给一个代码说明纹理映射过程

纹理映射（Texture Mapping）是计算机图形学中的一个重要概念，用于将纹理图像映射到三维模型表面上，从而增强模型的真实感和细节。以下是一个简单的代码示例，说明了纹理映射的过程：

# 导入所需库
import cv2
import numpy as np

# 加载模型和纹理图像
obj = cv2.imread('model.obj')
texture = cv2.imread('texture.jpg')

# 定义模型表面的三角形顶点和纹理坐标
vertices = [[0, 0, 0], [0, 1, 0], [1, 0, 0]]
tex_coords = [[0, 0], [0, 1], [1, 0]]

# 定义相机位置和投影矩阵
camera_pos = [0, 0, 1]
projection_matrix = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])

# 遍历模型表面的所有三角形，计算纹理映射后的颜色值
for i in range(len(obj) - 2):
    # 获取当前三角形的顶点和纹理坐标
    v1, v2, v3 = vertices[obj[i][0] - 1], vertices[obj[i][1] - 1], vertices[obj[i][2] - 1]
    t1, t2, t3 = tex_coords[obj[i][3] - 1], tex_coords[obj[i][4] - 1], tex_coords[obj[i][5] - 1]

    # 计算三角形的法向量和相机到三角形的距离
    normal = np.cross(v2 - v1, v3 - v1)
    distance = np.dot(normal, v1 - camera_pos)

    # 如果三角形背面朝向相机，则跳过该三角形
    if distance > 0:
        continue

    # 计算三角形在相机坐标系下的顶点和纹理坐标
    v1_cam = np.dot(projection_matrix, v1 - camera_pos)
    v2_cam = np.dot(projection_matrix, v2 - camera_pos)
    v3_cam = np.dot(projection_matrix, v3 - camera_pos)
    t1_cam = np.dot(projection_matrix, np.array([t1[0], t1[1], 1]))
    t2_cam = np.dot(projection_matrix, np.array([t2[0], t2[1], 1]))
    t3_cam = np.dot(projection_matrix, np.array([t3[0], t3[1], 1]))

    # 根据透视投影的原理，将相机坐标系下的顶点和纹理坐标归一化到屏幕坐标系下
    v1_screen = np.array([v1_cam[0] / v1_cam[2], v1_cam[1] / v1_cam[2]])
    v2_screen = np.array([v2_cam[0] / v2_cam[2], v2_cam[1] / v2_cam[2]])
    v3_screen = np.array([v3_cam[0] / v3_cam[2], v3_cam[1] / v3_cam[2]])
    t1_screen = np.array([t1_cam[0] / t1_cam[2], t1_cam[1] / t1_cam[2]])
    t2_screen = np.array([t2_cam[0] / t2_cam[2], t2_cam[1] / t2_cam[2]])
    t3_screen = np.array([t3_cam[0] / t3_cam[2], t3_cam[1] / t3_cam[2]])

    # 将屏幕坐标系下的顶点和纹理坐标转换成像素坐标系下的整数值
    v1_pixel = np.array([int(v1_screen[0] * texture.shape[1]), int(v1_screen[1] * texture.shape[0])])
    v2_pixel = np.array([int(v2_screen[0] * texture.shape[1]), int(v2_screen[1] * texture.shape[0])])
    v3_pixel = np.array([int(v3_screen[0] * texture.shape[1]), int(v3_screen[1] * texture.shape[0])])
    t1_pixel = np.array([int(t1_screen[0] * texture.shape[1]), int(t1_screen[1] * texture.shape[0])])
    t2_pixel = np.array([int(t2_screen[0] * texture.shape[1]), int(t2_screen[1] * texture.shape[0])])
    t3_pixel = np.array([int(t3_screen[0] * texture.shape[1]), int(t3_screen[1] * texture.shape[0])])

    # 根据三角形的顶点和纹理坐标，利用双线性插值计算每个像素的纹理颜色值
    for x in range(min(v1_pixel[0], v2_pixel[0], v3_pixel[0]), max(v1_pixel[0], v2_pixel[0], v3_pixel[0])):
        for y in range(min(v1_pixel[1], v2_pixel[1], v3_pixel[1]), max(v1_pixel[1], v2_pixel[1], v3_pixel[1])):
            if x < 0 or x >= texture.shape[1] or y < 0 or y >= texture.shape[0]:
                continue
            if point_in_triangle(np.array([x, y]), v1_pixel, v2_pixel, v3_pixel):
                weight1 = barycentric(np.array([x, y]), v2_pixel, v3_pixel, v1_pixel)
                weight2 = barycentric(np.array([x, y]), v1_pixel, v3_pixel, v2_pixel)
                weight3 = barycentric(np.array([x, y]), v1_pixel, v2_pixel, v3_pixel)
                tex_color1 = texture[t1_pixel[1], t1_pixel[0]]
                tex_color2 = texture[t2_pixel[1], t2_pixel[0]]
                tex_color3 = texture[t3_pixel[1], t3_pixel[0]]
                color = weight1 * tex_color1 + weight2 * tex_color2 + weight3 * tex_color3
                obj[y, x] = color

上述代码中，`vertices` 和 `tex_coords` 分别表示模型表面的三角形顶点和纹理坐标。在遍历模型表面的所有三角形时，我们首先计算每个三角形在相机坐标系下的顶点和纹理坐标，然后将它们归一化到屏幕坐标系下，并转换成像素坐标系下的整数值。接下来，我们根据双线性插值的原理，在三角形内部的每个像素位置计算出纹理颜色值，并将其赋值给模型表面的对应像素。