05_3DViewing(ch7)

05_3DViewing(ch7) - Three Three-Dimensional Dimensional...

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Unformatted text preview: Three Three-Dimensional Dimensional Viewing Viewing Chapter 7 Viewing Pipeline Viewing Pipeline How to define a window? How to project onto the window? Rendering Rendering " Create a picture (in a synthetic camera)” n Specification of projection type n Specification of viewing parameters n viewer's eye, viewing plane (viewing coordinates) n Clipping in 3D n window, view volume n Projection n the transformation of points from a coordinate system in n dimensions to a coordinate system in m dimensions where m<n n Display n Viewport General 3D Viewing Pipeline General 3D Viewing Pipeline n Modeling coordinates (MC) n World coordinates (WC) n Viewing coordinates (VC) – VRC, camera position n Projection coordinates (PC) – projection type n Normalized coordinates (NC) n Device coordinates (DC) – viewport in a screen Projections Projections n Projection coordinate system: n Left-handed – Core, DirectX n why? - screen coordinate system is left-handed n Right-handed - GKS, PHIGS, OpenGL n Projection plane (view plane) n viewing surface where objects are projected. n u v 3D Viewing 3D Viewing-Coordinate Parameters Coordinate Parameters n View point (Viewing position) n The viewing origin in WC : n Eye position, camera position ) , , ( z y x = P n Viewing Coordinates : x view , y view , z view (or uvn) n Defined by P , N , V n View plane ( Projection plane ) n View-plane normal vector, N n Perpendicular to N ( z view ) 3D Viewing 3D Viewing-Coordinate Parameters Coordinate Parameters n How we specify a view plane normal vector, N [Way I] along the line from the WC origin to a selected point position [Way II] the direction from a reference point P ref to the viewing origin: P ref : a look-at point Viewing direction: - N ref P P N- = 3D Viewing 3D Viewing-Coordinate Parameters Coordinate Parameters n View-up vector , V n Specified in the world coordinates n Used to establish the positive direction for the y view axis n V should be perpendicular to N , but it can be difficult to determine a direction for V that is precisely perpendicular to N n So, V is projected onto a plane perpendicular to N uvn uvn Viewing Viewing-Coordinate Coordinate Reference Frame Reference Frame n Using N and V , compute a third vector U n uvn viewing-coordinate reference coordinate (VRC) n The coordinate system formed with the three vectors n The origin of VRC: P ) , , ( ) , , ( ) , , ( z y x z y x z y x v v v u u u n n n = ´ = = ´ = = = u n v VUP n V u N N n u v V N View plane w.r.t. VRC n P World World-to to-Viewing Transformation Viewing Transformation n Transform object descriptions in WC to VRC 1. Translate the viewing-coordinate origin to the world-coordinate origin 2. Apply rotations to align the x view , y view , and z view axes with the world x w , y w , z w axes, respectively u n v u n v World World-to to-Viewing Transformation Viewing Transformation ú ú ú ú û ù ê ê ê ê ë é--- = ú ú ú ú û ù ê ê ê ê ë é = 1 1 1 1 1 z y x n n n v v v u u u z...
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05_3DViewing(ch7) - Three Three-Dimensional Dimensional...

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