import matplotlib.pyplot as plt
 
# x 값을 직접 생성하는 함수 (numpy 없이)
def generate_x(start, end, step):
    data = []
    v = start
    while v <= end:
        data.append(v)
        v += step
    return data
 
# 포물선 y = x^2
x = generate_x(-2, 2, 0.01)
y = [v**2 for v in x]
 
# 여러 광선을 시작할 x 좌표
ray_starts = [-1.5, -1.0, -0.5, 0.5, 1.0, 1.5]
 
plt.figure(figsize=(6,6))
 
# 포물선 그리기
plt.plot(x, y)
 
for xs in ray_starts:
    # 포물선과 만나는 점 (px, py)
    px = xs
    py = px**2
 
    # 포물선의 접선 기울기 m = 2x
    m_tan = 2 * px
 
    # 반사된 광선 기울기 (단순 반사용)
    m_ref = -m_tan
 
    # 들어오는 광선: y = 1에서 포물선으로 내려오는 선
    plt.plot([xs, px], [1, py])
 
    # 반사된 광선을 직접 생성 (x축 방향으로 1만큼)
    rx = generate_x(px, px + 1, 0.02)
    ry = [py + m_ref * (r - px) for r in rx]
 
    plt.plot(rx, ry)
 
plt.xlim(-2, 2)
plt.ylim(-0.2, 2)
plt.xlabel("x")
plt.ylabel("y")
plt.title("포물선 반사 시뮬레이션")
plt.show()
 

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