Chapters 5 2 March 2004

Classical & Computer Viewing Same elements –objects –viewer –projectors –projection plane

Classical and Computer Viewing Perspective views –fixed Center of Projection (COP) Parallel Views –COP at infinity

Viewing in OpenGL Perspective Parallel - Orthogonal

Perspective viewing glMatrixMode(GL_PROJECTION); gluPerspective(40.0, 1.0, 1.0, 40.0); // field of view,aspect ratio, z near, z far //0-180w/h + + glMatrixMode(GL_MODELVIEW); gluLookat(0.0, 0.0, 30.0, /* eye */ 0.0, 0.0, 0.0, /* center */ 0.0, 1.0, 0.0); /* up */

Camera Analogy and Transformations Projection transformations –adjust the lens of the camera Viewing transformations –tripod–define position and orientation of the viewing volume in the world Modeling transformations –moving the model Viewport transformations –enlarge or reduce the physical photograph

Coordinate Systems and Transformations Steps in Forming an Image –specify geometry (world coordinates) –specify camera (camera coordinates) –project (window coordinates) –map to viewport (screen coordinates) Each step uses transformations Every transformation is equivalent to a change in coordinate systems (frames)

Affine Transformations Want transformations which preserve geometry –lines, polygons, quadrics Affine = line preserving –Rotation, translation, scaling –Projection –Concatenation (composition)

Specifying Transformations Programmer has two styles of specifying transformations glLoadMatrix, glMultMatrix –specify matrices ( glLoadMatrix, glMultMatrix ) glRotate, glOrtho –specify operation ( glRotate, glOrtho ) Programmer does not have to remember the exact matrices

Programming Transformations Prior to rendering, view, locate, and orient: –eye/camera position –3D geometry Manage the matrices –including matrix stack Combine (composite) transformations

vertexvertex Modelview Matrix Projection Matrix Perspective Division Viewport Transform Modelview Projection object eye clip normalized device window other calculations here –material  color –shade model (flat) –polygon rendering mode –polygon culling –clipping Transformation Pipeline CPU DL Poly. Per Vertex Per Vertex Raster Frag FB Pixel Texture

Applying Projection Transformations Typical use (orthographic projection) glMatrixMode( GL_PROJECTION ); glLoadIdentity(); glOrtho( left, right, bottom, top, zNear, zFar ); Typical use (orthographic projection) glMatrixMode( GL_PROJECTION ); glLoadIdentity(); glOrtho( left, right, bottom, top, zNear, zFar );

Viewing Transformations Position the camera/eye in the scene –place the tripod down; aim camera To “fly through” a scene –change viewing transformation and redraw scene gluLookAt( eye x, eye y, eye z, aim x, aim y, aim z, up x, up y, up z ) –up vector determines unique orientation –careful of degenerate positions tripod

Projection Tutorial

Transformation Tutorial

Connection: Viewing and Modeling Moving camera is equivalent to moving every object in the world towards a stationary camera Viewing transformations are equivalent to several modeling transformations gluLookAt() has its own command can make your own polar view or pilot view

Projection is left handed Projection transformations ( gluPerspective, glOrtho ) are left handed –think of zNear and zFar as distance from view point Everything else is right handed, including the vertexes to be rendered x x y y z+ left handedright handed

18 resize() : Perspective & Translate Same effect as previous LookAt void resize( int w, int h ) { glViewport( 0, 0, (GLsizei) w, (GLsizei) h ); glMatrixMode( GL_PROJECTION ); glLoadIdentity(); gluPerspective( 65.0, (GLfloat) w/h, 1.0, ); glMatrixMode( GL_MODELVIEW ); glLoadIdentity(); glTranslatef( 0.0, 0.0, -5.0 ); } Same effect as previous LookAt void resize( int w, int h ) { glViewport( 0, 0, (GLsizei) w, (GLsizei) h ); glMatrixMode( GL_PROJECTION ); glLoadIdentity(); gluPerspective( 65.0, (GLfloat) w/h, 1.0, ); glMatrixMode( GL_MODELVIEW ); glLoadIdentity(); glTranslatef( 0.0, 0.0, -5.0 ); }

Hidden Surface Removal Modeling a cube –what causes only the 3 front facing sides to be visible? Hidden surface removal algorithms –object space algorithms –image space algorithms »z buffer algorithm (requires DEPTH buffer and the GL_DEPTH_TEST to be enabled)

Hidden Surface Removal Optimize the process by rendering only front facing polygons glEnable(GL_CULL_FACE) –what is a front facing polygon? One with its normal facing the viewer

Homework Begin Presentation. –No class Thursday. Go to the library or online. Browse Computer Graphics articles. Find a topic that interests you. You will need to cite a minimum of two sources for your 10 minute presentation. –Computer Graphics Quarterly - SIGGRAPHComputer Graphics Quarterly –Computer Graphics WorldComputer Graphics World

Program 2 due 3/18 Logic…