def drawControlCurve(self):
self.app.canvas.delete("obj")
if (self.mode):
p0, p1 = point(self.cps[1]), point(self.cps[2])
t0 = vector(self.cps[1], self.cps[0])
t1 = vector(self.cps[3], self.cps[2])
r = 1
#for v in range(5):
#r = 0.2*(1-v/5)+1.8*(v/5)
c1, c2, c3, a, b = biarc_h(p0, t0, p1, t1, r)
cx, rx = circparam(p0, proj(c1), proj(c2))
cy, ry = circparam(proj(c2), proj(c3), p1)
cid = self.app.canvas.create_oval(cx[0] - 15,
cx[1] - 15,
cx[0] + 15,
cx[1] + 15,
outline="black",
fill="green",
tags="obj")
cid = self.app.canvas.create_oval(cy[0] - 15,
cy[1] - 15,
cy[0] + 15,
cy[1] + 15,
outline="black",
fill="green",
tags="obj")
if (c1 == None): return
cl = [p0, c1, c2, c3, p1]
cas = []
for j in range(0, 11):
cas.append((circarc_h(j / 10, [hom(p0, 1), c1, c2])))
for j in range(0, 11):
cas.append((circarc_h(j / 10, [c2, c3, hom(p1, 1)])))
#clc = [*x for x in cl]
carc = [(x[0], x[1]) for x in cas]
#self.app.canvas.create_line(clc,fill="lightblue",tag="obj")
self.app.canvas.create_line(carc, fill="darkgreen", tag="obj")
else:
for i in range(2, len(self.cps)):
cas = []
for j in range(0, 11):
cas.append((circarc(j / 10, self.cls[i - 2],
self.cps[i - 2:i + 1])))
#print(cas)
cl = [(x[0], x[1]) for x in self.cps[i - 2:i + 1]]
carc = [(x[0], x[1]) for x in cas]
self.app.canvas.create_line(cl, fill="lightblue", tag="obj")
self.app.canvas.create_line(carc, fill="darkgreen", tag="obj")
sys.stdout.flush()
def circarc(t, v, ps):
n1, l1 = unit_length(vector(ps[1], ps[0]))
n2, l2 = unit_length(vector(ps[1], ps[2]))
l = min(l1, l2)
p0 = hom(point(ps[1]) - l * v * n1, 1)
p2 = hom(point(ps[1]) - l * v * n2, 1)
w = dot(n1, unit((p2[0] - p0[0], p2[1] - p0[1])))
p1 = hom(point(ps[1]), w)
x = bezier2(t, [p0, p1, p2])
return proj(x)
def drawControlCurve(self):
self.app.canvas.delete("obj")
if (self.mode):
p0, p1 = point(self.cps[1]), point(self.cps[2])
t0 = vector(self.cps[1], self.cps[0])
t1 = vector(self.cps[3], self.cps[2])
r = 1
#for v in range(5):
#r = 0.2*(1-v/5)+1.8*(v/5)
c1, c2, c3, a, b = biarc_h(p0, t0, p1, t1, r)
if (c1 == None): return
cl = [p0, c1, c2, c3, p1]
cas = []
for j in range(0, 11):
cas.append((circarc_h(j / 10, [hom(p0, 1), c1, c2])))
for j in range(0, 11):
cas.append((circarc_h(j / 10, [c2, c3, hom(p1, 1)])))
#clc = [self.app.o2c(*x) for x in cl]
carc = [self.app.o2c(*x) for x in cas]
#self.app.canvas.create_line(clc,fill="lightblue",tag="obj")
self.app.canvas.create_line(carc, fill="darkgreen", tag="obj")
else:
for i in range(2, len(self.cps)):
cas = []
for j in range(0, 11):
cas.append((circarc(j / 10, self.cls[i - 2],
self.cps[i - 2:i + 1])))
#print(cas)
cl = [self.app.o2c(*x) for x in self.cps[i - 2:i + 1]]
carc = [self.app.o2c(*x) for x in cas]
self.app.canvas.create_line(cl, fill="lightblue", tag="obj")
self.app.canvas.create_line(carc, fill="darkgreen", tag="obj")
sys.stdout.flush()
def __init__(self, app):
super().__init__()
self.app = app
self.cps = []
self.cls = []
self.cidmap = {}
self._ori = {"cx": 0, "cy": 0, "ox": 0, "oy": 0, "item": None}
self.cps = [
point((100, 100)),
point((100, 300)),
point((400, 300)),
point((400, 600))
]
self.cls = [0.5, 0.5, 0.5]
self.mode = 1
self.mode = 0
self.manip = Manip.Idle
self.inserter = MouseManipulator(self, self.app, 1, None, Manip.Insert)
def onHandleMotion(self, event):
if (self.manip is not Manip.Move): return
print("HandleMotion")
sys.stdout.flush()
cx, cy = self.app.w2c(event.x, event.y)
ox, oy = self.app.w2o(event.x, event.y)
delta_cx = cx - self._ori["cx"]
delta_cy = cy - self._ori["cy"]
delta_ox = ox - self._ori["ox"]
delta_oy = oy - self._ori["oy"]
self._ori["cx"] = cx
self._ori["cy"] = cy
self._ori["ox"] = ox
self._ori["oy"] = oy
# move the control point handle
self.app.canvas.move(self._ori["item"], delta_cx, delta_cy)
# move the control point in object coordinates
i = self.cidmap[self._ori["item"]]
self.cps[i] = point(self.cps[i]) + point((delta_ox, delta_oy))
self.drawControlCurve()
def biarc_h(p0, t0, p1, t1, r):
t0 = unit(t0)
t1 = unit(t1)
chord = point(p0) - point(p1)
f = dot(t0, t1)
g = dot(chord, r * t0 + t1)
r = (1 / 3) * (f + 1) / 2 + 1 * (1 - (f + 1) / 2)
r = 1
c = dot(chord, chord)
b = 2 * dot(chord, r * t0 + t1)
a = 2 * r * (dot(t0, t1) - 1)
if a == 0:
c2 = lerp(0.5, p0, p1)
c1 = lerp(0.5, p0, c2)
c3 = lerp(0.5, c2, p1)
w1 = 1 #dot( t0,unit(c2 - p0))
w2 = 1 #dot( t1,unit(p1 - c2))
return hom(c1, w1), hom(c2, 1), hom(c3, w2), 1, 1
D = b * b - 4 * a * c
if D < 0:
print(D, "<0")
beta = norm2(chord) / 4 * dot(chord, t0)
else:
sqD = D**.5
beta1 = (-b - sqD) / 2 / a
beta2 = (-b + sqD) / 2 / a
if beta1 > 0 and beta2 > 0:
print(beta1, beta2, ">0")
return None, None, None, 0, 0
beta = max(beta1, beta2)
if beta < 0:
print(beta, "<0")
return None, None, None, 0, 0
alpha = beta * r
ab = alpha + beta
c1 = point(p0) + alpha * t0
c3 = point(p1) - beta * t1
c2 = (beta / ab) * point(c1) + (alpha / ab) * point(c3)
#print(alpha,beta)
w1 = dot(t0, unit(c2 - p0))
w2 = dot(t1, unit(p1 - c2))
return hom(c1, w1), hom(c2, 1), hom(c3, w2), alpha, beta
def biarc(p0, t0, p1, t1, r):
t0 = unit(t0)
t1 = unit(t1)
chord = point(p0) - point(p1)
f = dot(t0, t1)
g = dot(chord, r * t0 + t1)
r = (1 / 3) * (f + 1) / 2 + 1 * (1 - (f + 1) / 2)
c = dot(chord, chord)
b = 2 * dot(chord, r * t0 + t1)
a = 2 * r * (dot(t0, t1) - 1)
if a == 0:
return None, None, None, 0, 0
D = b * b - 4 * a * c
if D < 0:
print(D, "<0")
beta = norm2(chord) / 4 * dot(chord, t0)
else:
sqD = D**.5
beta1 = (-b - sqD) / 2 / a
beta2 = (-b + sqD) / 2 / a
if beta1 > 0 and beta2 > 0:
print(beta1, beta2, ">0")
return None, None, None, 0, 0
beta = max(beta1, beta2)
if beta < 0:
print(beta, "<0")
return None, None, None, 0, 0
alpha = beta * r
ab = alpha + beta
c1 = point(p0) + alpha * t0
c3 = point(p1) - beta * t1
c2 = (beta / ab) * point(c1) + (alpha / ab) * point(c3)
#print(alpha,beta)
return c1, c2, c3, alpha, beta
def lerp(t, a, b):
return (1 - t) * point(a) + t * point(b)