Instance Transformation One Common Sequence of Transforms

1. y y y y x x x x z z z z Instance TransformationOne Common Sequence of Transforms S R T Model Coordinates

2. glLoadIdentity() glScalef() glRotatef() glTranslatef() Current Current Stack Stack Transformation Matrices in OpenGL 1.x – 2.x Matrix Mode = GL_MODELVIEW 3D Model Vertices 2D 3D Vertices Modelview Projection

3. Perspective Projection 3D Object Image (2D) Projection Plane COP

4. Classical Viewing:Parallel Projection 3D Object Image DOP Projection Plane

5. Canonical Perspective Transformation:Transformation of View Volume y y z = zfar z = -1 z = znear M x COP x z z z = 1 DOP Orthographic projection is applied as last step to project to plane z = 0.

6. Current Current Stack Stack Projection Matrices in OpenGL glOrtho() glFrustum() gluPerspective() Matrix Mode = GL_PROJECTION 3D Model Vertices 2D To Viewport Transform 3D Vertices Modelview Projection

7. y x Graphics Pipeline in OpenGL Model Coordinates Eye Coordinates Normalized Coordinates y Modelview Transform Projection Transform z = -1 z = 1 x z glScalef() glRotatef() glTranslatef() glFrustum() gluPerspective() Projected Normalized Coordinates Window Coordinates (1,1) Viewport Transform glViewport() (-1,-1)

8. Graphics Pipeline Example (from a Midterm)

9. Graphics Pipeline Example2 (from a Midterm)

10. Hidden Surface RemovalZ - Buffer Algorithm 2 Projection Plane 1 z2 COP z1 Z1 < Z2 Therefore red pixel from object 2 does not replace green pixel from object 1 Without z buffering enabled, red object, drawn last, would be drawn over green object.

11. Initializing and using Z-Buffer in GLUT/OpenGL Allocating the buffer: glutInitDisplayMode(GLUT_RGB|GLUT_DEPTH); Enable depth testing: glEnable(GL_DEPTH_TEST);

12. Positioning the Camera Initially, the camera is at (0,0,0) for perspective viewing looking in the -z direction. To move the camera away from modeled objects distance d along the the positive z axis: glTranslatef(0.0, 0.0, -d); What you are really doing is translating the modeled objects in the negative z direction. If you want to look at the model from the positive x direction at a distance d: glTranslatef(0.0, 0.0, -d); glRotatef(-90.0, 0.0, 1.0, 0.0);

13. A More Intuitive ApproachOffered by glu: gluLookAt(eyex, eyey, eyez, atx, aty, atz, upx, upy, upz); eyex, eyey, eyez specify the position of the eye point and are mapped to the origin. atx, aty, atz specify a point being looked at, that will be rendered in center of viewport. It is mapped to the -z axis. upx, upy, upz specify components of the camera up vector

14. Bit n Bit n Bit 4 Bit 4 Bit 3 Bit 3 Bit 2 Bit 2 Bit 1 Bit 1 Double Buffering Frame Buffer 1(drawing) Display Graphics System Frame Buffer 2 (displaying)

15. Bit n Bit n Bit 4 Bit 4 Bit 3 Bit 3 Bit 2 Bit 2 Bit 1 Bit 1 Double Buffering Frame Buffer 1(displaying) Display Graphics System Frame Buffer 2 (drawing)

16. Double Buffering:Implementation in GLUT/OpenGL Allocation of two frame buffers: glutInitDisplayMode(GLUT_RGB|GLUT_DEPTH|GLUT_DOUBLE); Swapping the buffers: display() { // Stuff being drawn into back buffer goes here glutSwapBuffers(); //makes back buffer the active buffer }

17. Simple Animation in GLUTMethod 1: Use Idle Callback Function Idle Function No Event in Queue Make Changes To Model; Post Display Event Yes Call Function n Pop Display Event From Queue Call Function n Call Function n Call Function n Call Function n Draw Scene Call Display Callback