OpenGL - Rotate a 'Curve' About the Y-Axis

Question

As per my question on Math Stackexchange:

I am working on a project for my 3D Graphics class. The project is built with C++ and OpenGL / Glut. Basically, I

Answer 1

Looks like you're trying to construct a surface of revolution/solid of revolution/"lathe object".

A working example:

#include <GL/glut.h>
#include <glm/glm.hpp>
#include <vector>
#include <cmath>

using namespace std;
using namespace glm;

struct Vertex
{
    Vertex( const vec3& position, const vec3& normal )
        : position( position )
        , normal( normal ) 
    {}
    vec3 position;
    vec3 normal;
};

// spin the pts array around the Z axis.
// pts.x will become the radius, and pts.y will become the height
// pts should be sorted by y-coordinate
vector< Vertex > Lathe( const vector< vec2 >& pts, unsigned int segments = 32 )
{
    // precalculate circle points
    vector< vec2 > circlePts;
    for( unsigned int i = 0; i <= segments; ++i )
    {
        float angle = ( i / (float)segments ) * 3.14159f * 2.0f;
        circlePts.push_back( vec2( cos( angle ), sin( angle ) ) );
    }

    // fill each layer
    typedef vector< vec3 > Layer;
    typedef vector< Layer > Layers;
    Layers layers( pts.size(), Layer( circlePts.size() ) );
    for( size_t i = 0; i < pts.size(); ++i )
    {
        for( unsigned int j = 0; j < circlePts.size(); ++j )
        {
            layers[i][j] = vec3( circlePts[j] * pts[i].x, pts[i].y );
        }
    }

    // move through layers generating triangles
    vector< Vertex > verts;
    for( size_t i = 1; i < layers.size(); ++i )
    {
        const Layer& prvLayer = layers[ i-1 ];
        const Layer& curLayer = layers[ i-0 ];
        for( size_t j = 1; j < circlePts.size(); ++j )
        {
            //    upper = cur layer
            //        UL -- UR  
            // left   | 0 /  |  right 
            // = j-1  |  / 1 |  = j-0
            //        LL -- LR  
            //    lower = prv layer
            const vec3& LL = prvLayer[ j-1 ]; // lower-left
            const vec3& LR = prvLayer[ j-0 ]; // lower-right
            const vec3& UL = curLayer[ j-1 ]; // upper-left
            const vec3& UR = curLayer[ j-0 ]; // upper-right

            // triangle0: LL -> UR -> UL
            const vec3 normal0 = normalize( cross( UR - LL, UL - LL ) );
            verts.push_back( Vertex( LL, normal0 ) );
            verts.push_back( Vertex( UR, normal0 ) );
            verts.push_back( Vertex( UL, normal0 ) );

            // triangle1: LL -> LR -> UR
            const vec3 normal1 = normalize( cross( LR - LL, UL - LL ) );
            verts.push_back( Vertex( LL, normal1 ) );
            verts.push_back( Vertex( LR, normal1 ) );
            verts.push_back( Vertex( UR, normal1 ) );
        }
    }

    return verts;
}

// mouse state
int btn;
ivec2 startMouse;
ivec2 startRot, curRot;

void mouse(int button, int state, int x, int y )
{
    if( button == GLUT_LEFT_BUTTON && state == GLUT_DOWN )
    {
        btn = button;
        startMouse = ivec2( x, glutGet( GLUT_WINDOW_HEIGHT ) - y );
        startRot = curRot;
    }
}

void motion( int x, int y )
{
    ivec2 curMouse( x, glutGet( GLUT_WINDOW_HEIGHT ) - y );
    if( btn == GLUT_LEFT_BUTTON )
    {
        curRot = startRot + ( curMouse - startMouse );
    }
    glutPostRedisplay();
}

vector< Vertex > model;
void display()
{
    glClear( GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT );

    glMatrixMode( GL_PROJECTION );
    glLoadIdentity();
    double w = glutGet( GLUT_WINDOW_WIDTH );
    double h = glutGet( GLUT_WINDOW_HEIGHT );
    double ar = w / h;
    gluPerspective( 60, ar, 0.1, 40 );

    glMatrixMode( GL_MODELVIEW );
    glLoadIdentity();
    glTranslatef( 0, 0, -10 );

    glPushMatrix();
    glRotatef( curRot.x % 360, 0, 1, 0 );
    glRotatef( -curRot.y % 360, 1, 0, 0 );

    // draw model
    if( !model.empty() )
    {
        glColor3ub( 255, 0, 0 );
        glEnableClientState( GL_VERTEX_ARRAY );
        glEnableClientState( GL_NORMAL_ARRAY );
        glVertexPointer( 3, GL_FLOAT, sizeof(Vertex), &model[0].position );
        glNormalPointer( GL_FLOAT, sizeof(Vertex), &model[0].normal );
        glDrawArrays( GL_TRIANGLES, 0, model.size() );
        glDisableClientState( GL_VERTEX_ARRAY );
        glDisableClientState( GL_NORMAL_ARRAY );
    }

    // draw bounding cube
    glDisable( GL_LIGHTING );
    glColor3ub( 255, 255, 255 );
    glutWireCube( 7 );
    glEnable( GL_LIGHTING );

    glPopMatrix();

    glutSwapBuffers();
}

int main( int argc, char **argv )
{
    vector< vec2 > pts;
    pts.push_back( vec2( 0.1, -3 ) );
    pts.push_back( vec2( 2, -2 ) );
    pts.push_back( vec2( 3, -1 ) );
    pts.push_back( vec2( 1, 0 ) );
    pts.push_back( vec2( 3, 1 ) );
    pts.push_back( vec2( 4, 2 ) );
    pts.push_back( vec2( 4, 3 ) );
    model = Lathe( pts );

    glutInit( &argc, argv );
    glutInitDisplayMode( GLUT_RGBA | GLUT_DEPTH | GLUT_DOUBLE );
    glutInitWindowSize( 640, 480 );
    glutCreateWindow( "GLUT" );
    glutDisplayFunc( display );
    glutMouseFunc( mouse );
    glutMotionFunc( motion );

    glEnable( GL_DEPTH_TEST );

    // set up lighting
    glShadeModel( GL_SMOOTH );
    glEnable( GL_COLOR_MATERIAL );
    glColorMaterial( GL_FRONT_AND_BACK, GL_AMBIENT_AND_DIFFUSE ) ;
    glLightModeli( GL_LIGHT_MODEL_TWO_SIDE, GL_TRUE );
    glEnable( GL_LIGHTING );

    // set up "headlamp"-like light
    glEnable( GL_LIGHT0 );
    glMatrixMode( GL_MODELVIEW );
    glLoadIdentity();
    GLfloat position[] = { 0, 0, 1, 0 };
    glLightfv( GL_LIGHT0, GL_POSITION, position );

    glPolygonMode( GL_FRONT, GL_FILL );
    glPolygonMode( GL_BACK, GL_LINE );

    glutMainLoop();
    return 0;
}

Answer 2

Edit 2: Okay, I see the problem you're running into -- it's a limitation I'd forgotten about (so the code I'd posted previously was dead wrong and wouldn't work at all). The problem is that you're not allowed to call glRotate between a glBegin/glEnd pair -- if you do, it'll set an error flag, and no more drawing will be done.

That does mean you pretty much have to handle the rotation yourself. Fortunately, that's a bit simpler than you've tried to make it:

static const double pi = 3.1416;

for (int point=0; point<NUM_POINTS; point++) {
    glBegin(GL_LINE_STRIP);
    for (double theta = 0.0; theta < 2.0 * pi; theta += pi/6.0) {
        double x = cos(theta);
        double z = sin(theta);
        glVertex3d(points[point][0]*x, points[point][1], -1.0-points[point][0]*z);
    }
    glEnd();
}   

As-is, this code uses -1.0 along the Z axis as the center of rotation. You can obviously move that where you wish, though anything outside your clipping frustum obviously won't display.

Also note that to get a wireframe, you'll have to draw both your "vertical", and your "horizontal" lines separately, so the code will look something like this:

for (int point=0; point<NUM_POINTS; point++) {
    glBegin(GL_LINE_STRIP);
    for (double theta = 0.0; theta < 2.0 * pi; theta += pi/6.0) {
        double x = cos(theta);
        double z = sin(theta);
        glVertex3d(points[point][0]*x, points[point][1], -1.0 - points[point][0]*z);
    }
    glEnd();
}

for (double theta = 0.0; theta < 2.0 * pi; theta += pi/6.0) {
    glBegin(GL_LINE_STRIP);
    for (int point=0; point<NUM_POINTS; point++) {
        double x = cos(theta);
        double z = sin(theta);
        glVertex3d(points[point][0]*x, points[point][1], -1.0 - points[point][0]*z);
    }
    glEnd();
}

Answer 3

The trig functions take angles in radians, not degrees.

I also suspect that your viewport isn't setup properly, which explains why you can't see anything on the screen. Typically when I think stuff isn't rendering, it usually is, however, I haven't configured the camera, lighting and other stuff correctly.