def curve4(a): # <<<
"""Some of the curves of Figs. 7 and 8 on page 8 of mpman.pdf
beginfig(7)
for a=-9 upto 7:
draw (0,0){dir 45}..{dir 10a}(6cm,0);
endfor
endfig;"""
if a == -90:
refpoints = [((None, None), (0, 0), (72.980957, 72.980957)),
((170.0787, 61.772141), (170.0787, 0), (None, None))]
elif a == 0:
refpoints = [((None, None), (0, 0), (44.36261, 44.36261)),
((110.4153, 0), (170.0787, 0), (None, None))]
elif a == 70:
refpoints = [((None, None), (0, 0), (41.195404, 41.195404)),
((138.80974, -85.909775), (170.0787, 0), (None, None))]
else:
refpoints = None
p = _knot(0, 0, mp_endpoint, None, None, mp_given, 0.25*pi, 1)
knots = p
p.next = _knot(170.078740157, 0, mp_given, radians(a), 1, mp_endpoint, None, None)
p = p.next
p.next = knots
return knots, refpoints
def curve5(): # <<<
"""The right curve of Fig. 9 on page 9 of mpman.pdf
draw z0{up}...z1{right}...z2{down}"""
p = _knot(0, 0, mp_endpoint, None, None, mp_given, 0.5*pi, -1)
knots = p
p.next = _knot(100, 20, mp_given, 0, -1, mp_given, 0, -1)
p = p.next
p.next = _knot(200, 0, mp_given, -0.5*pi, -1, mp_endpoint, None, None)
p = p.next
p.next = knots
refpoints = [
((None, None), (0, 0), (0, 19.995117)),
((56.625137, 20), (100, 20), (143.37486, 20)),
((200, 19.995117), (200, 0), (None, None))]
return knots, refpoints
def curve8b(): # <<<
"""Testing degenerate points
draw (0,0)..tension 2 and 3..(100,50)..tension 3 and 4..(100,50)..tension 4 and 2..{curl 1}(200,0)..tension 2 and 3..(100,-50)..tension 3 and 4..(100,-50)..tension 4 and 2..(0,0)"""
p = _knot(0.0, 0.0, mp_endpoint, None, None, mp_curl, 1, 2)
knots = p
p.next = _knot(100.0, 50.0, mp_open, None, 3, mp_open, None, 3)
p = p.next
p.next = _knot(100.0, 50.0, mp_open, None, 4, mp_open, None, 4)
p = p.next
p.next = _knot(200.0, 0.0, mp_curl, 1, 2, mp_curl, 1, 2)
p = p.next
p.next = _knot(100.0, -50.0, mp_open, None, 3, mp_open, None, 3)
p = p.next
p.next = _knot(100.0, -50.0, mp_open, None, 4, mp_open, None, 4)
p = p.next
p.next = _knot(0.0, 0.0, mp_curl, 1, 2, mp_endpoint, None, None)
p = p.next
p.next = knots
refpoints = [
((None, None), (0, 0), (16.666672, 8.3333282)),
((88.888885, 44.444443), (100, 50), (100, 50)),
((100, 50), (100, 50), (108.33333, 45.833328)),
((183.33333, 8.3333282), (200, 0), (183.33333, -8.3333282)),
((111.11111, -44.444443), (100, -50), (100, -50)),
((100, -50), (100, -50), (91.666672, -45.833328)),
((16.666672, -8.3333282), (0, 0), (None, None))]
return knots, refpoints
def curve8a(): # <<<
"""Testing degenerate points
draw (0,0)..(100,50)..(100,50)..{curl 1}(200,0)..(100,-50)..(100,-50)..(0,0)"""
p = _knot(0.0, 0.0, mp_endpoint, None, None, mp_curl, 1.0, 1.0)
knots = p
p.next = _knot(100.0, 50.0, mp_open, None, 1, mp_open, None, 1.0)
p = p.next
p.next = _knot(100.0, 50.0, mp_open, None, 1, mp_open, None, 1.0)
p = p.next
p.next = _knot(200.0, 0.0, mp_curl, 1, 1, mp_curl, 1, 1)
p = p.next
p.next = _knot(100.0, -50.0, mp_open, None, 1, mp_open, None, 1.0)
p = p.next
p.next = _knot(100.0, -50.0, mp_open, None, 1, mp_open, None, 1.0)
p = p.next
p.next = _knot(0.0, 0.0, mp_curl, 1, 1, mp_endpoint, None, None)
p = p.next
p.next = knots
refpoints = [
((None, None), (0, 0), (33.333328, 16.666672)),
((66.666672, 33.333328), (100, 50), (100, 50)),
((100, 50), (100, 50), (133.33333, 33.333328)),
((166.66667, 16.666672), (200, 0), (166.66667, -16.666672)),
((133.33333, -33.333328), (100, -50), (100, -50)),
((100, -50), (100, -50), (66.666672, -33.333328)),
((33.333328, -16.666672), (0, 0), (None, None))]
return knots, refpoints
def curve6a(): # <<<
"""The first curve of Fig.10 on page 9 of mpman.pdf
draw z0..z1..tension 1 and 1..z2..z3;"""
p = _knot(0, 0, mp_endpoint, None, None, mp_curl, 1, 1)
knots = p
p.next = _knot(50, 50, mp_open, None, 1, mp_open, None, 1)
p = p.next
p.next = _knot(150, 50, mp_open, None, 1, mp_open, None, 1)
p = p.next
p.next = _knot(200, 0, mp_curl, 1, 1, mp_endpoint, None, None)
p = p.next
p.next = knots
refpoints = [((None, None), (0, 0), (10.747421, 21.688171)),
((28.311829, 39.252579), (50, 50), (81.50528, 65.612213)),
((118.49472, 65.612213), (150, 50), (171.68817, 39.252579)),
((189.25258, 21.688171), (200, 0), (None, None))]
return knots, refpoints
def curve6c(): # <<<
"""The first curve of Fig.10 on page 9 of mpman.pdf
draw z0..z1..tension 2.5 and 1..z2..z3;"""
p = _knot(0, 0, mp_endpoint, None, None, mp_curl, 1, 1)
knots = p
p.next = _knot(50, 50, mp_open, None, 1, mp_open, None, 2.5)
p = p.next
p.next = _knot(150, 50, mp_open, None, 1, mp_open, None, 1)
p = p.next
p.next = _knot(200, 0, mp_curl, 1, 1, mp_endpoint, None, None)
p = p.next
p.next = knots
refpoints = [
((None, None), (0, 0), (5.4299469, 25.023956)),
((24.976044, 44.570053), (50, 50), (63.245346, 52.8741)),
((117.57947, 59.957458), (150, 50), (173.92447, 42.651978)),
((192.65198, 23.924469), (200, 0), (None, None))]
return knots, refpoints
def curve6b(): # <<<
"""The first curve of Fig.10 on page 9 of mpman.pdf
draw z0..z1..tension 1.3 and 1.3..z2..z3;"""
p = _knot(0, 0, mp_endpoint, None, None, mp_curl, 1, 1)
knots = p
p.next = _knot(50, 50, mp_open, None, 1, mp_open, None, 1.3)
p = p.next
p.next = _knot(150, 50, mp_open, None, 1.3, mp_open, None, 1)
p = p.next
p.next = _knot(200, 0, mp_curl, 1, 1, mp_endpoint, None, None)
p = p.next
p.next = knots
refpoints = [
((None, None), (0, 0), (7.0810547, 24.08403)),
((25.91597, 42.918945), (50, 50), (75.109573, 57.382568)),
((124.89043, 57.382568), (150, 50), (174.08403, 42.918945)),
((192.91895, 24.08403), (200, 0), (None, None))]
return knots, refpoints
def curve6a(): # <<<
"""The first curve of Fig.10 on page 9 of mpman.pdf
draw z0..z1..tension 1 and 1..z2..z3;"""
p = _knot(0, 0, mp_endpoint, None, None, mp_curl, 1, 1)
knots = p
p.next = _knot(50, 50, mp_open, None, 1, mp_open, None, 1)
p = p.next
p.next = _knot(150, 50, mp_open, None, 1, mp_open, None, 1)
p = p.next
p.next = _knot(200, 0, mp_curl, 1, 1, mp_endpoint, None, None)
p = p.next
p.next = knots
refpoints = [
((None, None), (0, 0), (10.747421, 21.688171)),
((28.311829, 39.252579), (50, 50), (81.50528, 65.612213)),
((118.49472, 65.612213), (150, 50), (171.68817, 39.252579)),
((189.25258, 21.688171), (200, 0), (None, None))]
return knots, refpoints
def curve1(): # <<<
"""The open curve of Fig.3 on page 6 of mpman.pdf
draw z0..z1..z2..z3..z4"""
p = _knot(0, 0, mp_endpoint, None, None, mp_curl, 1, 1)
knots = p
p.next = _knot(60, 40, mp_open, None, 1, mp_open, None, 1)
p = p.next
p.next = _knot(40, 90, mp_open, None, 1, mp_open, None, 1)
p = p.next
p.next = _knot(10, 70, mp_open, None, 1, mp_open, None, 1)
p = p.next
p.next = _knot(30, 50, mp_curl, 1.0, 1, mp_endpoint, None, None)
p = p.next
p.next = knots
refpoints = [((None, None), (0, 0), (26.764633, -1.8454285)),
((51.409393, 14.584412), (60, 40), (67.098755, 61.001877)),
((59.762527, 84.57518), (40, 90), (25.357147, 94.01947)),
((10.480637, 84.502197), (10, 70), (9.628952, 58.804214)),
((18.804214, 49.628952), (30, 50), (None, None))]
return knots, refpoints
def curve2(): # <<<
"""The closed curve of Fig.4a on page 6 of mpman.pdf
draw z0...z1...z2...z3...z4...cycle"""
p = _knot(0, 0, mp_open, None, 1, mp_open, None, 1)
knots = p
p.next = _knot(60, 40, mp_open, None, 1, mp_open, None, 1)
p = p.next
p.next = _knot(40, 90, mp_open, None, 1, mp_open, None, 1)
p = p.next
p.next = _knot(10, 70, mp_open, None, 1, mp_open, None, 1)
p = p.next
p.next = _knot(30, 50, mp_open, None, 1, mp_open, None, 1)
p = p.next
p.next = knots
refpoints = [((-4.105545, 21.238037), (0, 0), (5.187561, -26.835297)),
((60.360733, -18.40036), (60, 40), (59.877136, 59.889008)),
((57.338959, 81.642029), (40, 90), (22.399872, 98.483871)),
((4.7240448, 84.463684), (10, 70), (13.386368, 60.716507)),
((26.355911, 59.135101), (30, 50), (39.194092, 26.951981))]
return knots, refpoints
def curve2(): # <<<
"""The closed curve of Fig.4a on page 6 of mpman.pdf
draw z0...z1...z2...z3...z4...cycle"""
p = _knot(0, 0, mp_open, None, 1, mp_open, None, 1)
knots = p
p.next = _knot(60, 40, mp_open, None, 1, mp_open, None, 1)
p = p.next
p.next = _knot(40, 90, mp_open, None, 1, mp_open, None, 1)
p = p.next
p.next = _knot(10, 70, mp_open, None, 1, mp_open, None, 1)
p = p.next
p.next = _knot(30, 50, mp_open, None, 1, mp_open, None, 1)
p = p.next
p.next = knots
refpoints = [
((-4.105545, 21.238037), (0, 0), (5.187561, -26.835297)),
((60.360733, -18.40036), (60, 40), (59.877136, 59.889008)),
((57.338959, 81.642029), (40, 90), (22.399872, 98.483871)),
((4.7240448, 84.463684), (10, 70), (13.386368, 60.716507)),
((26.355911, 59.135101), (30, 50), (39.194092, 26.951981))]
return knots, refpoints
def curve1(): # <<<
"""The open curve of Fig.3 on page 6 of mpman.pdf
draw z0..z1..z2..z3..z4"""
p = _knot(0, 0, mp_endpoint, None, None, mp_curl, 1, 1)
knots = p
p.next = _knot(60, 40, mp_open, None, 1, mp_open, None, 1)
p = p.next
p.next = _knot(40, 90, mp_open, None, 1, mp_open, None, 1)
p = p.next
p.next = _knot(10, 70, mp_open, None, 1, mp_open, None, 1)
p = p.next
p.next = _knot(30, 50, mp_curl, 1.0, 1, mp_endpoint, None, None)
p = p.next
p.next = knots
refpoints = [
((None, None), (0, 0), (26.764633, -1.8454285)),
((51.409393, 14.584412), (60, 40), (67.098755, 61.001877)),
((59.762527, 84.57518), (40, 90), (25.357147, 94.01947)),
((10.480637, 84.502197), (10, 70), (9.628952, 58.804214)),
((18.804214, 49.628952), (30, 50), (None, None))]
return knots, refpoints
def curve7(): # <<<
"""The first curve of Fig.10 on page 9 of mpman.pdf
draw z0..z1..tension atleast 1..{curl 2}z2..z3{-1,-2}..tension 3 and 4..z4..controls z45 and z54..z5;"""
p = _knot(0, 0, mp_endpoint, None, None, mp_curl, 1, 1) # z0
knots = p
p.next = _knot(50, 50, mp_open, None, 1, mp_open, None, -1) # z1
p = p.next
# XXX: curl value is copied over from one side to the other:
# this is mimicked by the default values of roughknot
p.next = _knot(80, 0, mp_curl, 2, -1, mp_curl, 2, 1) # z2
p = p.next
p.next = _knot(0, -20, mp_given, atan2(-2, -1), 1, mp_given, atan2(-2, -1), 3) # z3
p = p.next
p.next = _knot(50, -20, mp_open, None, 4, mp_explicit, -10, -50) # z4
p = p.next
p.next = _knot(150, 0, mp_explicit, 100, 50, mp_endpoint, None, None) # z5
p = p.next
p.next = knots
refpoints = [
((None, None), (0, 0), (-2.2696381, 28.501495)),
((21.498505, 52.269638), (50, 50), (78.324738, 47.744446)),
((94.584061, 19.255417), (80, 0), (57.765503, 24.445801)),
((16.6745, 13.348999), (0, -20), (-11.100037, -42.200073)),
((80.924652, -4.537674), (50, -20), (-10, -50)),
((100, 50), (150, 0), (None, None))]
return knots, refpoints
def curve7(): # <<<
"""The first curve of Fig.10 on page 9 of mpman.pdf
draw z0..z1..tension atleast 1..{curl 2}z2..z3{-1,-2}..tension 3 and 4..z4..controls z45 and z54..z5;"""
p = _knot(0, 0, mp_endpoint, None, None, mp_curl, 1, 1) # z0
knots = p
p.next = _knot(50, 50, mp_open, None, 1, mp_open, None, -1) # z1
p = p.next
# XXX: curl value is copied over from one side to the other:
# this is mimicked by the default values of roughknot
p.next = _knot(80, 0, mp_curl, 2, -1, mp_curl, 2, 1) # z2
p = p.next
p.next = _knot(0, -20, mp_given, atan2(-2, -1), 1, mp_given, atan2(-2, -1),
3) # z3
p = p.next
p.next = _knot(50, -20, mp_open, None, 4, mp_explicit, -10, -50) # z4
p = p.next
p.next = _knot(150, 0, mp_explicit, 100, 50, mp_endpoint, None, None) # z5
p = p.next
p.next = knots
refpoints = [((None, None), (0, 0), (-2.2696381, 28.501495)),
((21.498505, 52.269638), (50, 50), (78.324738, 47.744446)),
((94.584061, 19.255417), (80, 0), (57.765503, 24.445801)),
((16.6745, 13.348999), (0, -20), (-11.100037, -42.200073)),
((80.924652, -4.537674), (50, -20), (-10, -50)),
((100, 50), (150, 0), (None, None))]
return knots, refpoints
def curve3(): # <<<
"""The open curve of Fig.6 on page 8 of mpman.pdf
draw z0..z1{up}..z2{left}..z3..z4"""
p = _knot(0, 0, mp_endpoint, None, None, mp_curl, 1, 1)
knots = p
# XXX: given angle is copied over from one side to the other:
# this is mimicked by the default values of roughknot
p.next = _knot(60, 40, mp_given, 0.5 * pi, 1, mp_given, 0.5 * pi, 1)
p = p.next
p.next = _knot(40, 90, mp_given, pi, 1, mp_given, pi, 1)
p = p.next
p.next = _knot(10, 70, mp_open, None, 1, mp_open, None, 1)
p = p.next
p.next = _knot(30, 50, mp_curl, 1, 1, mp_endpoint, None, None)
p = p.next
p.next = knots
refpoints = [((None, None), (0, 0), (28.543137, -11.892975)),
((60, 9.0782776), (60, 40), (60, 63.263458)),
((60.129883, 90), (40, 90), (25.690277, 90)),
((11.52742, 83.230453), (10, 70), (8.666214, 58.446793)),
((18.446793, 48.666214), (30, 50), (None, None))]
return knots, refpoints
def curve10(): # <<<
"""Testing all parts of the code: test the "else" in item 364
This cannot be tested on the command level."""
p = _knot(0, 0, mp_open, None, -1, mp_open, None, 1) # z0
knots = p
# ltype is curl, and not both tensions are 1:
# This is already corrected by the parser of metapost
p.next = _knot(60, 40, mp_curl, 2, 2, mp_open, None, -1) # z1
p = p.next
p.next = _knot(40, 90, mp_open, None, -1, mp_open, None, -1) # z2
p = p.next
p.next = _knot(10, 70, mp_open, None, -1, mp_open, None, -1) # z3
p = p.next
p.next = _knot(30, 50, mp_open, None, -1, mp_open, None, -1) # z4
p = p.next
p.next = knots
refpoints = [((-10.430161, 23.006058), (0, 0), (23.677628, -52.226303)),
((79.551056, 19.028336), (60, 40), (53.081604, 57.296005)),
((40, 90), (40, 90), (22.69722, 100.22987)),
((3.934021, 85.090485), (10, 70), (13.668121, 60.874741)),
((26.782501, 59.383743), (30, 50), (37.508362, 28.102051))]
return knots, refpoints
def curve3(): # <<<
"""The open curve of Fig.6 on page 8 of mpman.pdf
draw z0..z1{up}..z2{left}..z3..z4"""
p = _knot(0, 0, mp_endpoint, None, None, mp_curl, 1, 1)
knots = p
# XXX: given angle is copied over from one side to the other:
# this is mimicked by the default values of roughknot
p.next = _knot(60, 40, mp_given, 0.5*pi, 1, mp_given, 0.5*pi, 1)
p = p.next
p.next = _knot(40, 90, mp_given, pi, 1, mp_given, pi, 1)
p = p.next
p.next = _knot(10, 70, mp_open, None, 1, mp_open, None, 1)
p = p.next
p.next = _knot(30, 50, mp_curl, 1, 1, mp_endpoint, None, None)
p = p.next
p.next = knots
refpoints = [
((None, None), (0, 0), (28.543137, -11.892975)),
((60, 9.0782776), (60, 40), (60, 63.263458)),
((60.129883, 90), (40, 90), (25.690277, 90)),
((11.52742, 83.230453), (10, 70), (8.666214, 58.446793)),
((18.446793, 48.666214), (30, 50), (None, None))]
return knots, refpoints
def curve9(): # <<<
"""Testing all parts of the code.
This cannot be tested on the command level."""
p = _knot(0, 0, mp_endpoint, None, None, mp_curl, 1, 1)
knots = p
p.next = _knot(50, 10, mp_open, None, 1, mp_explicit, 50, 10)
p = p.next
p.next = _knot(100, 0, mp_explicit, 100, 0, mp_open, None, 1)
p = p.next
p.next = _knot(150, 50, mp_explicit, 149, 49, mp_open, None, 1)
p = p.next
p.next = _knot(200.0, 0.0, mp_curl, 1, 1, mp_endpoint, None, None)
p = p.next
p.next = knots
refpoints = [((None, None), (0, 0), (16.666672, 3.3333282)),
((33.333328, 6.6666718), (50, 10), (50, 10)),
((100, 0), (100, 0), (116.66667, 16.666672)),
((149.65987, 49.659866), (150, 50), (183.33333, 83.333328)),
((233.33333, 33.333328), (200, 0), (None, None))]
return knots, refpoints
def curve10(): # <<<
"""Testing all parts of the code: test the "else" in item 364
This cannot be tested on the command level."""
p = _knot(0, 0, mp_open, None, -1, mp_open, None, 1) # z0
knots = p
# ltype is curl, and not both tensions are 1:
# This is already corrected by the parser of metapost
p.next = _knot(60, 40, mp_curl, 2, 2, mp_open, None, -1) # z1
p = p.next
p.next = _knot(40, 90, mp_open, None, -1, mp_open, None, -1) # z2
p = p.next
p.next = _knot(10, 70, mp_open, None, -1, mp_open, None, -1) # z3
p = p.next
p.next = _knot(30, 50, mp_open, None, -1, mp_open, None, -1) # z4
p = p.next
p.next = knots
refpoints = [
((-10.430161, 23.006058), (0, 0), (23.677628, -52.226303)),
((79.551056, 19.028336), (60, 40), (53.081604, 57.296005)),
((40, 90), (40, 90), (22.69722, 100.22987)),
((3.934021, 85.090485), (10, 70), (13.668121, 60.874741)),
((26.782501, 59.383743), (30, 50), (37.508362, 28.102051))]
return knots, refpoints
def curve9(): # <<<
"""Testing all parts of the code.
This cannot be tested on the command level."""
p = _knot(0, 0, mp_endpoint, None, None, mp_curl, 1, 1)
knots = p
p.next = _knot(50, 10, mp_open, None, 1, mp_explicit, 50, 10)
p = p.next
p.next = _knot(100, 0, mp_explicit, 100, 0, mp_open, None, 1)
p = p.next
p.next = _knot(150, 50, mp_explicit, 149, 49, mp_open, None, 1)
p = p.next
p.next = _knot(200.0, 0.0, mp_curl, 1, 1, mp_endpoint, None, None)
p = p.next
p.next = knots
refpoints = [
((None, None), (0, 0), (16.666672, 3.3333282)),
((33.333328, 6.6666718), (50, 10), (50, 10)),
((100, 0), (100, 0), (116.66667, 16.666672)),
((149.65987, 49.659866), (150, 50), (183.33333, 83.333328)),
((233.33333, 33.333328), (200, 0), (None, None))]
return knots, refpoints
