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 draw(self, canvas, **kw):
#c1,c2,c3,a,b = biarc_h(self.p0,self.t0,self.p1,self.t1,self.r)
cas = []
for j in range(0, 50):
cas.append(self.eval(j / 49))
cl = [
self.p0,
proj(self.bp[0]),
proj(self.bp[1]),
proj(self.bp[2]), self.p1
]
return canvas.create_line([(x[0], x[1]) for x in cas], **kw)
def offset(self, o):
b = deepcopy(self)
pt0 = perp2(b.t0)
pt1 = perp2(b.t1)
c1 = proj(b.bp[0])
c2 = proj(b.bp[1])
c3 = proj(b.bp[2])
t2 = unit(c3 - c1)
pt2 = perp2(t2)
cc1 = unit(c2 - b.p0)
cc2 = unit(b.p1 - c2)
dp1 = dot(b.t0, cc1)
dp2 = dot(b.t1, cc2)
#t2 = unit(pt0 + refl(pt0,cc1))
#t3 = unit(pt1 + refl(pt1,cc2))
t2 = perp2(cc1)
t3 = perp2(cc2)
b.p0 = b.p0 + o * pt0
b.p1 = b.p1 + o * pt1
c2 = c2 + o * pt2
c1 = c1 + o / dp1 * t2
c3 = c3 + o / dp2 * t3
w1 = b.bp[0][2] #dot( b.t0,unit(c2 - b.p0))
w2 = b.bp[2][2] #dot( b.t1,unit(b.p1 - c2))
w1 = dot(b.t0, cc1)
w2 = dot(b.t1, cc2)
alpha = norm(c1 - c2)
beta = norm(c3 - c2)
b.r = alpha / beta
b.bp = (hom(c1, w1), hom(c2, 1), hom(c3, w2), alpha, beta)
b.h1 = [hom(b.p0, 1), b.bp[0], b.bp[1]]
b.h2 = [b.bp[1], b.bp[2], hom(b.p1, 1)]
return b
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 biarc_r_from_arcs(a1, a2):
alpha = norm(a1[0] - proj(a1[1]))
beta = norm(a1[3] - proj(a1[4]))
return alpha / beta
def circarc_h(t, hs):
x = bezier2(t, hs)
return proj(x)
return umt * umt * ps[0] + 2 * umt * t * ps[1] + t * t * ps[2]
def bezier2_d(t, ps):
umt = 1 - t
return 2 * umt * (ps[1] - ps[0]) + 2 * t * (ps[2] - ps[1])
def bezier2_dr(t, ps):
# use quotient rule
cut = [la.cut(ps[0]), la.cut(ps[1]), la.cut(ps[2])]
xt = bezier2(t, cut)
dxt = bezier2_d(t, cut)
w = [ps[0][2], ps[1][2], ps[2][2]]
wt = bezier2(t, w)
dwt = bezier2_d(t, w)
return (dxt * wt - dwt * xt) / (wt * wt)
def arc(p0, p1, p2):
w = la.dot(la.unit(p1 - p0), la.unit(p2 - p0))
return [la.hom(p0, 1), la.hom(p1, w), la.hom(p2, 1)]
#A = arc(la.coords(0,0),la.coords(1,1),la.coords(0,2))
A = [la.coords(1, 0, 1), la.coords(0, 4, 0), la.coords(5, 0, 1)]
p = bezier2(0.5, A)
t = bezier2_dr(0.5, A)
print(p, t)
print(la.proj(p))