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)
Exemple #3
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    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,
        )
Exemple #4
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    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,
        )
Exemple #5
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 def turn_toward(self, point):
     v = vec.vfrom(self._position, point)
     heading = math.degrees(vec.heading(v))
     self.turn_to(heading)
Exemple #6
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 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)))
Exemple #9
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    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
Exemple #10
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 def heading(self):
     return Heading.from_rad(vec.heading(vec.vfrom(self.a, self.b)))