3DView - Three-Dimensional Th Di i l Viewing Vi i Chap 7,...

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Three-Dimensional Viewing Chap 7, 2009 Spring Yeong Gil Shin
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Viewing Pipeline How to define a window? How to project onto the window?
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Rendering " Create a picture (in a synthetic camera)” ± Specification of projection type ± Specification of viewing parameters: ± viewer's eye, viewing plane (viewing coordinates) ± Clipping in 3D: window, view volume ± Projection : the transformation of points from a coordinate s stem in dimensions to a coordinate system in dimensions y y where m<n ± Display: view port
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General 3D Viewing Pipeline ± Modeling coordinates (MC) ± World coordinates (WC) iewing coordinates (VC) RC camera position ± Viewing coordinates (VC) – VRC, camera position ± Projection coordinates (PC) – window, projection type ormalized coordinates (NC) ± Normalized coordinates (NC) ± Device coordinates (DC) – view port in a screen
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Projections ± Projection coordinate system: ± Left-handed – Core, DirectX ± why? - screen coordinatesystem is left-handed ± Right-handed - GKS, PHIGS, OpenGL rojection plane (view plane): viewing surface where ± Projection plane (view plane): viewing surface where objects are projected. v n u
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Viewing-Coordinate Parameters ± View reference point (VRP) ± The viewing origin in WC : ye position camera position ) , , ( 0 0 0 0 z y x = P ± Eye position, camera position ± Viewing Coordinate : x view , y view , z view (or uvn) efined by P N ,VUP ± Defined by P 0 , N, VUP ± View-plane (Projection plane) ± Locates on z iew axis : z p view vp ± Perpendicular to z view
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Viewing-Coordinate Parameters ± How we specify a view plane normal vector, N [Way I] The origin of WC to a selected point position ay II] The direction from a reference point [Way II] The direction from a reference point P ref to the viewing origin: P ef : look-at point ref 0 P P N = ref Viewing direction: N (in RHS)
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Viewing-Coordinate Parameters ± View-up vector: VUP ± Specified in the world coordinates sed to establish the positive direction for the y xis ± Used to establish the positive direction for the y view axis ± VUP should be perpendicular to N , but it can be difficult to a direction for VUP that is precisely perpendicular to N view y UP RP ew x VUP N VRP 0 = P view view z
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Viewing-Coordinate Reference Frame (VRC) ± The camera orientation is determined by viewing reference frame, View Reference Coordinate (VRC), x view , y view , z view (or uvn) ± The origin of the viewing reference frame : P 0 (= VRP) ) , , ( n n n = = N n v z y x × n VUP N VUP 0 P ) , , ( z y x u u u = = VUP u u N n ) , , ( z y x v v v = × = u n v View plane w.r.t. VRC
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World-to-Viewing Transformation ± Transformation from WC to VRC ± Translate the viewing-coordinate origin to the world- coordinate origin ± Apply rotations to align the u , v , n axes with the world x w , y w , z w axes, respectively u n v
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World-to-Viewing Transformation 0 1 0 0 0 1 0 0 0 y x v v v u u u z y x = = 1 0 0 0 0 0 z n n n z y x z y x T R 1 0 0 0 1 0 0 0 u n v 0 P u z y x u u u = = 0 0 , P n P v T R M z y x z y x vc wc n n
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3DView - Three-Dimensional Th Di i l Viewing Vi i Chap 7,...

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