Chapters 5Chapters 5

2 March 2004

Classical & Computer ViewingClassical & Computer Viewing

• Same elements– objects– viewer– projectors– projection plane

Classical and Computer ViewingClassical and Computer Viewing

• Perspective views– fixed Center of Projection (COP)

• Parallel Views– COP at infinity

Viewing in OpenGLViewing in OpenGL

• Perspective

• Parallel - Orthogonal

Perspective viewingPerspective 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 */

Camera Analogy and TransformationsCamera 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 TransformationsCoordinate 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 TransformationsAffine Transformations

• Want transformations which preserve geometry– lines, polygons, quadrics

• Affine = line preserving– Rotation, translation, scaling– Projection– Concatenation (composition)

Specifying TransformationsSpecifying Transformations

• Programmer has two styles of specifying transformations– specify matrices (glLoadMatrix, glLoadMatrix, glMultMatrixglMultMatrix)

– specify operation (glRotate, glOrthoglRotate, glOrtho)

• Programmer does not have to remember the exact matrices

Programming TransformationsProgramming Transformations

• Prior to rendering, view, locate, and orient:– eye/camera position– 3D geometry

• Manage the matrices– including matrix stack

• Combine (composite) transformations

vertex

ModelviewMatrix

ProjectionMatrix

PerspectiveDivision

ViewportTransform

Modelview

Modelview

Projection

object eye

clip normalizeddevice

window

• other calculations here– material color– shade model (flat)– polygon rendering mode– polygon culling– clipping

Transformation PipelineTransformation PipelineCPUCPU

DLDL

Poly.Poly. Per

Vertex

PerVertex

RasterRaster

FragFrag

FBFB

PixelPixel

TextureTexture

Applying Projection TransformationsApplying 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 TransformationsViewing 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( eyex, eyey, eyez, aimx, aimy, aimz, upx, upy, upz )

– up vector determines unique orientation– careful of degenerate positions

tripod

Projection TutorialProjection Tutorial

Transformation TutorialTransformation Tutorial

Connection: Viewing and ModelingConnection: 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 transformationsgluLookAt() has its own command

can make your own polar view or pilot view

Projection is left handedProjection 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

xx

yy

z+

z+

left handed right handed

18

resize()resize(): Perspective & Translate: Perspective & Translate

• Same effect as previous LookAtvoid 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 );}

• Same effect as previous LookAtvoid 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 );}

Hidden Surface RemovalHidden 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 RemovalHidden 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

HomeworkHomework

• 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

Program 2 due 3/18Program 2 due 3/18

• Logic…