c++ - OpenGL:带三角剖分的贝塞尔曲面

Question

我尝试使用 OpenGL 绘制贝塞尔曲面。我的程序读取一个输入文件，其中包含用于绘图的样本点数、控制点和用于表面着色的调色板。它必须输出一个带有曲面图的新窗口，我可以在其中操纵曲面和控制点的属性。

从 Bernstein 多项式生成的点被三角化，并通过从三角形的最小和最大高度映射它来按调色板分配颜色。

当我执行它时，一排三角形被分配了错误的颜色。我以为我的一个循环中有错误，但更改值并没有证明什么。

代码如下:

#include <iostream>
#include <vector>
#include <string>
#include <fstream>
#include <GL/gl.h>
#include <GL/glu.h>
#include <GL/glut.h>
#include <cmath>


using namespace std;


struct vertex
{
    float x;
    float y;
    float z;
};


struct RGB
{
    float r;
    float g;
    float b;
};


int main_window;


bool TM = true;
vertex surfaceTranslate;
float surfaceRotate = 0;
vertex camera;
vertex up;
int currentPointX = 0, currentPointY = 0;
vertex toY;

int SampleR, SampleC;
int M, N;
int K;
vector < vector <vertex> > points;
vector <RGB> palette;
vector < vector <vertex> > control;
float minH, maxH;


int fact (int n)
{
    if (!n || n == 1)
    {
        return 1;
    }
    return n * fact (n - 1);
}

int C (int n, int i)
{
    return fact (n) / (fact (i) * fact (n - i));
}


void initialDisplay(void)
{
    glClearColor (1.0, 1.0, 1.0, 1.0);
    glDisable (GL_LIGHTING);
    glEnable (GL_RESCALE_NORMAL);
    glMatrixMode (GL_PROJECTION);
    glLoadIdentity();
    gluPerspective (60, 1, 1, 1000000);
    glMatrixMode (GL_MODELVIEW);
    glLoadIdentity();
}


void updateControl()
{
    control.clear();
    for (int i = 0; i < SampleR; ++i)
    {
        vector <vertex> temp;
        for (int j = 0; j < SampleC; ++j)
        {
            float u = (float)(i) / (SampleR - 1);
            float v = (float)(j) / (SampleC - 1);
            vertex p;
            p.x = p.y = p.z = 0;
            for (int k = 0; k < M; ++k)
            {
                for (int m = 0; m < N; ++m)
                {
                    float B_u = C (M - 1, k) * pow (u, k) * pow (1 - u, M - 1 - k);
                    float B_v = C (N - 1, m) * pow (v, m) * pow (1 - v, N - 1 - m);
                    p.x += B_u * B_v * points[k][m].x;
                    p.y += B_u * B_v * points[k][m].y;
                    p.z += B_u * B_v * points[k][m].z;
                }
            }
            temp.push_back (p);
        }
        control.push_back (temp);
    }
    maxH = 1 << ((sizeof(float) * 8) - 1);
    minH = -maxH;
    for (int i = 0; i < SampleR - 1; ++i)
    {
        for (int j = 0; j < SampleC - 1; ++j)
        {
            float h = (control[i][j].y + control[i + 1][j].y + control[i][j + 1].y) / 3;
            if (h > maxH)
            {
                maxH = h;
            }
            if (h < minH)
            {
                minH = h;
            }
            h = (control[i + 1][j].y + control[i][j + 1].y + control[i + 1][j + 1].y) / 3;
            if (h > maxH)
            {
                maxH = h;
            }
            if (h < minH)
            {
                minH = h;
            }
        }
    }
    for (int i = 0; i < SampleR; ++i)
    {
        for (int j = 0; j < SampleC; ++j)
        {
            toY.x += control[i][j].x;
            toY.z += control[i][j].z;
        }
        toY.x /= SampleR * SampleC;
        toY.z /= SampleR * SampleC;
    }
}


void display(void)
{
    glClear (GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
    glLoadIdentity();
    gluLookAt (camera.x, camera.y, camera.z, 0, 0, 0, up.x, up.y, up.z);
    glTranslatef (surfaceTranslate.x, surfaceTranslate.y, surfaceTranslate.z);
    glTranslatef (toY.x, toY.y, toY.z);
    glRotatef (surfaceRotate, 0, 1, 0);
    glTranslatef (- toY.x, -toY.y, -toY.z);
    if (!TM)
    {
        glPointSize (10);
        glBegin (GL_POINTS);
        for (int i = 0; i < M; ++i)
        {
            for (int j = 0; j < N; ++j)
            {
                if (i == currentPointX && j == currentPointY)
                {
                    glColor3f (1.0, 0.0, 0.0);
                }
                else
                {
                    glColor3f (0.0, 0.0, 1.0);
                }
                glVertex3f (points[i][j].x, points[i][j].y, points[i][j].z);
            }
        }
        glEnd();
    }
    glBegin (GL_TRIANGLES);
    for (int i = 0; i < SampleR - 1; ++i)
    {
        for (int j = 0; j < SampleC - 1; ++j)
        {
            glVertex3f (control[i][j].x, control[i][j].y, control[i][j].z);
            glVertex3f (control[i + 1][j].x, control[i + 1][j].y, control[i + 1][j].z);
            glVertex3f (control[i][j + 1].x, control[i][j + 1].y, control[i][j + 1].z);
            float h = (control[i][j].y + control[i + 1][j].y + control[i][j + 1].y) / 3;
            int index = K * (h - minH) / (maxH - minH);
            glColor3f (palette[index].r / 255, palette[index].g / 255, palette[index].b / 255);
            glVertex3f (control[i + 1][j].x, control[i + 1][j].y, control[i + 1][j].z);
            glVertex3f (control[i][j + 1].x, control[i][j + 1].y, control[i][j + 1].z);
            glVertex3f (control[i + 1][j + 1].x, control[i + 1][j + 1].y, control[i + 1][j + 1].z);
            h = (control[i + 1][j].y + control[i][j + 1].y + control[i + 1][j + 1].y) / 3;
            index = K * (h - minH) / (maxH - minH);
            glColor3f (palette[index].r / 255, palette[index].g / 255, palette[index].b / 255);
        }
    }
    glEnd();
    glutSwapBuffers();
}


void keyboardEvent (unsigned char key, int x, int y)
{
    if (TM)
    {
        switch (key)
        {
            case ('2'):
                TM = false;
                glutSetWindowTitle ("Surface Editing Mode");
                break;
            case ('q'):
                --surfaceTranslate.x;
                break;
            case ('w'):
                ++surfaceTranslate.x;
                break;
            case ('a'):
                --surfaceTranslate.y;
                break;
            case ('s'):
                ++surfaceTranslate.y;
                break;
            case ('z'):
                --surfaceTranslate.z;
                break;
            case ('x'):
                ++surfaceTranslate.z;
                break;
            case ('r'):
                ++surfaceRotate;
                break;
            case ('t'):
                --surfaceRotate;
                break;
        }
    }
    else
    {
        switch (key)
        {
            case ('1'):
                TM = true;
                glutSetWindowTitle ("Transformation Mode");
                break;
            case ('q'):
                --points[currentPointX][currentPointY].x;
                updateControl();
                break;
            case ('w'):
                ++points[currentPointX][currentPointY].x;
                updateControl();
                break;
            case ('a'):
                --points[currentPointX][currentPointY].y;
                updateControl();
                break;
            case ('s'):
                ++points[currentPointX][currentPointY].y;
                updateControl();
                break;
            case ('z'):
                --points[currentPointX][currentPointY].z;
                updateControl();
                break;
            case ('x'):
                ++points[currentPointX][currentPointY].z;
                updateControl();
                break;
            case ('i'):
                if (!(SampleR % 2))
                {
                    SampleR /= 2;
                    updateControl();
                }
                break;
            case ('o'):
                SampleR *= 2;
                updateControl();
                break;
            case ('k'):
                if (!(SampleC % 2))
                {
                    SampleC /= 2;
                    updateControl();
                }
                break;
            case ('l'):
                SampleC *= 2;
                updateControl();
                break;
        }
    }
    glutPostRedisplay();
}


void arrowKeys (int key, int x, int y)
{
    if (!TM)
    {
        switch (key)
        {
            case (GLUT_KEY_UP):
                if (currentPointY < N - 1)
                {
                    ++currentPointY;
                }
                break;
            case (GLUT_KEY_DOWN):
                if (currentPointY)
                {
                    --currentPointY;
                }
                break;
            case (GLUT_KEY_LEFT):
                if (currentPointX)
                {
                    --currentPointX;
                }
                break;
            case (GLUT_KEY_RIGHT):
                if (currentPointX < M - 1)
                {
                    ++currentPointX;
                }
                break;
        }
        glutPostRedisplay();
    }
}


void changeDirection (int x, int y)
{
    float dist = sqrt (pow (camera.x, 2) + pow (camera.y, 2) + pow (camera.z, 2));
    camera.x = dist * sin (360.0 / 800 * x * 0.0174532) * sin (360.0 / 800 * y * 0.0174532);
    camera.y = dist * cos (360.0 / 800 * y * 0.0174532);
    camera.z = dist * cos (360.0 / 800 * x * 0.0174532) * sin (360.0 / 800 * y * 0.0174532);
    up.x = dist * sin (360.0 / 800 * x * 0.0174532) * sin (360.0 / 800 * y * 0.0174532 - 1) - camera.x;
    up.y = dist * cos (360.0 / 800 * y * 0.0174532 - 1) - camera.y;
    up.z = dist * cos (360.0 / 800 * x * 0.0174532) * sin (360.0 / 800 * y * 0.0174532 - 1) - camera.z;
    glutPostRedisplay();
}


void mouseEvent (int key, int state, int x, int y)
{
    if (key == GLUT_KEY_LEFT)
    {
        changeDirection (x, y);
    }
}



void readFile (char *fname)
{
    ifstream file (fname);
    if (file.is_open())
    {
        file >> SampleR >> SampleC;
        file >> M >> N;
        for (int i = 0; i < M; ++i)
        {
            vector <vertex> tempv;
            for (int j = 0; j < N; ++j)
            {
                vertex temp;
                file >> temp.x >> temp.y >> temp.z;
                tempv.push_back (temp);
            }
            points.push_back (tempv);
        }
        file >> K;
        for (int i = 0; i < K; ++i)
        {
            RGB temp;
            file >> temp.r >> temp.g >> temp.b;
            palette.push_back (temp);
        }
    }
    file.close();
}


int main (int argc, char *argv[])
{
    surfaceTranslate.x = surfaceTranslate.y = surfaceTranslate.z = toY.x = toY.y = toY.z = up.x = up.z = 0;
    up.y = 1;
    camera.x = camera.y = camera.z = 100;
    readFile (argv[1]);
    updateControl();
    glutInit (&argc,argv);
    glutInitDisplayMode (GLUT_RGB | GLUT_DOUBLE | GLUT_DEPTH);
    glutInitWindowPosition (50, 50);
    glutInitWindowSize (800, 800);
    main_window = glutCreateWindow ("Transformation Mode");
    glutDisplayFunc (display);
    glutKeyboardFunc (keyboardEvent);
    glutSpecialFunc (arrowKeys);
    glutMouseFunc (mouseEvent);
    glutMotionFunc (changeDirection);
    initialDisplay();
    glutMainLoop();
}

Answer 1

display() 中有两个问题:

• 应该在调用 glVertex3f 之前调用 glColor3f 来为它们着色
• 当 h == maxH 时，您的调色板索引计算是错误的，它会导致越界访问

当 h == maxH 时，(h - minH)/(maxH - minH) 等于 1.0f，这意味着直线:

index = K * (h - minH) / (maxH - minH);

简化为:

index = K;

K 是调色板的大小。一个简单的解决方法是添加对 min() 的调用，如下所示:

index = min(K-1, K * (h - minH) / (maxH - minH));