推移的概念
Author: 藍邦偉  老師

推移的概念

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\left [ \begin{array}{cc} 1 & h \ 0 & 1 \ \end{array}  \right ]\left [ \begin{array}{cc} x \ y \ \end{array}  \right ]  =\left [  \begin{array}{cc} x+hy \  y \ \end{array} \right ] 

\left [\begin{array}{cc} 1 & 0 \ k & 1 \ \end{array}   \right ] \left [  \begin{array}{cc} x \ y \ \end{array} \right ] =\left [\begin{array}{cc} x \ kx+y \ \end{array}   \right ] 

u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
O = (0, 0)
h = 0 (slider from -5 to 5, step 0.1)
k = 0 (slider from -5 to 5, step 0.1)
text1: "沿x軸推y座標的" + h + "倍"
a = 5 (slider from 0.1 to 5, step 0.1)
A_1: O
A_2: A_1 + (a, 0)
A_3: (a + h * a, a)
A_4: (h * a, a)
b = Segment(A_4, A_1)
c = Segment(A_1, A_2)
d = Segment(A_3, A_2)
e = Segment(A_3, A_4)
O_1: 0.5 * (A_1 + A_3)
r: 0.2 * Distance[A_1, A_2]
B_0: O_1 + (r, 0)
B_3: B_1
B_4: B_1
B_5: B_1
B_6: B_1
B_7: B_1
B_8: O_1 + (r * cos(240°), r * sin(240°))
B_9: O_1 + (r * cos(270°), r * sin(270°))
B_{10}: O_1 + (r * cos(300°), r * sin(300°))
B_{11}: O_1 + (r * cos(330°), r * sin(330°))
f = Line(B_3, B_9)
B_2: B_1
g = Line(B_2, B_8)
i = Line(B_1, B_7)
j = Line(B_0, B_6)
l = Line(B_4, B_{10})
m = Line(B_5, B_{11})
C_3 = Intersect(f, e)
C_2 = Intersect(g, e)
C_1 = Intersect(i, d)
C_0 = Intersect(j, d)
C_{11} = Intersect(m, d)
C_{10} = Intersect(l, c)
C_9 = Intersect(f, c)
C_8 = Intersect(g, c)
C_7 = Intersect(i, b)
C_5 = Intersect(m, b)
C_4 = Intersect(l, e)
C_6 = Intersect(j, b)
q: (x - x(O_1) - h * (y - y(O_1)))^(2) + (y - y(O_1))^(2) = r^(2)
A = Midpoint(A_1, A_2)
B = Midpoint(A_2, A_3)
C = Midpoint(A_3, A_4)
D = Midpoint(A_4, A_1)
n = true
o = false
text3: "沿y軸推x座標的" + k + "倍"
Q_1: O
Q_4: Q_1 + (0, a)
ka: k * a
Q_2: Q_1 + (a, ka)
Q_3: Q_1 + (a, a + ka)
p = Segment(Q_4, O)
s = Segment(O, Q_2)
t = Segment(Q_2, Q_3)
a_1 = Segment(Q_3, Q_4)
u' = Vector((x(Corner[1]), 0), (x(Corner[2]), 0))
v' = Vector((0, y(Corner[1])), (0, y(Corner[3])))