C++ OpenGL 实现双三次 B-样条曲面片绘制

以下是一个简单的双三次 B-样条曲面片的 C++ 代码示例，使用 OpenGL 库进行绘制。

#include <GL/glut.h>

const int MAX_POINTS = 20; // 最大控制点数
const int ORDER = 4; // 阶数

int numPoints = 0; // 当前控制点数
GLfloat controlPoints[MAX_POINTS][MAX_POINTS][3]; // 控制点数组

void init() {
    glClearColor(1.0, 1.0, 1.0, 1.0);
    glEnable(GL_DEPTH_TEST);
    glShadeModel(GL_SMOOTH);
    glMatrixMode(GL_PROJECTION);
    gluPerspective(45.0, 1.0, 1.0, 100.0);
}

// 计算 B-样条基函数
GLfloat BSplineBasis(int i, int k, GLfloat u, GLfloat* knots) {
    if (k == 0) {
        if (u >= knots[i] && u < knots[i + 1]) {
            return 1.0;
        }
        return 0.0;
    }

    GLfloat w1 = 0.0, w2 = 0.0;

    if (knots[i + k] - knots[i] > 0.0) {
        w1 = ((u - knots[i]) / (knots[i + k] - knots[i])) * BSplineBasis(i, k - 1, u, knots);
    }

    if (knots[i + k + 1] - knots[i + 1] > 0.0) {
        w2 = ((knots[i + k + 1] - u) / (knots[i + k + 1] - knots[i + 1])) * BSplineBasis(i + 1, k - 1, u, knots);
    }

    return w1 + w2;
}

// 计算双三次 B-样条曲面片上某个点的坐标
void calculateBSplinePoint(GLfloat u, GLfloat v, GLfloat* point) {
    GLfloat uKnots[MAX_POINTS + ORDER] = {0.0, 0.0, 0.0, 0.0};
    GLfloat vKnots[MAX_POINTS + ORDER] = {0.0, 0.0, 0.0, 0.0};

    for (int i = 0; i < numPoints + ORDER; i++) {
        if (i >= ORDER && i < numPoints + ORDER) {
            uKnots[i] = (GLfloat)i / (numPoints + ORDER - 1);
            vKnots[i] = (GLfloat)i / (numPoints + ORDER - 1);
        }
    }

    GLfloat uBasis[ORDER], vBasis[ORDER];
    GLfloat x = 0.0, y = 0.0, z = 0.0;

    for (int i = 0; i < numPoints; i++) {
        for (int j = 0; j < numPoints; j++) {
            uBasis[0] = BSplineBasis(i, ORDER - 1, u, uKnots);
            vBasis[0] = BSplineBasis(j, ORDER - 1, v, vKnots);

            for (int k = 1; k < ORDER; k++) {
                uBasis[k] = BSplineBasis(i, ORDER - k - 1, u, uKnots);
                vBasis[k] = BSplineBasis(j, ORDER - k - 1, v, vKnots);
            }

            x += controlPoints[i][j][0] * uBasis[ORDER - 1] * vBasis[ORDER - 1];
            y += controlPoints[i][j][1] * uBasis[ORDER - 1] * vBasis[ORDER - 1];
            z += controlPoints[i][j][2] * uBasis[ORDER - 1] * vBasis[ORDER - 1];
        }
    }

    point[0] = x;
    point[1] = y;
    point[2] = z;
}

void display() {
    glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
    glMatrixMode(GL_MODELVIEW);
    glLoadIdentity();
    gluLookAt(5.0, 5.0, 5.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0);

    GLfloat point[3];

    for (GLfloat u = 0.0; u < 1.0; u += 0.1) {
        glBegin(GL_LINE_STRIP);

        for (GLfloat v = 0.0; v < 1.0; v += 0.1) {
            calculateBSplinePoint(u, v, point);
            glVertex3fv(point);
        }

        glEnd();
    }

    for (GLfloat v = 0.0; v < 1.0; v += 0.1) {
        glBegin(GL_LINE_STRIP);

        for (GLfloat u = 0.0; u < 1.0; u += 0.1) {
            calculateBSplinePoint(u, v, point);
            glVertex3fv(point);
        }

        glEnd();
    }

    glutSwapBuffers();
}

void keyboard(unsigned char key, int x, int y) {
    switch(key) {
        case 27:
            exit(0);
            break;
    }
}

void mouse(int button, int state, int x, int y) {
    if (button == GLUT_LEFT_BUTTON && state == GLUT_DOWN) {
        GLfloat winX = (GLfloat)x;
        GLfloat winY = (GLfloat)glutGet(GLUT_WINDOW_HEIGHT) - (GLfloat)y;
        GLfloat winZ = 0.0;
        GLfloat posX = 0.0, posY = 0.0, posZ = 0.0;

        glReadPixels(x, (int)winY, 1, 1, GL_DEPTH_COMPONENT, GL_FLOAT, &winZ);
        gluUnProject(winX, winY, winZ,
                     (GLfloat*)glutGet(GLUT_WINDOW_MODELVIEW_MATRIX),
                     (GLfloat*)glutGet(GLUT_WINDOW_PROJECTION_MATRIX),
                     (GLint*)glutGet(GLUT_WINDOW_VIEWPORT),
                     &posX, &posY, &posZ);

        if (numPoints < MAX_POINTS) {
            controlPoints[numPoints][0] = posX;
            controlPoints[numPoints][1] = posY;
            controlPoints[numPoints][2] = posZ;
            numPoints++;
        }
    }

    glutPostRedisplay();
}

int main(int argc, char** argv) {
    glutInit(&argc, argv);
    glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB | GLUT_DEPTH);
    glutInitWindowSize(500, 500);
    glutCreateWindow('B-Spline Surface');
    init();
    glutDisplayFunc(display);
    glutKeyboardFunc(keyboard);
    glutMouseFunc(mouse);
    glutMainLoop();
    return 0;
}

该代码使用双三次 B-样条曲面片算法，可以绘制曲面片并使用鼠标添加控制点。在 OpenGL 中使用 gluUnProject 函数将鼠标点击位置转换为三维坐标，然后将该坐标作为控制点添加到控制点数组中。在每次绘制时，使用 calculateBSplinePoint 函数计算出曲面片上每个点的坐标并绘制出来。