The Graphics Pipeline: Geometric Operations

Graphics Pipeline• Local Space• Local Coordinates - geometric• Object Definition - geometric• World Space• World Coordinates - geometric• Compose Scene - geometric• Define View - geometric• Define Lighting - geometric• Animation – geometric• Radiosity Rendering - algorithmic• View Space• View Coordinates• View volume - geometric• Culling – geometric• Clip to 3D – geometric/algorithmic• Back-Face Elimination - geometric• 3D Screen Space• Screen Space Coordinates• View Transformation – geometric• Clipping - algorithmic• Shading - algorthmic• Rasterization - algorithmic• Hidden surface removal - algorithmicLocal SpaceModeling TransformationWorld SpaceView TransformationView Space3D Screen SpaceDisplay or Image Space28-Sep-073D Computer Graphics, Alan Watt4

Local Space• Local Coordinate System• Object Origin or Pivot Point• Polygon x,y,z & normals• Vertex x,y,z & normals28-Sep-073D Computer Graphics, Alan Watt5

World Space• World Coordinate System• Compose Scene• Camera Location• Define Lighting• Animation• Surface AttributesLocal SpaceModeling TransformationWorld SpaceView Space3D Screen SpaceDisplay or Image Space28-Sep-073D Computer Graphics, Alan Watt7

World Space• World Coordinate System• Scenes x,y,z• Global origin• Local CoordinatesTransformations28-Sep-073D Computer Graphics, Alan Watt8

PRLL005PRLL0051 2 2b 3 4 5 6 7 8 9 10 11 12 13 14 IFFTERVP1VP2AMPCONCIDESORITEROSEZITTIDRCVADETMBTPunteggioLivelloDx 25 10 15 10 20 1 25 5 15 20 15 15 15 20 211 IISx 25 5 10 5 20 1 25 1 15 20 15 15 15 20 192 II-IIIInizio muro in sinistra – fine muro in sinistra ; lungh: 389 mNell’area immediatamente adiacente al corso d’acqua, oltre l’ontano verde, vi è anche una discretapresenza di salici. In destra la vegetazione è primaria ed ha un’ampiezza maggiore di 30 metri(data dalla somma dell’ampiezza della bordura di arbusti ripari e della formazione arborea nonriparia). In sinistra invece la vegetazione è secondaria e l’ampiezza è compresa tra i 10 e i 30metri. Sono sempre presenti interruzioni, più frequenti in sponda sinistra. Le rive hanno subitolimitati interventi artificiali, che comportano un peggioramento nella valutazione del parametroriguardante l’erosione. Gli altri parametri non si mutano rispetto quanto osservato per i tratti postipiù a valle.381

View Space• Viewpoint ‘C’• Viewing Direction ‘N’• View Plane• Normal to ‘N’• ‘d’ distance from ‘C’• View Coordinate System• Origin ‘C’• UV axes• Third axis NView VolumeView PlaneWCSVUdNNC28-Sep-07 3D Computer Graphics, Alan Watt10

View Space• View Coordinate System• Camera, Eye or View• ‘first person’• ‘third person’• View coordinates• Viewpoint = C• Viewing direction = N• View Plane = U,V• VCS = Xu, Yv, Zn• View VolumeView VolumeVUFrustumYvNZnView PlaneCXuView Coordinate System28-Sep-073D Computer Graphics, Alan Watt11

View Space• View volume• View normal (N)• View Plane (U,V)• Frustum• Far Clipping Plane• Near Clipping Plane• View VolumeFar FarClipping ClippingPlanePlaneFrustumFrustumFrustumNear Clipping PlaneView VolumeNViewView PlanePlaneView Plane28-Sep-073D Computer Graphics, Alan Watt12

View Space• View Coordinate System• Camera or Views• ‘first person’• ‘third person’• orthographic28-Sep-07 3D Computer Graphics, Alan Watt13

View Space• View Space Operations• Culling• Remove Objects that neednot be rendered.• View Volume• Bounding Box• In, Out, or Clipping• Far-Clipping/Fog• Clipping against the ViewVolume• Discard as many polygonsas possible28-Sep-073D Computer Graphics, Alan Watt14

View Space• View Space Operations• Back-Face Elimination• The Second step in rendering• Polygon Normals facing away from the View PlanImage 1 Image 228-Sep-073D Computer Graphics, Alan Watt15

3D Screen Space• Bulk of theRendering work• What color is thispixel?• Geometry Operations• View Transformation• Calculate Z-depth• Z-Buffer analysis3D ModelObject SpaceWorld SpaceView Space3D Screen SpaceDisplay or Image Space2D Raster Grid28-Sep-073D Computer Graphics, Alan Watt16

3D Screen SpaceProjection into Screen SpaceV2V1View Plane(Screen Space)L1View Plane(Screen Space)L2Center ofProjectionFigure 1.0 - Perspective ProjectionV1Center ofProjectionFigure 2.0 - Perspective ProjectionV2Projectors areparallelView Plane(Screen Space)28-Sep-07Figure 3.0 - Parallel Projection3D Computer Graphics, Alan Watt17

View Volume and Z-Depth• View Transformation ofa box from view spaceinto 3D screen space.CubeView SpaceView Transformation• Allows parallel projectionrays for vertices.TransformedCube28-Sep-073D Screen Space3D Computer Graphics, Alan Watt18

3D Screen Space• Calculation of Z-depths• Perspective distortion ofZ-depths.• Z-depths stored in theVZ-buffer2Z sY sV 1View planeZ 1Z 1X s3d Screen SpaceViewpoint (C)28-Sep-073D Computer Graphics, Alan Watt19

Graphics Pipeline• Local Space• Local Coordinates - geometric• Object Definition - geometric• World Space• World Coordinates - geometric• Compose Scene - geometric• Define View - geometric• Define Lighting - geometric• Animation – geometric• Radiosity Rendering - algorithmic• View Space• View Coordinates• View volume - geometric• Culling – geometric• Clip to 3D – geometric/algorithmic• Back-Face Elimination - geometric• 3D Screen Space• Screen Space Coordinates• View Transformation – geometric• Clipping - algorithmic• Shading - algorithmic• Rasterization - algorithmic• Hidden surface removal - algorithmicLocal SpaceModeling TransformationWorld SpaceView TransformationView SpaceView Transformation3D Screen SpaceDisplay or Image Space28-Sep-073D Computer Graphics, Alan Watt20