C++ gui QT4 OPENGL 开发6--使用遞迴分割繪製一顆茶壺形物體

关注

原创最新推荐文章于 2026-07-15 16:14:31 发布 1.2k 阅读 AI 写同款· GEO 优化 ›

Qt4.8下的OpenGL以及Glut画茶壶好多东西没弄懂，先记下来，省的以后再重复今天的麻烦 1.工程里的文件都怎么写？ QT += core gui opengl 这句话是指包含了G:\Qt\Qt481\Desktop\Qt\4.8.1\mingw\include下的那一堆qt自己的库其中的QT +=opengl 就是QtOpenGL文件夹的所在了，里面有QGLWidget类，这个类里有gl.h, 阅读详情

//main.cpp

#include <QApplication>
#include <iostream>

#include "teapots.h"

int main(int argc, char *argv[])
{
QApplication app(argc, argv);

    if (!QGLFormat::hasOpenGL()) {
        std::cerr << "This system has no OpenGL support" << std::endl;
        return 1;
    }

    Teapots teapots;
    teapots.setWindowTitle(QObject::tr("Teapots"));
    teapots.resize(400, 400);
    teapots.show();

return app.exec();
}

//teapots.h

#ifndef TEAPOTS_H
#define TEAPOTS_H

#include <QGLFramebufferObject>
#include <QGLWidget>

typedef GLfloat point[3];

class Teapots : public QGLWidget
{
Q_OBJECT

public:
Teapots(QWidget *parent = 0);
~Teapots();

protected:
    void initializeGL();
    void resizeGL(int width, int height);
    void paintGL();
    void mousePressEvent(QMouseEvent *event);
    void mouseMoveEvent(QMouseEvent *event);
    void mouseReleaseEvent(QMouseEvent *event);

private:
void createGLTeapotObject();

    GLuint glTeapotObject;

    point data[32][4][4];

    int level;
    void normal(point n, point p, point q, point r);
    void transpose(point a[4][4]);
    void divide_patch(point p[4][4], int n);
    void divide_curve(point c[4], point r[4], point l[4]);
    void draw_patch(point p[4][4]);

    int xRot;
    int yRot;
    int zRot;
    QPoint lastPos;
    void setXRotation(int angle);
    void normalizeAngle(int *angle);
};

#endif

//teapots.cpp

#include <QtGui>
#include <QtOpenGL>

#include "teapots.h"
/* 306 vertices */

point vertices[306]={{1.4 , 0.0 , 2.4}, {1.4 , -0.784 , 2.4},
{0.784 , -1.4 , 2.4}, {0.0 , -1.4 , 2.4}, {1.3375 , 0.0 , 2.53125},
{1.3375 , -0.749 , 2.53125}, {0.749 , -1.3375 , 2.53125}, {0.0 , -1.3375 , 2.53125},
{1.4375 , 0.0 , 2.53125}, {1.4375 , -0.805 , 2.53125}, {0.805 , -1.4375 , 2.53125},
{0.0 , -1.4375 , 2.53125}, {1.5 , 0.0 , 2.4}, {1.5 , -0.84 , 2.4},
{0.84 , -1.5 , 2.4}, {0.0 , -1.5 , 2.4}, {-0.784 , -1.4 , 2.4},
{-1.4 , -0.784 , 2.4}, {-1.4 , 0.0 , 2.4}, {-0.749 , -1.3375 , 2.53125},
{-1.3375 , -0.749 , 2.53125}, {-1.3375 , 0.0 , 2.53125}, {-0.805 , -1.4375 , 2.53125},
{-1.4375 , -0.805 , 2.53125}, {-1.4375 , 0.0 , 2.53125}, {-0.84 , -1.5 , 2.4},
{-1.5 , -0.84 , 2.4}, {-1.5 , 0.0 , 2.4}, {-1.4 , 0.784 , 2.4},
{-0.784 , 1.4 , 2.4}, {0.0 , 1.4 , 2.4}, {-1.3375 , 0.749 , 2.53125},
{-0.749 , 1.3375 , 2.53125}, {0.0 , 1.3375 , 2.53125}, {-1.4375 , 0.805 , 2.53125},
{-0.805 , 1.4375 , 2.53125}, {0.0 , 1.4375 , 2.53125}, {-1.5 , 0.84 , 2.4},
{-0.84 , 1.5 , 2.4}, {0.0 , 1.5 , 2.4}, {0.784 , 1.4 , 2.4},
{1.4 , 0.784 , 2.4}, {0.749 , 1.3375 , 2.53125}, {1.3375 , 0.749 , 2.53125},
{0.805 , 1.4375 , 2.53125}, {1.4375 , 0.805 , 2.53125}, {0.84 , 1.5 , 2.4},
{1.5 , 0.84 , 2.4}, {1.75 , 0.0 , 1.875}, {1.75 , -0.98 , 1.875},
{0.98 , -1.75 , 1.875}, {0.0 , -1.75 , 1.875}, {2.0 , 0.0 , 1.35},
{2.0 , -1.12 , 1.35}, {1.12 , -2.0 , 1.35}, {0.0 , -2.0 , 1.35},
{2.0 , 0.0 , 0.9}, {2.0 , -1.12 , 0.9}, {1.12 , -2.0 , 0.9},
{0.0 , -2.0 , 0.9}, {-0.98 , -1.75 , 1.875}, {-1.75 , -0.98 , 1.875},
{-1.75 , 0.0 , 1.875}, {-1.12 , -2.0 , 1.35}, {-2.0 , -1.12 , 1.35},
{-2.0 , 0.0 , 1.35}, {-1.12 , -2.0 , 0.9}, {-2.0 , -1.12 , 0.9},
{-2.0 , 0.0 , 0.9}, {-1.75 , 0.98 , 1.875}, {-0.98 , 1.75 , 1.875},
{0.0 , 1.75 , 1.875}, {-2.0 , 1.12 , 1.35}, {-1.12 , 2.0 , 1.35},
{0.0 , 2.0 , 1.35}, {-2.0 , 1.12 , 0.9}, {-1.12 , 2.0 , 0.9},
{0.0 , 2.0 , 0.9}, {0.98 , 1.75 , 1.875}, {1.75 , 0.98 , 1.875},
{1.12 , 2.0 , 1.35}, {2.0 , 1.12 , 1.35}, {1.12 , 2.0 , 0.9},
{2.0 , 1.12 , 0.9}, {2.0 , 0.0 , 0.45}, {2.0 , -1.12 , 0.45},
{1.12 , -2.0 , 0.45}, {0.0 , -2.0 , 0.45}, {1.5 , 0.0 , 0.225},
{1.5 , -0.84 , 0.225}, {0.84 , -1.5 , 0.225}, {0.0 , -1.5 , 0.225},
{1.5 , 0.0 , 0.15}, {1.5 , -0.84 , 0.15}, {0.84 , -1.5 , 0.15},
{0.0 , -1.5 , 0.15}, {-1.12 , -2.0 , 0.45}, {-2.0 , -1.12 , 0.45},
{-2.0 , 0.0 , 0.45}, {-0.84 , -1.5 , 0.225}, {-1.5 , -0.84 , 0.225},
{-1.5 , 0.0 , 0.225}, {-0.84 , -1.5 , 0.15}, {-1.5 , -0.84 , 0.15},
{-1.5 , 0.0 , 0.15}, {-2.0 , 1.12 , 0.45}, {-1.12 , 2.0 , 0.45},
{0.0 , 2.0 , 0.45}, {-1.5 , 0.84 , 0.225}, {-0.84 , 1.5 , 0.225},
{0.0 , 1.5 , 0.225}, {-1.5 , 0.84 , 0.15}, {-0.84 , 1.5 , 0.15},
{0.0 , 1.5 , 0.15}, {1.12 , 2.0 , 0.45}, {2.0 , 1.12 , 0.45},
{0.84 , 1.5 , 0.225}, {1.5 , 0.84 , 0.225}, {0.84 , 1.5 , 0.15},
{1.5 , 0.84 , 0.15}, {-1.6 , 0.0 , 2.025}, {-1.6 , -0.3 , 2.025},
{-1.5 , -0.3 , 2.25}, {-1.5 , 0.0 , 2.25}, {-2.3 , 0.0 , 2.025},
{-2.3 , -0.3 , 2.025}, {-2.5 , -0.3 , 2.25}, {-2.5 , 0.0 , 2.25},
{-2.7 , 0.0 , 2.025}, {-2.7 , -0.3 , 2.025}, {-3.0 , -0.3 , 2.25},
{-3.0 , 0.0 , 2.25}, {-2.7 , 0.0 , 1.8}, {-2.7 , -0.3 , 1.8},
{-3.0 , -0.3 , 1.8}, {-3.0 , 0.0 , 1.8}, {-1.5 , 0.3 , 2.25},
{-1.6 , 0.3 , 2.025}, {-2.5 , 0.3 , 2.25}, {-2.3 , 0.3 , 2.025},
{-3.0 , 0.3 , 2.25}, {-2.7 , 0.3 , 2.025}, {-3.0 , 0.3 , 1.8},
{-2.7 , 0.3 , 1.8}, {-2.7 , 0.0 , 1.575}, {-2.7 , -0.3 , 1.575},
{-3.0 , -0.3 , 1.35}, {-3.0 , 0.0 , 1.35}, {-2.5 , 0.0 , 1.125},
{-2.5 , -0.3 , 1.125}, {-2.65 , -0.3 , 0.9375}, {-2.65 , 0.0 , 0.9375},
{-2.0 , -0.3 , 0.9}, {-1.9 , -0.3 , 0.6}, {-1.9 , 0.0 , 0.6},
{-3.0 , 0.3 , 1.35}, {-2.7 , 0.3 , 1.575}, {-2.65 , 0.3 , 0.9375},
{-2.5 , 0.3 , 1.125}, {-1.9 , 0.3 , 0.6}, {-2.0 , 0.3 , 0.9},
{1.7 , 0.0 , 1.425}, {1.7 , -0.66 , 1.425}, {1.7 , -0.66 , 0.6},
{1.7 , 0.0 , 0.6}, {2.6 , 0.0 , 1.425}, {2.6 , -0.66 , 1.425},
{3.1 , -0.66 , 0.825}, {3.1 , 0.0 , 0.825}, {2.3 , 0.0 , 2.1},
{2.3 , -0.25 , 2.1}, {2.4 , -0.25 , 2.025}, {2.4 , 0.0 , 2.025},
{2.7 , 0.0 , 2.4}, {2.7 , -0.25 , 2.4}, {3.3 , -0.25 , 2.4},
{3.3 , 0.0 , 2.4}, {1.7 , 0.66 , 0.6}, {1.7 , 0.66 , 1.425},
{3.1 , 0.66 , 0.825}, {2.6 , 0.66 , 1.425}, {2.4 , 0.25 , 2.025},
{2.3 , 0.25 , 2.1}, {3.3 , 0.25 , 2.4}, {2.7 , 0.25 , 2.4},
{2.8 , 0.0 , 2.475}, {2.8 , -0.25 , 2.475}, {3.525 , -0.25 , 2.49375},
{3.525 , 0.0 , 2.49375}, {2.9 , 0.0 , 2.475}, {2.9 , -0.15 , 2.475},
{3.45 , -0.15 , 2.5125}, {3.45 , 0.0 , 2.5125}, {2.8 , 0.0 , 2.4},
{2.8 , -0.15 , 2.4}, {3.2 , -0.15 , 2.4}, {3.2 , 0.0 , 2.4},
{3.525 , 0.25 , 2.49375}, {2.8 , 0.25 , 2.475}, {3.45 , 0.15 , 2.5125},
{2.9 , 0.15 , 2.475}, {3.2 , 0.15 , 2.4}, {2.8 , 0.15 , 2.4},
{0.0 , 0.0 , 3.15}, {0.0 , -0.002 , 3.15}, {0.002 , 0.0 , 3.15},
{0.8 , 0.0 , 3.15}, {0.8 , -0.45 , 3.15}, {0.45 , -0.8 , 3.15},
{0.0 , -0.8 , 3.15}, {0.0 , 0.0 , 2.85}, {0.2 , 0.0 , 2.7},
{0.2 , -0.112 , 2.7}, {0.112 , -0.2 , 2.7}, {0.0 , -0.2 , 2.7},
{-0.002 , 0.0 , 3.15}, {-0.45 , -0.8 , 3.15}, {-0.8 , -0.45 , 3.15},
{-0.8 , 0.0 , 3.15}, {-0.112 , -0.2 , 2.7}, {-0.2 , -0.112 , 2.7},
{-0.2 , 0.0 , 2.7}, {0.0 , 0.002 , 3.15}, {-0.8 , 0.45 , 3.15},
{-0.45 , 0.8 , 3.15}, {0.0 , 0.8 , 3.15}, {-0.2 , 0.112 , 2.7},
{-0.112 , 0.2 , 2.7}, {0.0 , 0.2 , 2.7}, {0.45 , 0.8 , 3.15},
{0.8 , 0.45 , 3.15}, {0.112 , 0.2 , 2.7}, {0.2 , 0.112 , 2.7},
{0.4 , 0.0 , 2.55}, {0.4 , -0.224 , 2.55}, {0.224 , -0.4 , 2.55},
{0.0 , -0.4 , 2.55}, {1.3 , 0.0 , 2.55}, {1.3 , -0.728 , 2.55},
{0.728 , -1.3 , 2.55}, {0.0 , -1.3 , 2.55}, {1.3 , 0.0 , 2.4},
{1.3 , -0.728 , 2.4}, {0.728 , -1.3 , 2.4}, {0.0 , -1.3 , 2.4},
{-0.224 , -0.4 , 2.55}, {-0.4 , -0.224 , 2.55}, {-0.4 , 0.0 , 2.55},
{-0.728 , -1.3 , 2.55}, {-1.3 , -0.728 , 2.55}, {-1.3 , 0.0 , 2.55},
{-0.728 , -1.3 , 2.4}, {-1.3 , -0.728 , 2.4}, {-1.3 , 0.0 , 2.4},
{-0.4 , 0.224 , 2.55}, {-0.224 , 0.4 , 2.55}, {0.0 , 0.4 , 2.55},
{-1.3 , 0.728 , 2.55}, {-0.728 , 1.3 , 2.55}, {0.0 , 1.3 , 2.55},
{-1.3 , 0.728 , 2.4}, {-0.728 , 1.3 , 2.4}, {0.0 , 1.3 , 2.4},
{0.224 , 0.4 , 2.55}, {0.4 , 0.224 , 2.55}, {0.728 , 1.3 , 2.55},
{1.3 , 0.728 , 2.55}, {0.728 , 1.3 , 2.4}, {1.3 , 0.728 , 2.4},
{0.0 , 0.0 , 0.0}, {1.5 , 0.0 , 0.15}, {1.5 , 0.84 , 0.15},
{0.84 , 1.5 , 0.15}, {0.0 , 1.5 , 0.15}, {1.5 , 0.0 , 0.075},
{1.5 , 0.84 , 0.075}, {0.84 , 1.5 , 0.075}, {0.0 , 1.5 , 0.075},
{1.425 , 0.0 , 0.0}, {1.425 , 0.798 , 0.0}, {0.798 , 1.425 , 0.0},
{0.0 , 1.425 , 0.0}, {-0.84 , 1.5 , 0.15}, {-1.5 , 0.84 , 0.15},
{-1.5 , 0.0 , 0.15}, {-0.84 , 1.5 , 0.075}, {-1.5 , 0.84 , 0.075},
{-1.5 , 0.0 , 0.075}, {-0.798 , 1.425 , 0.0}, {-1.425 , 0.798 , 0.0},
{-1.425 , 0.0 , 0.0}, {-1.5 , -0.84 , 0.15}, {-0.84 , -1.5 , 0.15},
{0.0 , -1.5 , 0.15}, {-1.5 , -0.84 , 0.075}, {-0.84 , -1.5 , 0.075},
{0.0 , -1.5 , 0.075}, {-1.425 , -0.798 , 0.0}, {-0.798 , -1.425 , 0.0},
{0.0 , -1.425 , 0.0}, {0.84 , -1.5 , 0.15}, {1.5 , -0.84 , 0.15},
{0.84 , -1.5 , 0.075}, {1.5 , -0.84 , 0.075}, {0.798 , -1.425 , 0.0},
{1.425 , -0.798 , 0.0}};

/* 32 patches each defined by 16 vertices, arranged in a 4 x 4 array */
/* NOTE: numbering scheme for teapot has vertices labeled from 1 to 306 */
/* remnent of the days of FORTRAN */

int indices[32][4][4]={{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16},
{4, 17, 18, 19, 8, 20, 21, 22, 12, 23, 24, 25, 16, 26, 27, 28},
{19, 29, 30, 31, 22, 32, 33, 34, 25, 35, 36, 37, 28, 38, 39, 40},
{31, 41, 42, 1, 34, 43, 44, 5, 37, 45, 46, 9, 40, 47, 48, 13},
{13, 14, 15, 16, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60},
{16, 26, 27, 28, 52, 61, 62, 63, 56, 64, 65, 66, 60, 67, 68, 69},
{28, 38, 39, 40, 63, 70, 71, 72, 66, 73, 74, 75, 69, 76, 77, 78},
{40, 47, 48, 13, 72, 79, 80, 49, 75, 81, 82, 53, 78, 83, 84, 57},
{57, 58, 59, 60, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96},
{60, 67, 68, 69, 88, 97, 98, 99, 92, 100, 101, 102, 96, 103, 104, 105},
{69, 76, 77, 78, 99, 106, 107, 108, 102, 109, 110, 111, 105, 112, 113, 114},
{78, 83, 84, 57, 108, 115, 116, 85, 111, 117, 118, 89, 114, 119, 120, 93},
{121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136},
{124, 137, 138, 121, 128, 139, 140, 125, 132, 141, 142, 129, 136, 143, 144, 133},
{133, 134, 135, 136, 145, 146, 147, 148, 149, 150, 151, 152, 69, 153, 154, 155},
{136, 143, 144, 133, 148, 156, 157, 145, 152, 158, 159, 149, 155, 160, 161, 69},
{162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177},
{165, 178, 179, 162, 169, 180, 181, 166, 173, 182, 183, 170, 177, 184, 185, 174},
{174, 175, 176, 177, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197},
{177, 184, 185, 174, 189, 198, 199, 186, 193, 200, 201, 190, 197, 202, 203, 194},
{204, 204, 204, 204, 207, 208, 209, 210, 211, 211, 211, 211, 212, 213, 214, 215},
{204, 204, 204, 204, 210, 217, 218, 219, 211, 211, 211, 211, 215, 220, 221, 222},
{204, 204, 204, 204, 219, 224, 225, 226, 211, 211, 211, 211, 222, 227, 228, 229},
{204, 204, 204, 204, 226, 230, 231, 207, 211, 211, 211, 211, 229, 232, 233, 212},
{212, 213, 214, 215, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245},
{215, 220, 221, 222, 237, 246, 247, 248, 241, 249, 250, 251, 245, 252, 253, 254},
{222, 227, 228, 229, 248, 255, 256, 257, 251, 258, 259, 260, 254, 261, 262, 263},
{229, 232, 233, 212, 257, 264, 265, 234, 260, 266, 267, 238, 263, 268, 269, 242},
{270, 270, 270, 270, 279, 280, 281, 282, 275, 276, 277, 278, 271, 272, 273, 274},
{270, 270, 270, 270, 282, 289, 290, 291, 278, 286, 287, 288, 274, 283, 284, 285},
{270, 270, 270, 270, 291, 298, 299, 300, 288, 295, 296, 297, 285, 292, 293, 294},
{270, 270, 270, 270, 300, 305, 306, 279, 297, 303, 304, 275, 294, 301, 302, 271}};

Teapots::Teapots(QWidget *parent)
    : QGLWidget(parent)
{

    xRot = 0;
    yRot = 0;
    zRot = 0;

int i,j, k, m, n;

level=3;

for(i=0;i<32;i++) for(j=0;j<4;j++) for(k=0;k<4;k++) for(n=0;n<3;n++)
{

/* put teapot data into single array for subdivision */

        m=indices[i][j][k];
        for(n=0;n<3;n++) data[i][j][k][n]=vertices[m-1][n];
    }

}

Teapots::~Teapots()
{

}

void Teapots::initializeGL()
{

    static const GLfloat mat_specular[]={1.0, 1.0, 1.0, 1.0};
    static const GLfloat mat_diffuse[]={1.0, 1.0, 1.0, 1.0};
    static const GLfloat mat_ambient[]={1.0, 1.0, 1.0, 1.0};
    static const GLfloat mat_shininess={100.0};
    static const GLfloat light_ambient[]={0.0, 0.0, 0.0, 1.0};
    static const GLfloat light_diffuse[]={1.0, 1.0, 0.0, 1.0};
    static const GLfloat light_specular[]={1.0, 1.0, 1.0, 1.0};
    static const GLfloat light_position[]={10.0, 10.0, 10.0, 0.0};

    glLightfv(GL_LIGHT0, GL_POSITION, light_position);
    glLightfv(GL_LIGHT0, GL_AMBIENT, light_ambient);
    glLightfv(GL_LIGHT0, GL_DIFFUSE, light_diffuse);
    glLightfv(GL_LIGHT0, GL_SPECULAR, light_specular);

    glMaterialfv(GL_FRONT, GL_SPECULAR, mat_specular);
    glMaterialfv(GL_FRONT, GL_AMBIENT, mat_ambient);
    glMaterialfv(GL_FRONT, GL_DIFFUSE, mat_diffuse);
    glMaterialf(GL_FRONT, GL_SHININESS, mat_shininess);

    glEnable(GL_SMOOTH);
    glEnable(GL_LIGHTING);
    glEnable(GL_LIGHT0);

    glEnable(GL_DEPTH_TEST);
    glClearColor (0.0, 0.0, 0.0, 1.0);
    glColor3f (1.0, 1.0, 1.0);
    glEnable(GL_NORMALIZE); /* automatic normaization of normals */
    glEnable(GL_CULL_FACE); /* eliminate backfacing polygons */
    glCullFace(GL_BACK);

}

void Teapots::resizeGL(int width, int height)
{
     int w,h;
     w = width;
     h = height;
    glViewport(0, 0, w, h);
    glMatrixMode(GL_PROJECTION);
    glLoadIdentity();
    if (w <= h)
        glOrtho(-4.0, 4.0, -4.0 * (GLfloat) h / (GLfloat) w,
            4.0 * (GLfloat) h / (GLfloat) w, -10.0, 10.0);
    else
        glOrtho(-4.0 * (GLfloat) w / (GLfloat) h,
            4.0 * (GLfloat) w / (GLfloat) h, -4.0, 4.0, -10.0, 10.0);
    glMatrixMode(GL_MODELVIEW);

}

void Teapots::paintGL()
{
int i;

glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
glLoadIdentity();

/* data aligned along z axis, rotate to align with y axis */

    //glRotatef(-90.0, 1.0,0.0, 0.0);
    glRotated(xRot / 16.0, 1.0, 0.0, 0.0);
    for(i=0;i<32;i++) divide_patch(data[i], level); /* divide all 32 patches */

glFlush();

}

void Teapots::mousePressEvent(QMouseEvent *event)
{
lastPos = event->pos();
}

void Teapots::mouseMoveEvent(QMouseEvent *event)
{

    int dx = event->x() - lastPos.x();
    int dy = event->y() - lastPos.y();

    if (event->buttons() & Qt::LeftButton) {
        setXRotation(xRot + 8 * dy);
        //setYRotation(yRot + 8 * dx);
    } else if (event->buttons() & Qt::RightButton) {
        setXRotation(xRot + 8 * dy);
       // setZRotation(zRot + 8 * dx);
    }
    lastPos = event->pos();
}
void Teapots::setXRotation(int angle)
{
    normalizeAngle(&angle);
    if (angle != xRot) {
        xRot = angle;
        //emit xRotationChanged(angle);
        updateGL();
    }
}
void Teapots::normalizeAngle(int *angle)
{
    while (*angle < 0)
        *angle += 360 * 16;
    while (*angle > 360 * 16)
        *angle -= 360 * 16;
}
void Teapots::mouseReleaseEvent(QMouseEvent * /* event */)
{

}

void Teapots::createGLTeapotObject()
{

}

void Teapots::normal(point n, point p, point q, point r)
{
n[0]=(q[1]-p[1])*(r[2]-p[2])-(q[2]-p[2])*(r[1]-p[1]);
n[1]=(q[2]-p[2])*(r[0]-p[0])-(q[0]-p[0])*(r[2]-p[2]);
n[2]=(q[0]-p[0])*(r[2]-p[2])-(q[2]-p[2])*(r[0]-p[0]);
}

void Teapots::transpose(point a[4][4])
{

/* transpose wastes time but makes program more readable */

int i,j, k;
GLfloat tt;
for(i=0;i<4;i++) for(j=i;j<4; j++) for(k=0;k<3;k++)
    {
        tt=a[i][j][k];
        a[i][j][k]=a[j][i][k];
        a[j][i][k]=tt;
    }
}

void Teapots::divide_patch(point p[4][4], int n)
   {
   point q[4][4], r[4][4], s[4][4], t[4][4];
   point a[4][4], b[4][4];
   int i,j, k;
   if(n==0) draw_patch(p); /* draw patch if recursion done */

/* subdivide curves in u direction, transpose results, divide
in u direction again (equivalent to subdivision in v) */

   else
       {
       for(k=0; k<4; k++) divide_curve(p[k], a[k], b[k]);
       transpose(a);
       transpose(b);
       for(k=0; k<4; k++)
           {
           divide_curve(a[k], q[k], r[k]);
           divide_curve(b[k], s[k], t[k]);
           }

/* recursive division of 4 resulting patches */

       divide_patch(q, n-1);
       divide_patch(r, n-1);
       divide_patch(s, n-1);
       divide_patch(t, n-1);
       }
}

void Teapots::divide_curve(point c[4], point r[4], point l[4])
{

/* division of convex hull of Bezier curve */

   int i;
   point t;
   for(i=0;i<3;i++)
   {
       l[0][i]=c[0][i];
       r[3][i]=c[3][i];
       l[1][i]=(c[1][i]+c[0][i])/2;
       r[2][i]=(c[2][i]+c[3][i])/2;
       t[i]=(l[1][i]+r[2][i])/2;
       l[2][i]=(t[i]+l[1][i])/2;
       r[1][i]=(t[i]+r[2][i])/2;
       l[3][i]=r[0][i]=(l[2][i]+r[1][i])/2;
   }
}

void Teapots::draw_patch(point p[4][4])
{
    point n;
    normal(n, p[0][0], p[3][0], p[3][3]);
    glBegin(GL_QUADS);
    glNormal3fv(n);
    glVertex3fv(p[0][0]);
    glVertex3fv(p[3][0]);
    glVertex3fv(p[3][3]);
    glVertex3fv(p[0][3]);
    glEnd();
}