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Chapters 5

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.

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Chapters 5

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  1. Chapters 5 2 March 2004

  2. Classical & Computer Viewing • Same elements • objects • viewer • projectors • projection plane

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

  4. Viewing in OpenGL • Perspective • Parallel - Orthogonal

  5. Perspective viewing glMatrixMode(GL_PROJECTION); gluPerspective(40.0, 1.0, 1.0, 40.0); // field of view, aspect ratio, z near, z far // 0-180 w/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 */

  6. 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

  7. 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)

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

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

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

  11. Per Vertex Poly. Frag FB Raster CPU DL Texture Pixel Transformation Pipeline • other calculations here • material è color • shade model (flat) • polygon rendering mode • polygon culling • clipping normalized device eye object clip window v e r t e x Modelview Matrix Projection Matrix Perspective Division Viewport Transform Modelview Projection Modelview l l l

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

  13. tripod Viewing Transformations • Position the camera/eye in the scene • place the tripod down; aim camera • To “fly through” a scene • change viewing transformation andredraw scene • gluLookAt( eyex, eyey, eyez, aimx, aimy, aimz, upx, upy, upz ) • up vector determines unique orientation • careful of degenerate positions

  14. Projection Tutorial

  15. Transformation Tutorial

  16. 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

  17. 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 y y z+ left handed right handed x x z+

  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, 100.0 ); glMatrixMode( GL_MODELVIEW ); glLoadIdentity(); glTranslatef( 0.0, 0.0, -5.0 ); }

  19. 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)

  20. 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

  21. 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 - SIGGRAPH • Computer Graphics World

  22. Program 2 due 3/18 • Logic…

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