write a python program

lab CG/lab 3/L3-Q2.py

from OpenGL.GL import * from OpenGL.GLUT import * from OpenGL.GLU import * import math # Support math operations import numpy as np # Support efficient vectors and matrices def pBezierSurface(u, v, G_x, G_y): B = np.array([ [ 1, -3, 3, -1 ], [ 0, 3, -6, 3 ], [ 0, 0, 3, -3 ], [ 0, 0, 0, 1 ] ]) U = np.array([ [ 1 ], [ u ], [ u * u ], [ u * u * u ] ]) V = np.array([ [ 1 ], [ v ], [ v * v ], [ v * v * v ] ]) B_u = np.matmul(B, U).T B_v = np.matmul(B, V) p_x = np.matmul(B_u, np.matmul(G_x, B_v)) p_y = np.matmul(B_u, np.matmul(G_y, B_v)) return np.concatenate((p_x[0], p_y[0])) def display(): control_points = np.array([ [150, 200], # P 1,1 [200, 190], # P 1,2 [250, 200], # P 1,3 [300, 190], # P 1,4 [140, 250], # P 2,1 [210, 240], # P 2,2 [260, 250], # P 2,3 [290, 240], # P 2,4 [150, 300], # P 3,1 [200, 290], # P 3,2 [250, 300], # P 3,3 [300, 290], # P 3,4 [140, 350], # P 4,1 [210, 340], # P 4,2 [260, 350], # P 4,3 [290, 340] # P 4,4 ]) # Control points as a NumPy array n = 10 # Number of intervals for discretizing u, v # Create a 4*4 matrix for each coordinate of the control points G_x = np.zeros((4, 4)) G_y = np.zeros((4, 4)) for i in range(4): for j in range(4): k = i * 4 + j G_x[i][j] = control_points[k][0] G_y[i][j] = control_points[k][1] # Reset glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT) glLoadIdentity() # Create a matrix-like list of points P(u, v) glBegin(GL_POINTS) points = [] for i in range(n + 1): u = i / n points_by_u = [] for j in range(n + 1): v = j / n p = pBezierSurface(u, v, G_x, G_y) points_by_u.append(p) glVertex2fv(p) points.append(points_by_u) glEnd() # Draw the surface's skeleton glBegin(GL_LINES) for i in range(n): for j in range(n): p1 = points[i][j] p2 = points[i + 1][j] p3 = points[i + 1][j + 1] p4 = points[i][j + 1] glVertex2fv(p1) glVertex2fv(p2) glVertex2fv(p2) glVertex2fv(p3) glVertex2fv(p3) glVertex2fv(p4) glVertex2fv(p4) glVertex2fv(p1) glEnd() glutSwapBuffers() def idle(): display() def initRendering(): glEnable(GL_DEPTH_TEST) # glEnable(GL_LIGHTING) # glEnable(GL_LIGHT0) def reshape(w, h): glViewport(0, 0, w, h) glMatrixMode(GL_PROJECTION) glLoadIdentity() glOrtho(0.0, w, 0.0, h, 0.0, 1.0) glMatrixMode(GL_MODELVIEW) glLoadIdentity() w, h = 500, 500 u, v = 100, 100 glutInit() glutInitDisplayMode(GLUT_RGB | GLUT_DOUBLE | GLUT_DEPTH) glutInitWindowSize(w, h) glutInitWindowPosition(u, v) glutCreateWindow("Lab 03") initRendering() glutReshapeFunc(reshape, w, h) glutDisplayFunc(display) glutIdleFunc(idle) glutMainLoop()