import pygame import math import random # ========================================== # INITIALISATION & CONSTANTES # ========================================== pygame.init() WIDTH, HEIGHT = 1100, 850 screen = pygame.display.set_mode((WIDTH, HEIGHT)) pygame.display.set_caption("Construction Géométrique Interactive") clock = pygame.time.Clock() # Couleurs BLACK = (0, 0, 0) BLUE = (30, 144, 255) ORANGE = (255, 165, 0) RED = (220, 20, 60) MAUVE = (224, 176, 255) GRAY = (130, 130, 160) WHITE = (255, 255, 255) FOCUS_BG = (25, 35, 55) FOCUS_BORDER = (70, 110, 200) # Système de caméra / Focus cam_x, cam_y = 0.0, 0.0 zoom = 1.0 dragging = False drag_start = (0, 0) # Géométrie v1, v2, theta = None, None, None pts = {} show_trisection = True # ========================================== # FONCTIONS MATHÉMATIQUES & TRANSFORMATIONS # ========================================== def screen_to_world(sx, sy): """Convertit coordonnées écran -> monde""" return ((sx - WIDTH/2) / zoom + cam_x, (sy - HEIGHT/2) / zoom + cam_y) def world_to_screen(wx, wy): """Convertit coordonnées monde -> écran""" return (int((wx - cam_x) * zoom + WIDTH/2), int((wy - cam_y) * zoom + HEIGHT/2)) def calculate_geometry(): """Génère ou recalcule toute la construction""" global v1, v2, theta, pts v1 = random.randint(140, 320) v2 = random.randint(60, 2*v1 - 1) theta = 2 * math.asin(v2 / (2 * v1)) # Points de base O = (0, 0) A = (v1, 0) B = (v1 * math.cos(theta), v1 * math.sin(theta)) # Trisection de l'arc T1 = (v1 * math.cos(theta/3), v1 * math.sin(theta/3)) T2 = (v1 * math.cos(2*theta/3), v1 * math.sin(2*theta/3)) # Bissectrice phi = theta / 2 dir_ = (math.cos(phi), math.sin(phi)) M = (v1 * dir_[0], v1 * dir_[1]) # Prolongement + double du côté : OM + 2*OA = 3*OA P = (3 * v1 * dir_[0], 3 * v1 * dir_[1]) # O' : intersection cercle(M, v1) et bissectrice O_prime = (2 * v1 * dir_[0], 2 * v1 * dir_[1]) # M' : intersection arc(O', v1) et prolongement bissectrice (loin de O) M_prime = (3 * v1 * dir_[0], 3 * v1 * dir_[1]) # Distance MA MA = math.hypot(A[0] - M[0], A[1] - M[1]) # Intersections : cercle(O', v1) ∩ cercle(M', MA) d = math.hypot(M_prime[0] - O_prime[0], M_prime[1] - O_prime[1]) # Doit valoir v1 a = (v1**2 - MA**2 + d**2) / (2 * d) h = math.sqrt(max(0, v1**2 - a**2)) mid_x = O_prime[0] + a * dir_[0] mid_y = O_prime[1] + a * dir_[1] perp = (-dir_[1], dir_[0]) A_prime = (mid_x + h * perp[0], mid_y + h * perp[1]) B_prime = (mid_x - h * perp[0], mid_y - h * perp[1]) pts = { 'O': O, 'A': A, 'B': B, 'T1': T1, 'T2': T2, 'M': M, 'P': P, 'O\'': O_prime, 'M\'': M_prime, 'A\'': A_prime, 'B\'': B_prime } calculate_geometry() # ========================================== # FONCTIONS DE DESSIN # ========================================== def draw_line(color, p1, p2, width=2): s1, s2 = world_to_screen(p1[0], p1[1]), world_to_screen(p2[0], p2[1]) pygame.draw.line(screen, color, s1, s2, width) def draw_circle(color, center, radius, width=2): s = world_to_screen(center[0], center[1]) pygame.draw.circle(screen, color, s, max(1, int(radius * zoom)), width) def draw_arc_math(color, center, radius, start, end, width=2): """Dessine un arc avec angles mathématiques (0=Est, +CCW)""" sx, sy = world_to_screen(center[0], center[1]) r = max(1, int(radius * zoom)) rect = pygame.Rect(sx - r, sy - r, 2 * r, 2 * r) # Pygame: angles croissants CW, Y inversé. On inverse les angles. pygame.draw.arc(screen, color, rect, -end, -start, width) def draw_point(color, pos, radius=5): s = world_to_screen(pos[0], pos[1]) pygame.draw.circle(screen, color, s, radius) def draw_label(text, pos, color=WHITE, offset=(10, -10), size=20): font = pygame.font.SysFont(None, size) surf = font.render(text, True, color) s = world_to_screen(pos[0], pos[1]) screen.blit(surf, (s[0] + offset[0], s[1] + offset[1])) def draw_focus_indicator(): """Indicateur visuel du centre de zoom/focus""" cx, cy = WIDTH//2, HEIGHT//2 size = 200 # Fond subtil focus_surf = pygame.Surface((size, size), pygame.SRCALPHA) focus_surf.fill((*FOCUS_BG[:3], 40)) screen.blit(focus_surf, (cx - size//2, cy - size//2)) # Bordure & croix pygame.draw.rect(screen, FOCUS_BORDER, (cx - size//2, cy - size//2, size, size), 2) pygame.draw.line(screen, FOCUS_BORDER, (cx - 15, cy), (cx + 15, cy), 2) pygame.draw.line(screen, FOCUS_BORDER, (cx, cy - 15), (cx, cy + 15), 2) # ========================================== # BOUCLE PRINCIPALE # ========================================== running = True while running: for event in pygame.event.get(): if event.type == pygame.QUIT: running = False elif event.type == pygame.KEYDOWN: if event.key == pygame.K_t: show_trisection = not show_trisection elif event.key == pygame.K_r: calculate_geometry() elif event.key == pygame.K_f: # Reset focus au centre cam_x, cam_y, zoom = 0.0, 0.0, 1.0 elif event.type == pygame.MOUSEBUTTONDOWN: if event.button == 1: dragging = True drag_start = event.pos elif event.button == 4: # Molette haut wx, wy = screen_to_world(event.pos[0], event.pos[1]) zoom = min(5.0, zoom * 1.25) cam_x = wx - (event.pos[0] - WIDTH/2) / zoom cam_y = wy - (event.pos[1] - HEIGHT/2) / zoom elif event.button == 5: # Molette bas wx, wy = screen_to_world(event.pos[0], event.pos[1]) zoom = max(0.2, zoom / 1.25) cam_x = wx - (event.pos[0] - WIDTH/2) / zoom cam_y = wy - (event.pos[1] - HEIGHT/2) / zoom elif event.type == pygame.MOUSEMOTION: if dragging: dx = event.pos[0] - drag_start[0] dy = event.pos[1] - drag_start[1] cam_x -= dx / zoom cam_y -= dy / zoom drag_start = event.pos elif event.type == pygame.MOUSEBUTTONUP: if event.button == 1: dragging = False # ---- DESSIN ---- screen.fill(BLACK) draw_focus_indicator() # 1) Bissectrice (orange) & point M draw_line(ORANGE, pts['O'], pts['P'], 3) draw_point(ORANGE, pts['M'], 6) draw_label("M", pts['M'], ORANGE) # 2) Cercle de centre M (rouge) & point O' draw_circle(RED, pts['M'], v1, 2) draw_point(RED, pts['O\''], 7) draw_label("O'", pts['O\''], RED) # 3) Arc reporté (mauve), M', cercle M', et points A', B' draw_arc_math(MAUVE, pts['O\''], v1, 0, theta, 2) draw_point(MAUVE, pts['M\''], 6) draw_label("M'", pts['M\''], MAUVE) MA = math.hypot(pts['A'][0]-pts['M'][0], pts['A'][1]-pts['M'][1]) draw_circle(MAUVE, pts['M\''], MA, 2) draw_point(MAUVE, pts['A\''], 6) draw_point(MAUVE, pts['B\''], 6) draw_label("A'", pts['A\''], MAUVE) draw_label("B'", pts['B\''], MAUVE) # 4) Segments OA' et OB' (mauve) draw_line(MAUVE, pts['O'], pts['A\''], 3) draw_line(MAUVE, pts['O'], pts['B\''], 3) # Angle de base (bleu) draw_line(BLUE, pts['O'], pts['A'], 3) draw_line(BLUE, pts['O'], pts['B'], 3) draw_arc_math(BLUE, pts['O'], v1, 0, theta, 3) draw_point(BLUE, pts['A'], 6) draw_point(BLUE, pts['B'], 6) draw_label("O", pts['O'], WHITE, offset=(10, 10)) draw_label("A", pts['A'], BLUE) draw_label("B", pts['B'], BLUE) # Cercles de trisection (toggle T) if show_trisection: draw_circle(GRAY, pts['T1'], v1, 1) draw_circle(GRAY, pts['T2'], v1, 1) draw_point(GRAY, pts['T1'], 4) draw_point(GRAY, pts['T2'], 4) draw_label("T1", pts['T1'], GRAY, offset=(-20, -10)) draw_label("T2", pts['T2'], GRAY, offset=(-20, -10)) # UI & Infos font_ui = pygame.font.SysFont(None, 22) info = font_ui.render(f"OA={v1} | AB={v2} | θ={math.degrees(theta):.1f}° | Zoom={zoom:.2f}x", True, WHITE) screen.blit(info, (15, HEIGHT - 45)) help_text = font_ui.render("🖱️ Clic+Glisser: Déplacer | 🖱️ Molette: Zoom | T: Cercles | R: Random | F: Reset", True, (120, 140, 180)) screen.blit(help_text, (15, HEIGHT - 20)) pygame.display.flip() clock.tick(60) pygame.quit()