3D Polygon Rendering Pipeline

Transcription

1 2008 סמסטר ב' ליאור שפירא קורס גרפיקה ממוחשבת 3D Rederg Ppele (for drect llumato) 3D Polygo Rederg Ppele Sca Coverso & Shadg Thomas Fukhouser Prceto Uversty C0S 426, Fall D Prmtves 3D Modelg Coordates Modelg Trasformato Lghtg 3D Camera Coordates Projecto Trasformato Clppg 2D Scree Coordates Vewport Trasformato 2D Image Coordates Sca Coverso Image 3D World Coordates 3D World Coordates Vewg Trasformato 2D Scree Coordates 2D Image Coordates Sca Coverso & Shadg Overvew Sca coverso Fgure out whch pxels to fll Shadg Determe a color for each flled pxel Texture Mappg Descrbe shadg varato wth polygo terors Vsble Surface Determato Fgure out whch surface s frot-most at every pxel Sca Coverso Reder a mage of a geometrc prmtve by settg pxel colors vod SetPxel(t x, t y, Color rgba) xample: Fllg the sde of a tragle Sca Coverso Reder a mage of a geometrc prmtve by settg pxel colors vod SetPxel(t x, t y, Color rgba) xample: Fllg the sde of a tragle Tragle Sca Coverso Propertes of a good algorthm Symmetrc Straght edges Atalased edges No cracks betwee adjacet prmtves MUST B FAST! P 4 1

2 Tragle Sca Coverso Propertes of a good algorthm Symmetrc Straght edges Atalased edges No cracks betwee adjacet prmtves MUST B FAST! Smple Algorthm Color all pxels sde tragle vod ScaTragle(Tragle T, Color rgba){ for each pxel P at (x,y){ f (Isde(T, P)) SetPxel(x, y, rgba); P 4 Isde Tragle Test A pot s sde a tragle f t s the postve halfspace of all three boudary les Tragle vertces are ordered couter-clockwse Pot must be o the left sde of every boudary le Isde Tragle Test Boolea Isde(Tragle T, Pot P) { for each boudary le L of T { Scalar d = L.a*P.x + L.b*P.y + L.c; f (d < 0.0) retur FALS; retur TRU; L 1 P L 3 L 1 L 3 L 2 L 2 Smple Algorthm What s bad about ths algorthm? vod ScaTragle(Tragle T, Color rgba){ for each pxel P at (x,y){ f (Isde(T, P)) SetPxel(x, y, rgba); Tragle Sweep-Le Algorthm Take advatage of spatal coherece Compute whch pxels are sde usg horzotal spas Process horzotal spas sca-le order Take advatage of edge learty Use edge slopes to update coordates cremetally dx dy 2

3 Tragle Sweep-Le Algorthm vod ScaTragle(Tragle T, Color rgba){ for each edge par { talze x L, x R ; compute dx L /dy L ad dx R /dy R ; for each scale at y for (t x = x L ; x <= x R ; x++) SetPxel(x, y, rgba); x L += dx L /dy L ; x R += dx R /dy R ; dx L dx R dy L dy R Polygo Sca Coverso Fll pxels sde a polygo Tragle Quadrlateral Covex Star-shaped Cocave Self-tersectg Holes x L x R What problems do we ecouter wth arbtrary polygos? Polygo Sca Coverso Need better test for pots sde polygo Tragle method works oly for covex polygos Isde Polygo Rule What s a good rule for whch pxels are sde? L 5 L 4 L 5 L 4 L 1 L 1 L 3B L 2 L 3 Covex Polygo L 3A L 2 Cocave Polygo Cocave Self-Itersectg Wth Holes Isde Polygo Rule Odd-party rule Ay ray from P to fty crosses odd umber of edges Polygo Sweep-Le Algorthm Icremetal algorthm to fd spas, ad determe sdeess wth odd party rule Takes advatage of scale coherece x L x R Cocave Self-Itersectg Wth Holes Tragle Polygo 3

4 Polygo Sweep-Le Algorthm vod ScaPolygo(Tragle T, Color rgba){ sort edges by maxy make empty actve edge lst for each scale (top-to-bottom) { sert/remove edges from actve edge lst update x coordate of every actve edge sort actve edges by x coordate for each par of actve edges (left-to-rght) SetPxels(x, x +1, y, rgba); Hardware Sca Coverso Covert everythg to tragles Sca covert the tragles Hardware Atalasg Supersample pxels Multple samples per pxel Average subpxel testes (box flter) Trades testy resoluto for spatal resoluto Overvew Sca coverso Fgure out whch pxels to fll Shadg Determe a color for each flled pxel Texture Mappg Descrbe shadg varato wth polygo terors Vsble Surface Determato Fgure out whch surface s frot-most at every pxel Shadg How do we choose a color for each flled pxel? ach llumato calculato for a ray from the eyepot through the vew plae provdes a radace sample How do we choose where to place samples? How do we flter samples to recostruct mage? Ray Castg Smplest shadg approach s to perform depedet lghtg calculato for every pxel Whe s ths uecessary? mphass o methods that ca be mplemeted hardware Agel Fgure 6.34 I I K I A AL ( K D ( N L ) I K ( V R ) I ) S 4

5 Polygo Shadg Ca take advatage of spatal coherece Illumato calculatos for pxels covered by same prmtve are related to each other Polygo Shadg Algorthms Flat Shadg Gouraud Shadg Phog Shadg I I K I A AL ( K D ( N L ) I K ( V R ) I ) S Flat Shadg What f a faceted object s llumated oly by drectoal lght sources ad s ether dffuse or vewed from ftely far away Flat Shadg Oe llumato calculato per polygo Assg all pxels sde each polygo the same color N I I K I A AL ( K D ( N L ) I K ( V R ) I ) S Flat Shadg Objects look lke they are composed of polygos OK for polyhedral objects Not so good for oes wth smooth surfaces Polygo Shadg Algorthms Flat Shadg Gouraud Shadg Phog Shadg 5

6 Gouraud Shadg What f smooth surface s represeted by polygoal mesh wth a ormal at each vertex? Gouraud Shadg Method 1: Oe lghtg calculato per vertex Assg pxels sde polygo by terpolatg colors computed at vertces I I K I A AL ( K D ( N L ) I K ( V R ) I ) Watt Plate 7 S Gouraud Shadg Blearly terpolate colors at vertces dow ad across sca les Gouraud Shadg Smooth shadg over adjacet polygos Curved surfaces Illumato hghlghts Soft shadows Mesh wth shared ormals at vertces Watt Plate 7 Gouraud Shadg Produces smoothly shaded polygoal mesh Pecewse lear approxmato Need fe mesh to capture subtle lghtg effects Polygo Shadg Algorthms Flat Shadg Gouraud Shadg Phog Shadg Flat Shadg Gouraud Shadg 6

7 Phog Shadg What f polygoal mesh s too coarse to capture llumato effects polygo terors? Phog Shadg Oe lghtg calculato per pxel Approxmate surface ormals for pots sde polygos by blear terpolato of ormals from vertces I I K I A AL ( K D ( N L ) I K ( V R ) I ) S Phog Shadg Blearly terpolate surface ormals at vertces dow ad across sca les Polygo Shadg Algorthms Wreframe Flat Gouraud Phog Watt Plate 7 Shadg Issues Problems wth terpolated shadg: Polygoal slhouettes Perspectve dstorto Oretato depedece (due to blear terpolato) Problems at T-vertces Problems computg shared vertex ormals Overvew Sca coverso Fgure out whch pxels to fll Shadg Determe a color for each flled pxel Texture Mappg Descrbe shadg varato wth polygo terors Vsble Surface Determato Fgure out whch surface s frot-most at every pxel 7

8 Textures Descrbe color varato teror of 3D polygo Whe sca covertg a polygo, vary pxel colors accordg to values fetched from a texture Surface Textures Add vsual detal to surfaces of 3D objects Texture Surface Image Wth surface texture Agel Fgure 9.3 Polygoal model Surface Textures 3D Rederg Ppele (for drect llumato) 3D Prmtves 3D Modelg Coordates Modelg Trasformato 3D World Coordates Lghtg 3D World Coordates Vewg Trasformato 3D Camera Coordates Projecto Trasformato 2D Scree Coordates Clppg 2D Scree Coordates Vewport Trasformato 2D Image Coordates Sca Coverso Image 2D Image Coordates Texture mappg Overvew Texture mappg methods Mappg Flterg Parameterzato Texture mappg applcatos Modulato textures Illumato mappg Bump mappg vromet mappg Image-based rederg No-photorealstc rederg Texture Mappg Steps: Defe texture Specfy mappg from texture to surface Lookup texture values durg sca coverso t s Texture Coordate System (0,1) (1,0) v u (0,0) Modelg Coordate System y x Image Coordate System 8

9 Texture Mappg Whe sca covert, map from mage coordate system (x,y) to modelg coordate system (u,v) to texture mage (t,s) Texture Mappg Texture mappg s a 2D projectve trasformato texture coordate system: (t,s) to mage coordate system (x,y) (0,1) (1,1) t s Texture Coordate System (1,0) v u (0,0) Modelg Coordate System y x Image Coordate System Chrs Buehler & Leoard McMlla, MIT Texture Mappg Texture Mappg Sca coverso Iterpolate texture coordates dow/across sca les Dstorto due to blear terpolato approxmato Cut polygos to smaller oes, or Perspectve dvde at each pxel Lear terpolato of texture coordates Correct terpolato wth perspectve dvde Hll Fgure 8.42 Overvew Texture Flterg Texture mappg methods Mappg Flterg Parameterzato Must sample texture to determe color at each pxel mage Texture mappg applcatos Modulato textures Illumato mappg Bump mappg vromet mappg Image-based rederg No-photorealstc rederg Agel Fgure 9.4 9

10 Texture Flterg Alasg s a problem Texture Mappg Sca coverso Iterpolate texture coordates dow/across sca les Dstorto due to blear terpolato approxmato Cut polygos to smaller oes, or Perspectve dvde at each pxel Pot samplg Area flterg Agel Fgure 9.5 Texture Mappg Overvew Texture mappg methods Mappg Flterg Parameterzato Lear terpolato of texture coordates Correct terpolato wth perspectve dvde Hll Fgure 8.42 Texture mappg applcatos Modulato textures Illumato mappg Bump mappg vromet mappg Image-based rederg No-photorealstc rederg Texture Flterg Texture Flterg Must sample texture to determe color at each pxel mage Alasg s a problem Pot samplg Area flterg Agel Fgure 9.4 Agel Fgure

11 Texture Flterg Ideally, use ellptcally shaped covoluto flters Texture Flterg Sze of flter depeds o projectve warp Ca preflterg mages Mp maps Summed area tables Magfcato Mfcato I practce, use rectagles Agel Fgure 9.14 Mp Maps Keep textures prefltered at multple resolutos For each pxel, learly terpolate betwee two closest levels (e.g., trlear flterg) Fast, easy for hardware Summed-area tables At each texel keep sum of all values dow&rght To compute sum of all values wth a rectagle smply subtract two etres Better ablty to capture very oblque projectos But, caot store values a sgle byte Overvew Texture mappg methods Mappg Flterg Parameterzato Texture mappg applcatos Modulato textures Illumato mappg Bump mappg vromet mappg Image-based rederg No-photorealstc rederg Overvew Texture mappg methods Mappg Flterg Parameterzato Texture mappg applcatos Modulato textures Illumato mappg Bump mappg vromet mappg Image-based rederg No-photorealstc rederg 11

12 Wood texture Modulato textures Illumato Mappg Map texture values to scale factor Map texture values to surface materal parameter K A K D K S K T Texture value K T = T(s,t) I T( s, t)( I K AI A ( KD( N L) KS ( V R) ) SLI L KT IT KSIS ) L I I K AI A ( K L D( N L) KS ( V R) ) S I K I K I L L T T S S Bump Mappg Bump Mappg Map texture values to perturbatos of surface ormals H&B Fgure vromet Mappg Image-Based Rederg Map texture values to perturbatos of surface ormals Map photographc textures to provde detals for coarsely detaled polygoal model H&B Fgure

13 Sold Textures Texture values dexed by 3D locato xpesve storage, or Compute o the fly,.g Perl ose Sold Textures Texture values dexed by 3D locato xpesve storage, or Compute o the fly,.g Perl ose 13