))
assert_almost_equal(joint_angle % 180, target_angle)
joint_angle = math.degrees(vec.heading(vec.vfrom(s1.a_right, s1.a_left)))
assert_almost_equal(joint_angle % 180, target_angle)
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 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 turn_toward(self, point):
v = vec.vfrom(self._position, point)
heading = math.degrees(vec.heading(v))
self.turn_to(heading)
def turn_toward(self, point):
v = vec.vfrom(self._position, point)
heading = math.degrees(vec.heading(v))
self.turn_to(heading)
def join_with_line(self, other):
v_self = self._vector()
v_other = other._vector()
# Check turn angle.
self_heading = Heading.from_rad(vec.heading(v_self))
other_heading = Heading.from_rad(vec.heading(v_other))
turn_angle = self_heading.angle_to(other_heading)
# Special case equal widths.
if(
abs(turn_angle) <= MAX_TURN_ANGLE and
float_equal(self.width, other.width)
):
# When joints between segments of equal width are straight or
# almost straight, the line-intersection method becomes very
# numerically unstable, so use another method instead.
# For each segment, get a vector perpendicular to the
# segment, then add them. This is an angle bisector for
# the angle of the joint.
w_self = self._width_vector()
w_other = other._width_vector()
v_bisect = vec.add(w_self, w_other)
# Make the bisector have the correct length.
half_angle = vec.angle(v_other, v_bisect)
v_bisect = vec.norm(
v_bisect,
(self.width / 2) / math.sin(half_angle)
)
# Determine the left and right joint spots.
p_left = vec.add(self.b, v_bisect)
p_right = vec.sub(self.b, v_bisect)
else:
a, b = self.offset_line_left()
c, d = other.offset_line_left()
p_left = intersect_lines(a, b, c, d)
a, b = self.offset_line_right()
c, d = other.offset_line_right()
p_right = intersect_lines(a, b, c, d)
# Make sure the joint points are "forward" from the perspective
# of each segment.
if p_left is not None:
if vec.dot(vec.vfrom(self.a_left, p_left), v_self) < 0:
p_left = None
if p_right is not None:
if vec.dot(vec.vfrom(self.a_right, p_right), v_self) < 0:
p_right = None
# Don't join the outer sides if the turn angle is too steep.
if abs(turn_angle) > MAX_TURN_ANGLE:
if turn_angle > 0:
p_right = None
else:
p_left = None
if p_left is not None:
self.b_left = other.a_left = Point(*p_left)
if p_right is not None:
self.b_right = other.a_right = Point(*p_right)
if p_left is None or p_right is None:
self.end_joint_illegal = True
other.start_joint_illegal = True
def heading(self):
return Heading.from_rad(vec.heading(vec.vfrom(self.a, self.b)))
def join_with_line(self, other):
v_self = self._vector()
v_other = other._vector()
# Check turn angle.
self_heading = Heading.from_rad(vec.heading(v_self))
other_heading = Heading.from_rad(vec.heading(v_other))
turn_angle = self_heading.angle_to(other_heading)
# Special case equal widths.
if(
abs(turn_angle) <= MAX_TURN_ANGLE
and float_equal(self.width, other.width)
):
# When joints between segments of equal width are straight or
# almost straight, the line-intersection method becomes very
# numerically unstable, so use another method instead.
# For each segment, get a vector perpendicular to the
# segment, then add them. This is an angle bisector for
# the angle of the joint.
w_self = self._width_vector()
w_other = other._width_vector()
v_bisect = vec.add(w_self, w_other)
# Make the bisector have the correct length.
half_angle = vec.angle(v_other, v_bisect)
v_bisect = vec.norm(
v_bisect,
(self.width / 2) / math.sin(half_angle)
)
# Determine the left and right joint spots.
p_left = vec.add(self.b, v_bisect)
p_right = vec.sub(self.b, v_bisect)
else:
a, b = self.offset_line_left()
c, d = other.offset_line_left()
p_left = intersect_lines(a, b, c, d)
a, b = self.offset_line_right()
c, d = other.offset_line_right()
p_right = intersect_lines(a, b, c, d)
# Make sure the joint points are "forward" from the perspective
# of each segment.
if p_left is not None:
if vec.dot(vec.vfrom(self.a_left, p_left), v_self) < 0:
p_left = None
if p_right is not None:
if vec.dot(vec.vfrom(self.a_right, p_right), v_self) < 0:
p_right = None
# Don't join the outer sides if the turn angle is too steep.
if abs(turn_angle) > MAX_TURN_ANGLE:
if turn_angle > 0:
p_right = None
else:
p_left = None
if p_left is not None:
self.b_left = other.a_left = Point(*p_left)
if p_right is not None:
self.b_right = other.a_right = Point(*p_right)
if p_left is None or p_right is None:
self.end_joint_illegal = True
other.start_joint_illegal = True
def heading(self):
return Heading.from_rad(vec.heading(vec.vfrom(self.a, self.b)))