html5-img
1 / 14

Circles, Ellipses, Curves

Circles, Ellipses, Curves. Soon Tee Teoh CS 116A. Circle. Circle equation: (x-xc) 2 + (y-yc) 2 = r 2 Can use mid-point algorithm to rasterize circle Useful to use polar coordinates: x = xc + r cos q y = yc + r sin q Sweep through q to draw circle: glBegin(GL_LINE_STRIP);

sorcha
Télécharger la présentation

Circles, Ellipses, Curves

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Circles, Ellipses, Curves Soon Tee Teoh CS 116A

  2. Circle • Circle equation: (x-xc)2 + (y-yc)2 = r2 • Can use mid-point algorithm to rasterize circle • Useful to use polar coordinates: x = xc + r cos q y = yc + r sin q • Sweep through q to draw circle: glBegin(GL_LINE_STRIP); for (theta=0; theta<TWO_PI; theta+=0.01) { glVertex3f(xc+r*cos(theta),yc+r*sin(theta),0.0); } glEnd(); • Exercise: • How do you draw a filled circle using GL_TRIANGLES?

  3. Bresenham’s Circle Algorithm • Adapt Line Algorithm to Circle • Start with first quadrant • Check the value of fcirc(x,y) to determine next pixel: end start fcirc(x,y) = x2 + y2 - r2

  4. Ellipse • All points on an ellipse satisfies: • What’s the ellipse equation? d1 + d2 = constant d2 d1

  5. Ellipse • Axis-aligned ellipse y ry 2 2 y - yc yc x - xc rx + = 1 rx ry x xc

  6. Conic Section • Circles and ellipses belong to a class called “conic sections”

  7. Conic Section • Conic section equation: • Discriminant B2 – 4AC Ax2 + By2 + Cxy + Dx + Ey + F = 0 < 0, generates ellipse = 0, generates parabola > 0, generates hyperbola

  8. Parabola • A parabola is the set of all points in the plane equidistant from a given plane (called the directrix) and a given point not on the line (called the focus). • For a parabola opening to the right with vertex at (0, 0), the equation in Cartesian coordinates is:

  9. Other curves • Hyperbola • Polynomials y = f(x) • x can go up to the nth degree • Splines: control points

  10. GLUI notes #include <time.h> clock_t old_time; float delay = 1.0; void playbutton_cb(int id) { playing = id; glutSetWindow(win); glutPostRedisplay(); } void myGlutIdle( void ) { clock_t new_time; new_time = clock(); if (((double)(new_time-old_time)/(double)CLOCKS_PER_SEC)>delay) { old_time = new_time; if (playing) { // if playing flag is set, then update graphics here ... glutSetWindow(win); glutPostRedisplay(); } } } int main() { win = glutCreateWindow(“Game”); ... dynamics_glui = GLUI_Master.create_glui( "Animation", 0, controlx2, controly2 ); GLUI_Panel *dynamics_panel1 = dynamics_glui->add_panel( "", GLUI_PANEL_NONE ); GLUI_Panel *dynamics_animation_panel = dynamics_glui->add_panel_to_panel ( dynamics_panel2, "Animation" ); dynamics_glui->add_button_to_panel(dynamics_animation_panel, "Play", 1, playbutton_cb); dynamics_glui->add_button_to_panel(dynamics_animation_panel, “Stop", 0, playbutton_cb); … GLUI_Master.set_glutIdleFunc( myGlutIdle ); } Set current window to the display window Argument to the callback function Called every time button is pressed

  11. GLUT Window Resizing int main(int argc, char* argv[]) { // ********* GLUT stuff ******************************************** glutInitDisplayMode( GLUT_RGB | GLUT_DOUBLE | GLUT_DEPTH ); side_window = glutCreateWindow( "BGPViz" ); glutPositionWindow( 10 , 10 ); // starting x, y of window glutReshapeWindow( 512, 512 ); // x, y size of window glutDisplayFunc( sideGlutDisplay ); glutReshapeFunc( sideGlutReshape ); glutKeyboardFunc( sideGlutKeyboard ); glutMotionFunc( sideGlutMotion ); glutMouseFunc( sideGlutMouse ); // ********* GLUI stuff ********************************************* glui = GLUI_Master.create_glui( "Control Panel", 0, 520,20 ); /* name, flags, x, and y */ /*** Add invisible panel to hold rest of controls ***/ GLUI_Panel *panel1 = glui->add_panel( "", GLUI_PANEL_NONE ); /*** Start a new column in this panel ***/ glui->add_column_to_panel(panel1, false); /* 'false' means don't draw bar */ glui->add_button_to_panel(panel1, "Clear", 0, clear_cb); mode_chkbx[0] = glui->add_checkbox_to_panel(panel1, "OpenGL Line", &(DL.mode), 0, mode_cb); mode_chkbx[1] = glui->add_checkbox_to_panel(panel1, "DDL", &(DL.mode), 1, mode_cb); mode_chkbx[2] = glui->add_checkbox_to_panel(panel1, "Bresenham", &(DL.mode), 2, mode_cb); mode_cb(0); GLUI_Master.set_glutIdleFunc( myGlutIdle ); // ********* GLUT stuff ******************************************** glutMainLoop(); return 0; } This function called whenever the window size is changed.

  12. GLUT Window Resizing 512 • Consider the following code int winx = 512; int winy = 512; void display_func() { glMatrixMode(GL_PROJECTION); glLoadIdentity(); gluOrtho2D(0.0,1.0,0.0,1.0); // left, right, bottom, top glViewport(0,0,winx,winy); // startx, starty, xsize, ysize glMatrixMode(GL_MODELVIEW); glLoadIdentity(); DrawSquare(0.3,0.3,0.5); // startx, starty, size } void reshape_func(int x, int y) { winx = x; winy = y; } int main() { window = glutCreateWindow( “Hex" ); glutPositionWindow( 10 , 10 ); // starting x, y of window glutReshapeWindow( winx, winy); // x, y size of window glutDisplayFunc( display_func ); glutReshapeFunc( reshape_func ); … } 512 User resizes window 496 270

  13. GLUT Window Resizing 512 • Now consider the following code int winx = 512; int winy = 512; void display_func() { glMatrixMode(GL_PROJECTION); glLoadIdentity(); gluOrtho2D(0.0,1.0,0.0,1.0); // left, right, bottom, top glViewport(0,0,winx,winy); // startx, starty, xsize, ysize glMatrixMode(GL_MODELVIEW); glLoadIdentity(); DrawSquare(0.3,0.3,0.5); // startx, starty, size } void reshape_func(int x, int y) { winx = x; winy = y; if (winy < winx) winx = winy; if (winx < winy) winy = winx; } int main() { window = glutCreateWindow( “Hex" ); glutPositionWindow( 10 , 10 ); // starting x, y of window glutReshapeWindow( winx, winy); // x, y size of window glutDisplayFunc( display_func ); glutReshapeFunc( reshape_func ); … } 512 User resizes window 496 270

  14. GLUT Window Resizing 512 • Alternatively … 512 Exercise: How would you write code to do this? User resizes window 496 270

More Related