キューブの球へのモーフィング

Question

球の作成の後ろの数学について学んでいるIm。私はちょうど開始時に私はいくつかの研究を行い、私はポイントのグリッドを作成し、球を作成するために数式を使用する必要があると言う。私の質問は、キューブ上の四角を含む別の方法ですか？そうでない場合は、私のプロジェクトを傷つけ、キューブの面の四角形ではなく、点グリッドを持つ立方体の作成を開始します。

#include <GL/glut.h> 
#include <iostream> 

     void DrawArea(){ 
     glColor3f(1,1, 1); 
     glBegin(GL_QUADS); 

     glVertex3f(-10, -1.1, 10); 
     glVertex3f(10, -1.1, 10); 
     glVertex3f(10, -1.1, -10); 
     glVertex3f(-10, -1.1, -10); 
     glEnd(); 

    } 

GLfloat n[6][3] = { /* Normals for the 6 faces of a cube. */ 
    {-1.0, 0.0, 0.0}, {0.0, 1.0, 0.0}, { 1.0, 0.0, 0.0}, 
    {0.0, -1.0, 0.0}, {0.0, 0.0, 1.0}, {0.0, 0.0, -1.0} }; 
GLint faces[6][4] = { /* Vertex indices for the 6 faces of a cube. */ 
    {0, 1, 2, 3}, {3, 2, 6, 7}, {7, 6, 5, 4}, 
    {4, 5, 1, 0}, {5, 6, 2, 1}, {7, 4, 0, 3} }; 
GLfloat v[8][3]; /* Will be filled in with X,Y,Z vertexes. */ 
void init(void) 
{ 
    /* Setup cube vertex data. */ 
    v[0][0] = v[1][0] = v[2][0] = v[3][0] = -1; 
    v[4][0] = v[5][0] = v[6][0] = v[7][0] = 1; 
    v[0][1] = v[1][1] = v[4][1] = v[5][1] = -1; 
    v[2][1] = v[3][1] = v[6][1] = v[7][1] = 1; 
    v[0][2] = v[3][2] = v[4][2] = v[7][2] = 1; 
    v[1][2] = v[2][2] = v[5][2] = v[6][2] = -1; 

    /* Use depth buffering for hidden surface elimination. */ 
    glEnable(GL_DEPTH_TEST); 

    /* Setup the view of the cube. */ 
    glMatrixMode(GL_PROJECTION); 
    gluPerspective(/* field of view in degree */ 70.0, 
    /* aspect ratio */ 1.0, 
    /* Z near */ 1.0, /* Z far */ 500.0); 
    glMatrixMode(GL_MODELVIEW); 
    gluLookAt(0.0, 0.0, 10, /* eye is at (0,0,5) */ 
    0.0, 0.0, 0.0,  /* center is at (0,0,0) */ 
    0.0, 1.0, 0.);  /* up is in positive Y direction */ 

    /* Adjust cube position to be asthetic angle. */ 
    //glTranslatef(0.0, 0.0, -1.0); 

} 

void drawLines() { 


     glBegin(GL_LINES); 
     int y = 0; 
     for (int i = 10; i != 0; i--) { 

     // po x osi 
     glVertex2f(-i, -0.1); 
     glVertex2f(-i, 0.1); 
     glVertex2f(i, -0.1); 
     glVertex2f(i, 0.1); 

     //po y osi 
     glVertex2f(-0.1, -i); 
     glVertex2f(0.1, -i); 
     glVertex2f(-0.1, i); 
     glVertex2f(0.1, i); 
//  
//  //po z osi 
//  // glColor3f(0.0f, 1.0f, 0.0f); //seems it doesnt register 
     glVertex3f(0, -0.3, -i); 
     glVertex3f(0, 0.3, -i); 
     glVertex3f(0, -0.3, i); 
     glVertex3f(0, 0.3, i); 
     } 
     glEnd(); 
    } 

void drawGrid(){ 
    for(int a = 0; a<=10; a++){ 
    glBegin(GL_LINES); 
//po x-u 
    glVertex3f(-a, 0, 10); 
    glVertex3f(-a, 0, -10); 
    glVertex3f(a, 0, 10); 
    glVertex3f(a, 0, -10); 
    //po z 
    glVertex3f(-10, 0, -a); 
    glVertex3f(10, 0, -a); 

    glVertex3f(10, 0, a); 
    glVertex3f(-10, 0, a); 
    glEnd(); 
    } 

} 
void drawCP() { 
     drawLines(); 
     glBegin(GL_LINES); 

     glVertex2f(-10.0f, 0); 
     glVertex2f(10.0f, 0); 

     glVertex3f(0.0f, 0.0f, -10); 
     glVertex2f(0,0); 
     glEnd(); 
    } 

GLfloat color[8][3] = 
{ 
    {0.0,1.0,1.0}, 
    {1.0,0.0,0.0}, 
    {1.0,1.0,0.0}, 
    {0.0,1.0,0.0}, 
    {0.0,0.0,1.0}, 
    {1.0,0.0,1.0}, 
    {1.0,1.0,1.0}, 
    {0.0,1.0,1.0}, 
}; 

void drawBox() 
{ 
    int i; 

    for (i = 0; i < 6; i++) { 
    glBegin(GL_QUADS); 
    glNormal3fv(&n[i][0]); 
    glColor3fv(color[i]); 
    glVertex3fv(&v[faces[i][0]][0]); 
    glVertex3fv(&v[faces[i][1]][0]); 
    glVertex3fv(&v[faces[i][2]][0]); 
    glVertex3fv(&v[faces[i][3]][0]); 

    glEnd(); 
    } 
} 
void display(void) 
{ 
    glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT); 


    drawBox(); 
    glColor3f(0.0,0.0,0.0); 
    drawGrid(); 
    glColor3f(1.0,1.0,1.0); 
    drawCP(); 
    glPopMatrix(); 
    glutSwapBuffers(); 
} 

void timer (int mili){ 
    glutPostRedisplay(); 
    glutTimerFunc(mili, timer, mili); 
} 

int main(int argc, char **argv) 
{ 
    glutInit(&argc, argv); 
    glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB | GLUT_DEPTH); 
    glutInitWindowSize(800, 800); 
    glEnable(GL_COLOR_MATERIAL); 
    glutCreateWindow("red 3D lighted cube"); 
    init(); 
    glutDisplayFunc(display); 
    glClearColor(0.6, 0.6, 0.6, 1); 
    glutMainLoop(); 
    return 0;    /* ANSI C requires main to return int. */ 
} 

Answer 1

変換/レンダリングに使用されるほとんどのアルゴリズムは三角形の数学に基づいているので、私はめったに（彼らは確かに球を生成することができますが）使用QUADSを見ていません。 GL_TRIANGLESまたはGL_TRIANGLE_STRIPに切り替えるほうがずっと良いでしょう。

三角形を使用して球の頂点を生成するアルゴリズムは非常に簡単で、通常は基本的な三角関数を使用します。これは私が単純な半球のために使用するものです

float Hincrement = PI/(Hresolution - 1); 
float Vincrement = PI/(Vresolution - 1); 

float theta = 0; 
float phi = Vincrement; 

for (int i = 0; i < Vresolution; i += 1){ 
    for (int j = 0; j < Hresolution - 2; j++){ 
     hemisphereVertices[currentIndex] = (radius * cos(phi)) + transX; 
     hemisphereVertices[currentIndex + 1] = (radius * sin(theta) * sin(phi)) + transY; 
     hemisphereVertices[currentIndex + 2] = (radius * cos(theta) * sin(phi)) + transZ; 

     phi += Vincrement; 
     currentIndex += 3; 
    } 
    phi = Vincrement; 
    theta += Hincrement; 
} 

難しい部分はインデックスバッファを作成していますが、同様の方法を使用できます。