2D 座標架
Author: 藍邦偉  老師

$Step=%v$

1

2

3

4

5

$ 三角形的五心 $

$A$

$B$

$C$

$ 重心 $

$ 外心 $

內心

$ 垂心 $

$ 傍心 $

u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
Q_2: 0.7 * Corner[1] + 0.3 * Corner[2]
Q_3: (x(Q_2), y(Corner[4]))
poly1, q_1, q_2, q_4, q_3 = Polygon(Corner[1], Q_2, Q_3, Corner[4])
s = 2 (slider from 0 to 5, step 1)
t1 = 1 (slider from 0 to 1, step 0.01)
t2 = 1 (slider from 0 to 1, step 0.01)
t3 = 0 (slider from 0 to 1, step 0.01)
t4 = 0 (slider from 0 to 1, step 0.01)
t5 = 0 (slider from 0 to 1, step 0.01)
a0 = false
b0 = false
c0 = false
d0 = false
e0 = false
A = (2.7252083089257484, 0.5192098882600913)
B = (0.9872816020822708, 2.3526266786189667)
C = (3.6419169015464843, 2.9828637003048297)
a = Segment(B, C)
b = Segment(C, A)
c = Segment(A, B)
M_1 = Midpoint(a)
M_2 = Midpoint(b)
M_3 = Midpoint(c)
A_2: A + t2 * Vector[A, M_1]
B_2: B + t2 * Vector[B, M_2]
C_2: C + t2 * Vector[C, M_3]
u_1 = Vector(A, A_2)
u_2 = Vector(B, B_2)
u_3 = Vector(C, C_2)
G: 1 / 3 * (A + B + C)
p_1 = Segment(A, M_1)
p_2 = Segment(B, M_2)
p_3 = Segment(C, M_3)
d_1 = OrthogonalLine(M_1, a)
d_2 = OrthogonalLine(M_2, b)
d_3 = OrthogonalLine(M_3, c)
O_2 = Intersect(d_1, d_2)
T_2: M_1 - 4 * t2 * Vector[M_1, O_2]
T_6: M_3 - 4 * t2 * Vector[M_3, O_2]
T_1: M_1 + 4 * t2 * Vector[M_1, O_2]
T_3: M_2 + 4 * t2 * Vector[M_2, O_2]
T_5: M_3 + 4 * t2 * Vector[M_3, O_2]
v_4 = Vector(M_1, T_1)
v_3 = Vector(M_1, T_2)
v_1 = Vector(M_3, T_6)
v_2 = Vector(M_3, T_5)
v_5 = Vector(M_2, T_3)
T_4: M_2 - 4 * t2 * Vector[M_2, O_2]
v_6 = Vector(M_2, T_4)
r_1: 1 / 3 * Min[c, b]
r_2: 1 / 3 * Min[c, a]
r_3: 1 / 3 * Min[b, a]
d = Circle(A, r_1)
e = Circle(B, r_2)
f = Circle(C, r_3)
g, h = AngularBisector(c, b)
i, j = AngularBisector(b, a)
k, l = AngularBisector(a, c)
I = Intersect(h, j)
I_1 = Intersect(h, i)
I_2 = Intersect(g, j)
I_3 = Intersect(g, l)