drawing curved surfaces Class 3:Chaps 2 cont. trig review drawing curves depth buffer perspective drawing curved surfaces

Trig Review: Definition of sine and cosine (Unit circle, radius=1) (cos sin ) (cos sin )  From Wikipedia, modified

cos(0) = sin(0) = 1.0 0.0 (cos(0), sin(0))

cos(PI/2) = sin(PI/2) = 0.0 1.0 (cos(PI/2), sin(PI/2))

cos(PI) = sin(PI) = -1.0 0.0 (cos(PI), sin(PI))

Change the radius from 1 to R (Rcos(), Rsin()) R 

Move the center from (0,0) to (X,Y) (X+Rcos(), Y+Rsin()) R  (X,Y) Y X (0,0)

Curved Objects Run the program circle.cpp. Observe instructions in comment and console screen global variables new version of color: glColor3ub use of rand() glutPostRedisplay in keyInput

parametric equation of circle

The book also has parabola.cpp, another example of a curve described parametrically. Run it on your own.

3-D Depth Buffer Perspective

circularAnnuluses.cpp (modified)

Overwritten void drawDisc(float R, float X, float Y, float Z); glColor3f(0.0, 0.0, 1.0); drawDisc(20.0, 25.0, 75.0, 0.0); glColor3f(1.0, 1.0, 1.0); drawDisc(10.0, 25.0, 75.0, 0.0);

The real deal if (isWire) glPolygonMode(GL_FRONT, GL_LINE); else glPolygonMode(GL_FRONT, GL_FILL); glColor3f(1.0, 0.0, 0.0); glBegin(GL_TRIANGLE_STRIP); for(i = 0; i <= N; ++i) { angle = 2 * PI * i / N; glVertex3f(50 + cos(angle) * 10.0, 30 + sin(angle) * 10.0, 0.0); glVertex3f(50 + cos(angle) * 20.0, 30 + sin(angle) * 20.0, 0.0); } glEnd();

Floating glEnable(GL_DEPTH_TEST); // Enable depth testing. glColor3f(0.0, 1.0, 0.0); drawDisc(20.0, 75.0, 75.0, 0.0); glColor3f(1.0, 1.0, 1.0); drawDisc(10.0, 75.0, 75.0, 0.5); // Compare this z-value with that of the green disc. glDisable(GL_DEPTH_TEST); // Disable depth testing.

To use the depth buffer, you must initialize it in main. glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB | GLUT_DEPTH); And clear it glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);

Hidden surface removal. glOrtho(0.0, 100.0, 0.0, 100.0, -1.0, 1.0);

What is it? x = Rcos(t) -10*PI <= t <= 10*PI y = Rsin(t) z = t - 60.0 -10*PI <= t <= 10*PI

Helix.cpp x = Rcos(t) -10*PI <= t <= 10*PI y = Rsin(t) z = t - 60.0 -10*PI <= t <= 10*PI -31.4 31.4 -60 -60 _____ _____ z: -91.4 -28.6

Helixmod.cpp cont after a modification of view

How do we indicate depth in pictures?

glFrustum(left, right, bottom, top, near, far)

glFrustum(-5.0,5.0,-5.0,5.0,4.0,100.0);