使用 Visual C++ 在 Opengl 中创建 3D 球体

Question

I am not able to create a simple 3D sphere using the OpenGL library function glutSolidSphere() in C++.

Here's what I tried:

#include<GL/glu.h> 
void display() 
{ 
    glClear(GL_COLOR_BUFFER_BIT); 
    glColor3f(1.0,0.0,0.0); 
    glLoadIdentity(); 
    glutSolidSphere( 5.0, 20.0, 20.0); 
    glFlush(); 
} 

void myInit() 
{
    glClearColor(1.0,1.0,1.0,1.0); 
    glColor3f(1.0,0.0,0.0); 
    glMatrixMode(GL_PROJECTION); 
    glLoadIdentity(); 
    gluOrtho2D(0.0,499.0,0.0,499.0); 
    glMatrixMode(GL_MODELVIEW); 
} 

void main(int argc,char **argv) 
{ 
    qobj = gluNewQuadric(); 
    glutInit(&argc,argv); 
    glutInitDisplayMode(GLUT_SINGLE|GLUT_RGB); 
    glutInitWindowSize(500,500); 
    glutCreateWindow("pendulum");         
    glutDisplayFunc(display); 
    myInit(); 
    glutMainLoop(); 
}

Answer 1

In OpenGL you don't create objects, you just draw them. Once they are drawn, OpenGL no longer cares about what geometry you sent it.

glutSolidSphere is just sending drawing commands to OpenGL. However there's nothing special in and about it. And since it's tied to GLUT I'd not use it. Instead, if you really need some sphere in your code, how about create if for yourself?

#define _USE_MATH_DEFINES
#include <GL/gl.h>
#include <GL/glu.h>
#include <vector>
#include <cmath>

// your framework of choice here

class SolidSphere
{
protected:
    std::vector<GLfloat> vertices;
    std::vector<GLfloat> normals;
    std::vector<GLfloat> texcoords;
    std::vector<GLushort> indices;

public:
    SolidSphere(float radius, unsigned int rings, unsigned int sectors)
    {
        float const R = 1./(float)(rings-1);
        float const S = 1./(float)(sectors-1);
        int r, s;

        vertices.resize(rings * sectors * 3);
        normals.resize(rings * sectors * 3);
        texcoords.resize(rings * sectors * 2);
        std::vector<GLfloat>::iterator v = vertices.begin();
        std::vector<GLfloat>::iterator n = normals.begin();
        std::vector<GLfloat>::iterator t = texcoords.begin();
        for(r = 0; r < rings; r++) for(s = 0; s < sectors; s++) {
                float const y = sin( -M_PI_2 + M_PI * r * R );
                float const x = cos(2*M_PI * s * S) * sin( M_PI * r * R );
                float const z = sin(2*M_PI * s * S) * sin( M_PI * r * R );

                *t++ = s*S;
                *t++ = r*R;

                *v++ = x * radius;
                *v++ = y * radius;
                *v++ = z * radius;

                *n++ = x;
                *n++ = y;
                *n++ = z;
        }

        indices.resize(rings * sectors * 4);
        std::vector<GLushort>::iterator i = indices.begin();
        for(r = 0; r < rings; r++) for(s = 0; s < sectors; s++) {
                *i++ = r * sectors + s;
                *i++ = r * sectors + (s+1);
                *i++ = (r+1) * sectors + (s+1);
                *i++ = (r+1) * sectors + s;
        }
    }

    void draw(GLfloat x, GLfloat y, GLfloat z)
    {
        glMatrixMode(GL_MODELVIEW);
        glPushMatrix();
        glTranslatef(x,y,z);

        glEnableClientState(GL_VERTEX_ARRAY);
        glEnableClientState(GL_NORMAL_ARRAY);
        glEnableClientState(GL_TEXTURE_COORD_ARRAY);

        glVertexPointer(3, GL_FLOAT, 0, &vertices[0]);
        glNormalPointer(GL_FLOAT, 0, &normals[0]);
        glTexCoordPointer(2, GL_FLOAT, 0, &texcoords[0]);
        glDrawElements(GL_QUADS, indices.size(), GL_UNSIGNED_SHORT, &indices[0]);
        glPopMatrix();
    }
};

SolidSphere sphere(1, 12, 24);

void display()
{
    int const win_width  = …; // retrieve window dimensions from
    int const win_height = …; // framework of choice here
    float const win_aspect = (float)win_width / (float)win_height;

    glViewport(0, 0, win_width, win_height);

    glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);

    glMatrixMode(GL_PROJECTION);
    glLoadIdentity();
    gluPerspective(45, win_aspect, 1, 10);

    glMatrixMode(GL_MODELVIEW);
    glLoadIdentity();

#ifdef DRAW_WIREFRAME
    glPolygonMode(GL_FRONT_AND_BACK, GL_LINE);
#endif
    sphere.draw(0, 0, -5);

    swapBuffers();
}

int main(int argc, char *argv[])
{
    // initialize and register your framework of choice here
    return 0;
}

Answer 2

It doesn't seem like anyone so far has addressed the actual problem with your original code, so I thought I would do that even though the question is quite old at this point.

The problem originally had to do with the projection in relation to the radius and position of the sphere. I think you'll find that the problem isn't too complicated. The program actually works correctly, it's just that what is being drawn is very hard to see.

First, an orthogonal projection was created using the call

gluOrtho2D(0.0, 499.0, 0.0, 499.0);

which " is equivalent to calling glOrtho with near = -1 and far = 1. " This means that the viewing frustum has a depth of 2. So a sphere with a radius of anything greater than 1 (diameter = 2) will not fit entirely within the viewing frustum.

Then the calls

glLoadIdentity();
glutSolidSphere(5.0, 20.0, 20.0);

are used, which loads the identity matrix of the model-view matrix and then " [r]enders a sphere centered at the modeling coordinates origin of the specified radius. " Meaning, the sphere is rendered at the origin, (x, y, z) = (0, 0, 0), and with a radius of 5.

Now, the issue is three-fold:

1. Since the window is 500x500 pixels and the width and height of the viewing frustum is almost 500 (499.0), the small radius of the sphere (5.0) makes its projected area only slightly over one fiftieth (2*5/499) of the size of the window in each dimension. This means that the apparent size of the sphere would be roughly 1/2,500th (actually pi*5^2/499^2 , which is closer to about 1/3170th) of the entire window, so it might be difficult to see . This is assuming the entire circle is drawn within the area of the window. It is not, however, as we will see in point 2.
2. Since the viewing frustum has it's left plane at x = 0 and bottom plane at y = 0, the sphere will be rendered with its geometric center in the very bottom left corner of the window so that only one quadrant of the projected sphere will be visible! This means that what would be seen is even smaller, about 1/10,000th (actually pi*5^2/(4*499^2) , which is closer to 1/12,682nd) of the window size. This would make it even more difficult to see . Especially since the sphere is rendered so close to the edges/corner of the screen where you might not think to look.
3. Since the depth of the viewing frustum is significantly smaller than the diameter of the sphere (less than half), only a sliver of the sphere will be within the viewing frustum, rendering only that part. So you will get more like a hollow circle on the screen than a solid sphere/circle. As it happens, the thickness of that sliver might represent less than 1 pixel on the screen which means we might even see nothing on the screen, even if part of the sphere is indeed within the viewing frustum.

The solution is simply to change the viewing frustum and radius of the sphere. For instance,

gluOrtho2D(-5.0, 5.0, -5.0, 5.0);
glutSolidSphere(5.0, 20, 20);

renders the following image.

As you can see, only a small part is visible around the "equator", of the sphere with a radius of 5. (I changed the projection to fill the window with the sphere.) Another example,

gluOrtho2D(-1.1, 1.1, -1.1, 1.1);
glutSolidSphere(1.1, 20, 20);

renders the following image.

The image above shows more of the sphere inside of the viewing frustum, but still the sphere is 0.2 depth units larger than the viewing frustum. As you can see, the "ice caps" of the sphere are missing, both the north and the south. So, if we want the entire sphere to fit within the viewing frustum which has depth 2, we must make the radius less than or equal to 1.

gluOrtho2D(-1.0, 1.0, -1.0, 1.0);
glutSolidSphere(1.0, 20, 20);

renders the following image.

I hope this has helped someone. Take care!

Answer 3

I don't understand how can datenwolf`s index generation can be correct. But still I find his solution rather clear. This is what I get after some thinking:

inline void push_indices(vector<GLushort>& indices, int sectors, int r, int s) {
    int curRow = r * sectors;
    int nextRow = (r+1) * sectors;

    indices.push_back(curRow + s);
    indices.push_back(nextRow + s);
    indices.push_back(nextRow + (s+1));

    indices.push_back(curRow + s);
    indices.push_back(nextRow + (s+1));
    indices.push_back(curRow + (s+1));
}

void createSphere(vector<vec3>& vertices, vector<GLushort>& indices, vector<vec2>& texcoords,
             float radius, unsigned int rings, unsigned int sectors)
{
    float const R = 1./(float)(rings-1);
    float const S = 1./(float)(sectors-1);

    for(int r = 0; r < rings; ++r) {
        for(int s = 0; s < sectors; ++s) {
            float const y = sin( -M_PI_2 + M_PI * r * R );
            float const x = cos(2*M_PI * s * S) * sin( M_PI * r * R );
            float const z = sin(2*M_PI * s * S) * sin( M_PI * r * R );

            texcoords.push_back(vec2(s*S, r*R));
            vertices.push_back(vec3(x,y,z) * radius);
            push_indices(indices, sectors, r, s);
        }
    }
}

Answer 4

Here's the code:

glPushMatrix();
glTranslatef(18,2,0);
glRotatef(angle, 0, 0, 0.7);
glColor3ub(0,255,255);
glutWireSphere(3,10,10);
glPopMatrix();

Answer 5

Datanewolf's code is ALMOST right. I had to reverse both the winding and the normals to make it work properly with the fixed pipeline. The below works correctly with cull on or off for me:

std::vector<GLfloat> vertices;
std::vector<GLfloat> normals;
std::vector<GLfloat> texcoords;
std::vector<GLushort> indices;

float const R = 1./(float)(rings-1);
float const S = 1./(float)(sectors-1);
int r, s;

vertices.resize(rings * sectors * 3);
normals.resize(rings * sectors * 3);
texcoords.resize(rings * sectors * 2);
std::vector<GLfloat>::iterator v = vertices.begin();
std::vector<GLfloat>::iterator n = normals.begin();
std::vector<GLfloat>::iterator t = texcoords.begin();
for(r = 0; r < rings; r++) for(s = 0; s < sectors; s++) {
    float const y = sin( -M_PI_2 + M_PI * r * R );
    float const x = cos(2*M_PI * s * S) * sin( M_PI * r * R );
    float const z = sin(2*M_PI * s * S) * sin( M_PI * r * R );

    *t++ = s*S;
    *t++ = r*R;

    *v++ = x * radius;
    *v++ = y * radius;
    *v++ = z * radius;

    *n++ = -x;
    *n++ = -y;
    *n++ = -z;
}

indices.resize(rings * sectors * 4);
std::vector<GLushort>::iterator i = indices.begin();
for(r = 0; r < rings-1; r++)
    for(s = 0; s < sectors-1; s++) {
       /* 
        *i++ = r * sectors + s;
        *i++ = r * sectors + (s+1);
        *i++ = (r+1) * sectors + (s+1);
        *i++ = (r+1) * sectors + s;
        */
         *i++ = (r+1) * sectors + s;
         *i++ = (r+1) * sectors + (s+1);
        *i++ = r * sectors + (s+1);
         *i++ = r * sectors + s;

}

Edit: There was a question on how to draw this... in my code I encapsulate these values in a G3DModel class. This is my code to setup the frame, draw the model, and end it:

void GraphicsProvider3DPriv::BeginFrame()const{
        int win_width;
        int win_height;// framework of choice here
        glfwGetWindowSize(window, &win_width, &win_height); // retrieve window
        float const win_aspect = (float)win_width / (float)win_height;
        // set lighting
        glEnable(GL_LIGHTING);
        glEnable(GL_LIGHT0);
        glEnable(GL_DEPTH_TEST);
        GLfloat lightpos[] = {0, 0.0, 0, 0.};
        glLightfv(GL_LIGHT0, GL_POSITION, lightpos);
        GLfloat lmodel_ambient[] = { 0.2, 0.2, 0.2, 1.0 };
        glLightModelfv(GL_LIGHT_MODEL_AMBIENT, lmodel_ambient);
        glLightModeli(GL_LIGHT_MODEL_TWO_SIDE, GL_TRUE);
        // set up world transform
        glClearColor(0.f, 0.f, 0.f, 1.f);
        glClear(GL_COLOR_BUFFER_BIT|GL_DEPTH_BUFFER_BIT|GL_STENCIL_BUFFER_BIT|GL_ACCUM_BUFFER_BIT);
        glMatrixMode(GL_PROJECTION);
        glLoadIdentity();

        gluPerspective(45, win_aspect, 1, 10);

        glMatrixMode(GL_MODELVIEW);

    }


    void GraphicsProvider3DPriv::DrawModel(const G3DModel* model, const Transform3D transform)const{
        G3DModelPriv* privModel = (G3DModelPriv *)model;
        glPushMatrix();
        glLoadMatrixf(transform.GetOGLData());

        glEnableClientState(GL_VERTEX_ARRAY);
        glEnableClientState(GL_NORMAL_ARRAY);
        glEnableClientState(GL_TEXTURE_COORD_ARRAY);

        glVertexPointer(3, GL_FLOAT, 0, &privModel->vertices[0]);
        glNormalPointer(GL_FLOAT, 0, &privModel->normals[0]);
        glTexCoordPointer(2, GL_FLOAT, 0, &privModel->texcoords[0]);

        glEnable(GL_TEXTURE_2D);
        //glFrontFace(GL_CCW);
        glEnable(GL_CULL_FACE);
        glActiveTexture(GL_TEXTURE0);
        glBindTexture(GL_TEXTURE_2D, privModel->texname);

        glDrawElements(GL_QUADS, privModel->indices.size(), GL_UNSIGNED_SHORT, &privModel->indices[0]);
        glPopMatrix();
        glDisable(GL_TEXTURE_2D);

    }

    void GraphicsProvider3DPriv::EndFrame()const{
        /* Swap front and back buffers */
        glDisable(GL_LIGHTING);
        glDisable(GL_LIGHT0);
        glDisable(GL_CULL_FACE);
        glfwSwapBuffers(window);

        /* Poll for and process events */
        glfwPollEvents();
    }

Answer 6

I like the answer of coin. It's simple to understand and works with triangles. However the indexes of his program are sometimes over the bounds. So I post here his code with two tiny corrections:

inline void push_indices(vector<GLushort>& indices, int sectors, int r, int s) {
    int curRow = r * sectors;
    int nextRow = (r+1) * sectors;
    int nextS = (s+1) % sectors;

    indices.push_back(curRow + s);
    indices.push_back(nextRow + s);
    indices.push_back(nextRow + nextS);

    indices.push_back(curRow + s);
    indices.push_back(nextRow + nextS);
    indices.push_back(curRow + nextS);
}

void createSphere(vector<vec3>& vertices, vector<GLushort>& indices, vector<vec2>& texcoords,
                  float radius, unsigned int rings, unsigned int sectors)
{
    float const R = 1./(float)(rings-1);
    float const S = 1./(float)(sectors-1);

    for(int r = 0; r < rings; ++r) {
        for(int s = 0; s < sectors; ++s) {
            float const y = sin( -M_PI_2 + M_PI * r * R );
            float const x = cos(2*M_PI * s * S) * sin( M_PI * r * R );
            float const z = sin(2*M_PI * s * S) * sin( M_PI * r * R );

            texcoords.push_back(vec2(s*S, r*R));
            vertices.push_back(vec3(x,y,z) * radius);
            if(r < rings-1)
                push_indices(indices, sectors, r, s);
        }
    }
}