鏡射示例
Author: 藍邦偉  老師

$ A(x,y) $

$ 鏡射示例 $

$ O $

A'(x',y')

k = 1 (slider from 1 to 10, step 1)
list_1: {0.2679491924311227, 0.5773502691896257, 0.9999999999999999, 1.7320508075688767, 3.7320508075688776, -3.7320508075688763, -1.7320508075688783, -1.0000000000000002, -0.5773502691896257, -0.267949192431123, 0.2679491924311227, 0.577350269189626, 0.9999999999999997, 1.7320508075688754, 3.732050807568879, -3.7320508075688847, -1.732050807568877, -1.0000000000000004, -0.5773502691896264, -0.26794919243112264}
m = Element(list_1, k)
L: y = m * x
F = Point(L)
O = (0, 0)
c = Circle(O, 2)
D, E = Intersect(c, xAxis)
u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
Q_2: 0.66 * Corner[1] + 0.34 * 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])
A = (2, 2)
A' = Mirror(A, L)
B, C = Intersect(c, L)
α = Angle(E, O, F)
text1: "     $ \left [ \begin{array}{cc} x'  \\ y' \\ \end{array}  \right ]$
$=\left [ \begin{array}{cc} cos" + (LaTeX[2 * α]) + " & -sin" + (LaTeX[2 * α]) + " \\ sin" + (LaTeX[2 * α]) + " & cos" + (LaTeX[2 * α]) + " \\ \end{array}  \right ] \left [\begin{array}{cc} x \\ y \\ \end{array}   \right ] $
$=\left [ \begin{array}{cc} cos" + (LaTeX[2 * α]) + " & -sin" + (LaTeX[2 * α]) + " \\ sin" + (LaTeX[2 * α]) + " & cos" + (LaTeX[2 * α]) + " \\ \end{array}  \right ] \left [ \begin{array}{cc}  " + (LaTeX[x(A)]) + " \\  " + (LaTeX[y(A)]) + " \\ \end{array}  \right ]   $"
G = Point(L)
β = Angle(E, O, G)