# -*- coding: utf-8 -*- """ 三棱镜光的色散 · 交互式演示 (Pygame + 七色简化模型) 物理模型 -------- 1. 斯涅尔定律: n1 * sin(theta1) = n2 * sin(theta2) 2. 简化色散: 玻璃对七种色光的折射率不同 ( violet 1.53 -> red 1.51 ) —— 这就是"色散"的来源: 紫光偏折最多, 红光最少 3. 白光 = 七条彩色光线叠加的视觉效果 4. 棱镜内部发生第二次折射, 两次偏折同向叠加 -> 出射光展开成扇形 操作 ---- 鼠标拖动 : 改变入射光方向 (也可拖动左上角的入射光手柄) 滚轮 / ↑↓ : 微调入射角 ← → : 改变棱镜顶角 (30° ~ 90°) A D : 旋转整个棱镜 R : 重置 空格 : 暂停 / 继续 白光脉冲动画 H : 隐藏 / 显示辅助线(法线、入射点) 数字 1-4 : 切换玻璃材质 (冕牌玻璃 / 火石玻璃 / 重火石 / 水) ESC : 退出 """ import math import sys import pygame # ---------------------------------------------------------------------- # 基本设置 # ---------------------------------------------------------------------- WIDTH, HEIGHT = 1180, 760 FPS = 60 BG_COLOR = (16, 18, 28) PANEL_COLOR = (26, 30, 45) PRISM_FILL = (96, 110, 140) PRISM_EDGE = (200, 215, 245) PRISM_ALPHA_FILL = (60, 70, 100, 90) TEXT_COLOR = (225, 230, 245) SUB_COLOR = (150, 160, 185) GRID_COLOR = (34, 39, 56) # 七色光: 名称, 颜色(RGB), 折射率 SPECTRUM = [ ("红 Red", (255, 56, 56), 1.508), ("橙 Orange", (255, 145, 40), 1.511), ("黄 Yellow", (255, 226, 60), 1.514), ("绿 Green", ( 56, 220, 105), 1.518), ("蓝 Blue", ( 52, 145, 255), 1.523), ("靛 Indigo", (110, 85, 240), 1.528), ("紫 Violet", (200, 80, 255), 1.534), ] # 不同玻璃材质: 名称 -> 折射率偏移量(整体缩放色散强度) MATERIALS = [ ("冕牌玻璃 (色散弱)", 1.00), ("火石玻璃 (色散强)", 2.15), ("重火石 (色散极强)", 3.30), ("水 (色散很弱)", 0.35), ] BASE_N = 1.52 # 基准折射率 DISPERSION_SPREAD = 0.026 # 红-紫折射率差(基准) AIR_N = 1.0 # ---------------------------------------------------------------------- # 几何工具 # ---------------------------------------------------------------------- def rotate(p, ang, origin): c, s = math.cos(ang), math.sin(ang) x, y = p[0] - origin[0], p[1] - origin[1] return (origin[0] + x * c - y * s, origin[1] + x * s + y * c) def seg_intersect(p1, p2, p3, p4): """线段 p1p2 与 p3p4 的交点, 无交点返回 None""" x1, y1 = p1 x2, y2 = p2 x3, y3 = p3 x4, y4 = p4 den = (x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4) if abs(den) < 1e-12: return None t = ((x1 - x3) * (y3 - y4) - (y1 - y3) * (x3 - x4)) / den u = -((x1 - x2) * (y1 - y3) - (y1 - y2) * (x1 - x3)) / den if 1e-9 <= t <= 1.0001 and -0.0001 <= u <= 1.0001: # t>0: 排除起点所在边 return (x1 + t * (x2 - x1), y1 + t * (y2 - y1)) return None def refract(d, n, eta): """ 折射方向。d 为单位入射向量, n 为单位法线(朝向入射侧), eta = n1/n2 全反射返回 None """ cosi = -max(-1.0, min(1.0, d[0] * n[0] + d[1] * n[1])) if cosi < 0: # 法线方向反了, 翻过来 n = (-n[0], -n[1]) cosi = -cosi sin2t = eta * eta * (1.0 - cosi * cosi) if sin2t > 1.0: return None # 全反射 cost = math.sqrt(1.0 - sin2t) return (eta * d[0] + (eta * cosi - cost) * n[0], eta * d[1] + (eta * cosi - cost) * n[1]) def reflect(d, n): dot = d[0] * n[0] + d[1] * n[1] return (d[0] - 2 * dot * n[0], d[1] - 2 * dot * n[1]) def norm(v): m = math.hypot(*v) or 1e-9 return (v[0] / m, v[1] / m) # ---------------------------------------------------------------------- # 棱镜 # ---------------------------------------------------------------------- class Prism: def __init__(self, center, apex_deg=60, size=240): self.center = center self.apex_deg = apex_deg self.size = size self.rot = 0.0 # 整体旋转(弧度) self.build() def build(self): """等腰三角形, 顶点朝右""" a = math.radians(self.apex_deg) / 2 L = self.size top = (self.center[0] + L * math.cos(a) * 0.55, self.center[1] - L * math.sin(a)) bot = (self.center[0] + L * math.cos(a) * 0.55, self.center[1] + L * math.sin(a)) left = (self.center[0] - L * 0.62, self.center[1]) self.apex = top self.verts = [left, top, bot] self.edges = [(left, top), (top, bot), (bot, left)] self.normals = [] for p1, p2 in self.edges: e = (p2[0] - p1[0], p2[1] - p1[1]) nrm = norm((-e[1], e[0])) mid = ((p1[0] + p2[0]) / 2, (p1[1] + p2[1]) / 2) to_c = (self.center[0] - mid[0], self.center[1] - mid[1]) if nrm[0] * to_c[0] + nrm[1] * to_c[1] < 0: nrm = (-nrm[0], -nrm[1]) self.normals.append(nrm) def set_apex(self, deg): self.apex_deg = max(20.0, min(95.0, deg)) self.build() def rotate(self, d): self.rot += d self.verts = [rotate(v, d, self.center) for v in self.verts] self.edges = [(self.verts[0], self.verts[1]), (self.verts[1], self.verts[2]), (self.verts[2], self.verts[0])] self.apex = self.verts[1] self.normals = [] for p1, p2 in self.edges: e = (p2[0] - p1[0], p2[1] - p1[1]) nrm = norm((-e[1], e[0])) mid = ((p1[0] + p2[0]) / 2, (p1[1] + p2[1]) / 2) to_c = (self.center[0] - mid[0], self.center[1] - mid[1]) if nrm[0] * to_c[0] + nrm[1] * to_c[1] < 0: nrm = (-nrm[0], -nrm[1]) self.normals.append(nrm) # ---------------------------------------------------------------------- # 光线追踪: 一条光穿过棱镜 # ---------------------------------------------------------------------- def trace_ray(origin, direction, prism, ior): """ 返回 (路径点列表, 是否全反射, 各段出射点法线信息) """ pts = [origin] d = norm(direction) p = origin eta_in = AIR_N / ior eta_out = ior / AIR_N total_internal = False hit_info = [] for bounce in range(6): best = None best_t = 1e18 for idx, (p1, p2) in enumerate(prism.edges): ip = seg_intersect(p, (p[0] + d[0] * 4000, p[1] + d[1] * 4000), p1, p2) if ip: t = math.hypot(ip[0] - p[0], ip[1] - p[1]) if t < best_t: best_t = t best = (ip, idx) if best is None: pts.append((p[0] + d[0] * 3000, p[1] + d[1] * 3000)) break ip, idx = best pts.append(ip) n = prism.normals[idx] inside = (bounce % 2 == 1) eta = eta_out if inside else eta_in rd = refract(d, n, eta) if rd is None: total_internal = True rn = reflect(d, n) hit_info.append((ip, n, True)) d = rn p = (ip[0] + d[0] * 1e-4, ip[1] + d[1] * 1e-4) continue hit_info.append((ip, n, False)) # 沿法线朝折射侧偏移, 保证进入/离开介质而不是立即再碰到同一界面 shift = 1e-3 p = (ip[0] + n[0] * shift, ip[1] + n[1] * shift) d = rd if inside and bounce >= 1: pts.append((p[0] + d[0] * 3000, p[1] + d[1] * 3000)) break return pts, total_internal, hit_info # ---------------------------------------------------------------------- # 绘制辅助 # ---------------------------------------------------------------------- def draw_grid(surf): for x in range(0, WIDTH, 40): pygame.draw.line(surf, GRID_COLOR, (x, 0), (x, HEIGHT)) for y in range(0, HEIGHT, 40): pygame.draw.line(surf, GRID_COLOR, (0, y), (WIDTH, y)) def draw_glow_line(surf, color, p1, p2, width=3, glow=12): """带辉光的光线""" if glow: for g in range(glow, 0, -3): a = surf.copy() a.set_alpha(28) pygame.draw.line(a, color, p1, p2, width + g) surf.blit(a, (0, 0)) pygame.draw.line(surf, color, p1, p2, width) def blend(c1, c2, t): return tuple(int(c1[i] + (c2[i] - c1[i]) * t) for i in range(3)) # ---------------------------------------------------------------------- # 主程序 # ---------------------------------------------------------------------- def main(): pygame.init() screen = pygame.display.set_mode((WIDTH, HEIGHT)) pygame.display.set_caption("三棱镜 · 光的色散 Dispersion of Light | 拖动鼠标改变入射角") clock = pygame.time.Clock() font = pygame.font.SysFont("microsoftyahei,pingfangsc,wenquanyimicrohei,dejavusans", 20) small = pygame.font.SysFont("microsoftyahei,pingfangsc,wenquanyimicrohei,dejavusans", 15) title_font = pygame.font.SysFont("microsoftyahei,pingfangsc,wenquanyimicrohei,dejavusans", 26, bold=True) prism = Prism((640, 400), apex_deg=60, size=250) incident_deg = -8.0 # 入射光相对水平方向的角度(略向上, 打在迎光面上) mat_idx = 0 show_help_lines = True dragging = False paused = False pulse = 0.0 # 白光脉冲相位 def light_origin(): return (110.0, 400.0) def light_dir(): a = math.radians(incident_deg) return (math.cos(a), math.sin(a)) running = True while running: dt = clock.tick(FPS) / 1000.0 if not paused: pulse = (pulse + dt * 0.55) % 1.0 for ev in pygame.event.get(): if ev.type == pygame.QUIT: running = False elif ev.type == pygame.KEYDOWN: if ev.key == pygame.K_ESCAPE: running = False elif ev.key == pygame.K_r: prism = Prism((640, 400), 60, 250) incident_deg = -8.0 mat_idx = 0 elif ev.key == pygame.K_SPACE: paused = not paused elif ev.key == pygame.K_h: show_help_lines = not show_help_lines elif ev.key == pygame.K_UP: incident_deg = max(-70.0, incident_deg - 2) elif ev.key == pygame.K_DOWN: incident_deg = min(70.0, incident_deg + 2) elif ev.key == pygame.K_LEFT: prism.set_apex(prism.apex_deg - 3) elif ev.key == pygame.K_RIGHT: prism.set_apex(prism.apex_deg + 3) elif ev.key == pygame.K_a: prism.rotate(-math.radians(3)) elif ev.key == pygame.K_d: prism.rotate(math.radians(3)) elif ev.key in (pygame.K_1, pygame.K_2, pygame.K_3, pygame.K_4): mat_idx = ev.key - pygame.K_1 elif ev.type == pygame.MOUSEWHEEL: incident_deg = max(-70.0, min(70.0, incident_deg - ev.y * 1.5)) elif ev.type == pygame.MOUSEBUTTONDOWN and ev.button == 1: mx, my = ev.pos if my > HEIGHT - 200: # 点在说明栏上不改变入射角 continue o = light_origin() # 点手柄附近或直接点画面上半部分 => 拖动入射方向 if math.hypot(mx - o[0], my - o[1]) < 90 or my < HEIGHT - 210: dragging = True elif ev.type == pygame.MOUSEBUTTONUP and ev.button == 1: dragging = False elif ev.type == pygame.MOUSEMOTION and dragging: mx, my = ev.pos if my > HEIGHT - 200: # 点在说明栏上不改变入射角 continue o = light_origin() incident_deg = math.degrees(math.atan2(my - o[1], mx - o[0])) # ---------------- 绘制 ---------------- screen.fill(BG_COLOR) draw_grid(screen) # 棱镜 poly = prism.verts pygame.draw.polygon(screen, PRISM_FILL, poly) pygame.draw.polygon(screen, PRISM_EDGE, poly, 2) # 玻璃高光 hl = screen.copy() hl.set_alpha(40) pygame.draw.polygon(hl, (255, 255, 255), [prism.verts[0], prism.verts[1], ((prism.verts[1][0] + prism.verts[2][0]) / 2, (prism.verts[1][1] + prism.verts[2][1]) / 2)]) screen.blit(hl, (0, 0)) origin = light_origin() d = light_dir() endpoint = (origin[0] + d[0] * 260, origin[1] + d[1] * 260) # 入射白光 draw_glow_line(screen, (255, 255, 255), origin, endpoint, 5, 16) # 脉冲光点 if not paused: px = origin[0] + d[0] * 260 * pulse py = origin[1] + d[1] * 260 * pulse pygame.draw.circle(screen, (255, 255, 255), (int(px), int(py)), 6) strength = MATERIALS[mat_idx][1] rays = [] for name, col, base_ior in SPECTRUM: ior = AIR_N + (BASE_N + (base_ior - BASE_N) * strength - AIR_N) pts, tir, info = trace_ray(endpoint, d, prism, ior) rays.append((name, col, pts, tir, info)) # 棱镜内部: 各色光轻微分离 for name, col, pts, tir, info in rays: if len(pts) >= 3: for i in range(1, len(pts) - 1): draw_glow_line(screen, col, pts[i], pts[i + 1], 2, 6) # 出射扇形光谱 exit_segs = [] for name, col, pts, tir, info in rays: if len(pts) >= 3: last = pts[-1] prev = pts[-2] exit_segs.append((col, prev, last, name)) for col, prev, last, name in exit_segs: draw_glow_line(screen, col, prev, last, 3, 14) if not paused: t = pulse gx = prev[0] + (last[0] - prev[0]) * t gy = prev[1] + (last[1] - prev[1]) * t pygame.draw.circle(screen, col, (int(gx), int(gy)), 5) # 法线与入射点 if show_help_lines and rays: for _, _, pts, tir, info in rays[:1]: for ip, n, is_tir in info: L = 42 pygame.draw.line(screen, (120, 200, 255), (ip[0] - n[0] * L, ip[1] - n[1] * L), (ip[0] + n[0] * L, ip[1] + n[1] * L), 1) pygame.draw.circle(screen, (120, 200, 255), (int(ip[0]), int(ip[1])), 4, 1) # 屏幕上的光谱投影条 proj_y = HEIGHT - 150 pygame.draw.line(screen, (60, 66, 90), (60, proj_y), (WIDTH - 60, proj_y), 1) for col, prev, last, name in exit_segs: if last[0] > WIDTH or last[1] < 0 or last[1] > HEIGHT: continue x = max(60, min(WIDTH - 60, last[0])) pygame.draw.line(screen, col, (x, proj_y - 14), (x, proj_y + 14), 3) # ---------------- UI ---------------- # 标题 screen.blit(title_font.render("三棱镜 · 光的色散", True, TEXT_COLOR), (24, 18)) screen.blit(small.render("Dispersion of Light — 白光由多种色光组成，玻璃对不同色光折射率不同，" "紫光偏折最大、红光最小，于是白光被展开成光谱。", True, SUB_COLOR), (26, 50)) # 左侧数据面板 px0, py0 = 20, 92 pw, ph = 250, 196 s = pygame.Surface((pw, ph), pygame.SRCALPHA) s.fill((20, 24, 38, 190)) screen.blit(s, (px0, py0)) pygame.draw.rect(screen, (70, 80, 110), (px0, py0, pw, ph), 1, border_radius=6) y = py0 + 12 screen.blit(font.render("实时参数", True, TEXT_COLOR), (px0 + 14, y)) y += 32 screen.blit(small.render(f"入射角 (相对水平) {incident_deg:6.1f}°", True, SUB_COLOR), (px0 + 14, y)); y += 24 screen.blit(small.render(f"棱镜顶角 {prism.apex_deg:6.1f}°", True, SUB_COLOR), (px0 + 14, y)); y += 24 screen.blit(small.render(f"玻璃整体旋转 {math.degrees(prism.rot)%360:6.1f}°", True, SUB_COLOR), (px0 + 14, y)); y += 24 screen.blit(small.render(f"材质 {MATERIALS[mat_idx][0]}", True, SUB_COLOR), (px0 + 14, y)); y += 24 n_red = AIR_N + (BASE_N + (SPECTRUM[0][2] - BASE_N) * strength - AIR_N) n_vio = AIR_N + (BASE_N + (SPECTRUM[-1][2] - BASE_N) * strength - AIR_N) screen.blit(small.render(f"n(红) = {n_red:.3f} n(紫) = {n_vio:.3f}", True, SUB_COLOR), (px0 + 14, y)); y += 24 screen.blit(small.render(f"Δn = {n_vio - n_red:.4f} (色散强度)", True, (255, 210, 120)), (px0 + 14, y)) # 右侧光谱图例 lx, ly = WIDTH - 232, 92 lw, lh = 212, 250 s2 = pygame.Surface((lw, lh), pygame.SRCALPHA) s2.fill((20, 24, 38, 190)) screen.blit(s2, (lx, ly)) pygame.draw.rect(screen, (70, 80, 110), (lx, ly, lw, lh), 1, border_radius=6) y = ly + 12 screen.blit(font.render("七色光折射率", True, TEXT_COLOR), (lx + 14, y)) y += 34 for name, col, base_ior in SPECTRUM: n_i = AIR_N + (BASE_N + (base_ior - BASE_N) * strength - AIR_N) pygame.draw.rect(screen, col, (lx + 14, y + 3, 16, 12), border_radius=3) screen.blit(small.render(f"{name:<11s} n = {n_i:.3f}", True, SUB_COLOR), (lx + 38, y)) y += 26 y += 4 screen.blit(small.render("偏折角: 红 < 橙 < 黄 < 绿 < 蓝 < 靛 < 紫", True, (255, 210, 120)), (lx + 14, y)) # 未击中棱镜时给出提示 if not exit_segs: tip = font.render("光线没有打在棱镜的迎光面上 —— 请向上拖动或按 ↓ 调整入射角", True, (255, 190, 120)) screen.blit(tip, (WIDTH // 2 - tip.get_width() // 2, HEIGHT - 200)) # 底部操作说明 help_txt = ("拖动鼠标 = 改变入射角 | 滚轮/↑↓ = 微调 | ←→ = 顶角 | A/D = 旋转棱镜 | " "1-4 = 切换材质 | 空格 = 暂停 | H = 法线 | R = 重置 | ESC = 退出") screen.blit(small.render(help_txt, True, (130, 140, 168)), (24, HEIGHT - 34)) # 入射光手柄 pygame.draw.circle(screen, (255, 255, 255), (int(origin[0]), int(origin[1])), 9, 2) pygame.draw.circle(screen, (90, 100, 130), (int(origin[0]), int(origin[1])), 4) pygame.display.flip() pygame.quit() sys.exit(0) if __name__ == "__main__": main()