#include #include #include #include // General constants const double PI = 3.14159263; const double MINDIST = 0.25; // Hide points closer to ball than this const double SCALE = 0.5; // View extends SCALE * MAXPOINTS from origin const double BALLRAD = 0.1; // Radius of balls // Constants for line view. const double BRIGHT = 0.3; const double RAD = 10.0; // Radius of sphere of starting points. double SEGLEN = 0.1; // Length of line segment const int MAXLEN = 500; // Max # steps on path. const int STEPS = 5; // Steps on sphere of starting points. // Constants for vector view. double VECLEN = 0.2; // Length of vectors const int MAXPOINTS = 10; // (2 * (MAXPOINTS + 1))^3 will be plotted // First ball is at origin, second is at (a, b, c). double a = 1.0; double b = 0.0; double c = 0.0; // Rotation angles for viewing. double ax = 0.0; double ay = 0.0; double az = 0.0; // Current mode. enum { LINES, VECTORS } mode = LINES; // Current window dimensions. int window_width = 600; int window_height = 400; // Utility functions. // Distance from (x,y,z) to (0,0,0). double dist (double x, double y, double z) { return sqrt(x*x + y*y + z*z); } // Compute (x^2 + y^2 + z^2)^(3/2) double tht (double x, double y, double z) { double mag = x*x + y*y + z*z; return sqrt(mag * mag * mag); } // OpenGL display function. void display () { glClear(GL_COLOR_BUFFER_BIT); glMatrixMode(GL_MODELVIEW); glLoadIdentity(); glTranslatef(0.0, 0.0, -3.0); // Apply rotations. glRotatef(ax, 1.0, 0.0, 0.0); glRotatef(ay, 0.0, 1.0, 0.0); glRotatef(az, 0.0, 0.0, 1.0); // Draw axes. glBegin(GL_LINES); glColor3f(1.0, 0.0, 0.0); glVertex3f(0.0, 0.0, 0.0); glVertex3f(1.0, 0.0, 0.0); glColor3f(0.0, 1.0, 0.0); glVertex3f(0.0, 0.0, 0.0); glVertex3f(0.0, 1.0, 0.0); glColor3f(0.0, 0.0, 1.0); glVertex3f(0.0, 0.0, 0.0); glVertex3f(0.0, 0.0, 1.0); glEnd(); int i, j, k; glColor3f(0.8, 0.8, 0.5); switch (mode) { // Vector view case VECTORS: glBegin(GL_LINES); for (i = -MAXPOINTS; i <= MAXPOINTS; i++) { double x = double(i) * SCALE; for (j = -MAXPOINTS; j <= MAXPOINTS; j++) { double y = double(j) * SCALE; for (k = -MAXPOINTS; k <= MAXPOINTS; k++) { double z = double(k) * SCALE; double D1 = tht(x, y, z); double D2 = tht(x-a, y-b, z-c); if (D1 > MINDIST && D2 > MINDIST) { // Compute vector field. double vx = - x/D1 - (x-a)/D2; double vy = - y/D1 - (y-b)/D2; double vz = - z/D1 - (z-c)/D2; // Draw a short line through this point showing // direction and strength of field.. glVertex3f(x - VECLEN * vx, y - VECLEN * vy, z - VECLEN * vz); glVertex3f(x + VECLEN * vx, y + VECLEN * vy, z + VECLEN * vz); } } } } glEnd(); break; // Line view case LINES: for (i = 0; i <= 2 * STEPS; i++) { double theta = (PI * i) / STEPS; for (j = 0; j <= STEPS; j++) { double phi = (PI * j) / STEPS; // 0 <= phi <= PI // (x,y,z) is a point on the enclosing sphere. double x = RAD * cos(theta) * sin(phi); double y = RAD * sin(theta) * sin(phi); double z = RAD * cos(phi); glBegin(GL_LINE_STRIP); int n = 0; // Move in the direction of the field at (x,y,z). while (true) { glVertex3f(x, y, z); // Stop when limit or ball reached. if (n++ > MAXLEN || dist(x,y,z) <= BALLRAD || dist(x-a,y-a,z-a) <= BALLRAD) break; double D1 = tht(x, y, z); double D2 = tht(x - a, y - b, z - c); double dx = - x/D1 - (x-a)/D2; double dy = - y/D1 - (y-b)/D2; double dz = - z/D1 - (z-c)/D2; double len = dist(dx, dy, dz) / SEGLEN; // Set brightness according to field strength. glColor3f(BRIGHT * len, BRIGHT * len, BRIGHT * len); // Move to next point. x += dx / len; y += dy / len; z += dz / len; } glEnd(); } } break; } // Draw balls. glColor3f(1.0, 0.0, 0.0); glutSolidSphere(BALLRAD, 10,10); glPushMatrix(); glTranslatef(a, b, c); glColor3f(0.0, 1.0, 0.0); glutSolidSphere(BALLRAD, 10,10); glPopMatrix(); glutSwapBuffers(); glFlush(); } // Mouse controls position of second ball. void mouse_movement (int x, int y) { ay = 90.0 * (double(x) / double(window_width) - 0.5); ax = - 90.0 * (double(y) / double(window_height) - 0.5); glutPostRedisplay(); } // Allow user to reshape/resize window. void reshape (int w, int h) { window_width = w; window_height = h; glViewport(0, 0, window_width, window_height); glMatrixMode(GL_PROJECTION); glLoadIdentity(); gluPerspective(90.0, GLfloat(window_width)/GLfloat(window_height), 1.0, 10.0); glutPostRedisplay(); } void help () { cout << "Demonstration of a vector field. The red and green balls generate a" << endl; cout << "field (electrostatic or gravitational). The yellow lines show the" << endl; cout << "direction of magnitude of the vector field created by the balls at" << endl; cout << "various points in 3D space. The red ball is at the origin. The axes" << endl; cout << "are shown as red (X), green (Y), and blue (Z) lines." << endl; cout << "Horizontal mouse movement rotates view about Y axis." << endl; cout << "Vertical mouse movement rotates view about X axis." << endl; cout << "Pressing:" << endl; cout << " x, y, or z moves the green ball along the corresponding axis." << endl; cout << " X, Y, or Z moves the green ball in the opposite direction." << endl; cout << " l selects line view." << endl; cout << " v selects vector view." << endl; cout << " h displays theis message." << endl; cout << " ESC quites." << endl; } // Respond to keyboard events. void keyboard (unsigned char key, int x, int y) { switch (key) { case 'h': help(); break; case 'l': mode = LINES; break; case 'v': mode = VECTORS; break; case 'x': a += 0.1; break; case 'y': b += 0.1; break; case 'z': c += 0.1; break; case 'X': a -= 0.1; break; case 'Y': b -= 0.1; break; case 'Z': c -= 0.1; break; case 27: exit(0); } glutPostRedisplay(); } int main (int argc, char *argv[]) { glutInit(&argc, argv); glutInitDisplayMode (GLUT_RGB | GLUT_DOUBLE); glutInitWindowSize(window_width, window_height); glutCreateWindow("Potential"); glutDisplayFunc(display); glutMotionFunc(mouse_movement); glutReshapeFunc(reshape); glutKeyboardFunc(keyboard); help(); glutMainLoop(); return 0; }