Scan Conversion & Shading

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1 1 3D Renderng Ppelne (for drect llumnaton) 2 Scan Converson & Shadng Adam Fnkelsten Prnceton Unversty C0S 426, Fall DPrmtves 3D Modelng Coordnates Modelng Transformaton 3D World Coordnates Lghtng 3D World Coordnates Vewng Transformaton 3D Camera Coordnates Projecton Transformaton 2D Screen Coordnates Clppng 2D Screen Coordnates Vewport Transformaton 2D Image Coordnates Scan Converson 2D Image Coordnates Image Scan Converson & Shadng Overvew 3 Scan Converson 4 Scan converson ο Fgure out whch pxels to fll Render an mage of a geometrc prmtve by settng pxel colors Shadng ο Determne a color for each flled pxel vod SetPxel(nt x, nt y, Color rgba) Example: Fllng the nsde of a trangle Scan Converson 5 Trangle Scan Converson 6 Render an mage of a geometrc prmtve by settng pxel colors vod SetPxel(nt x, nt y, Color rgba) Example: Fllng the nsde of a trangle Propertes of a good algorthm ο Symmetrc ο Straght edges ο Antalased edges ο No cracks between adjacent prmtves ο MUST BE FAST! P 4 1

2 Trangle Scan Converson 7 Smple Algorthm 8 Propertes of a good algorthm ο Symmetrc ο Straght edges ο Antalased edges ο No cracks between adjacent prmtves ο MUST BE FAST! Color all pxels nsde trangle vod ScanTrangle(Trangle T, Color rgba){ for each pxel P at (x,y){ f (Insde(T, P)) SetPxel(x, y, rgba); P 4 Insde Trangle Test A pont s nsde a trangle f t s n the postve halfspace of all three boundary lnes ο Trangle vertces are ordered counter-clockwse ο Pont must be on the left sde of every boundary lne 9 Insde Trangle Test Boolean Insde(Trangle T, Pont P) { for each boundary lne L of T { Scalar d = L.a*P.x + L.b*P.y + L.c; f (d < 0.0) return FALSE; return TRUE; 10 L 1 P L 3 L 1 L 3 L 2 L 2 Smple Algorthm What s bad about ths algorthm? vod ScanTrangle(Trangle T, Color rgba){ for each pxel P at (x,y){ f (Insde(T, P)) SetPxel(x, y, rgba); 11 Trangle Sweep-Lne Algorthm Take advantage of spatal coherence ο Compute whch pxels are nsde usng horzontal spans ο Process horzontal spans n scan-lne order Take advantage of edge lnearty ο Use edge slopes to update coordnates ncrementally 12 dx dy 2

3 Trangle Sweep-Lne Algorthm 13 Polygon Scan Converson 14 vod ScanTrangle(Trangle T, Color rgba){ for each edge par { ntalze x L, x R ; compute dx L /dy L and dx R /dy R ; for each scanlne at y for (nt 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 Fll pxels nsde a polygon ο Trangle ο Quadrlateral ο Convex ο Star-shaped ο Concave ο Self-ntersectng ο Holes x L x R What problems do we encounter wth arbtrary polygons? Polygon Scan Converson 15 Insde Polygon Rule 16 Need better test for ponts nsde polygon ο Trangle method works only for convex polygons What s a good rule for whch pxels are nsde? L 5 L 4 L 5 L 4 L 1 L 1 L 3B L 2 L 3 Convex Polygon L 3A L 2 Concave Polygon Concave Self-Intersectng Wth Holes Insde Polygon Rule Odd-party rule ο Any ray from P to nfnty crosses odd number of edges 17 Polygon Sweep-Lne Algorthm Incremental algorthm to fnd spans, and determne nsdeness wth odd party rule ο Takes advantage of scanlne coherence 18 x L x R Concave Self-Intersectng Wth Holes Trangle Polygon 3

4 Polygon Sweep-Lne Algorthm vod ScanPolygon(Trangle T, Color rgba){ sort edges by maxy make empty actve edge lst for each scanlne (top-to-bottom) { nsert/remove edges from actve edge lst update x coordnate of every actve edge sort actve edges by x coordnate for each par of actve edges (left-to-rght) SetPxels(x, x +1, y, rgba); 19 Hardware Scan Converson Convert everythng nto trangles ο Scan convert the trangles 20 Hardware Antalasng 21 Overvew 22 Supersample pxels ο Multple samples per pxel ο Average subpxel ntenstes (box flter) ο Trades ntensty resoluton for spatal resoluton Scan converson ο Fgure out whch pxels to fll Shadng ο Determne a color for each flled pxel Shadng How do we choose a color for each flled pxel? ο Each llumnaton calculaton for a ray from the eyepont through the vew plane provdes a radance sample» How do we choose where to place samples?» How do we flter samples to reconstruct mage? 23 Ray Castng Smplest shadng approach s to perform ndependent lghtng calculaton for every pxel ο When s ths unnecessary? 24 Emphass on methods that can be mplemented n hardware Angel Fgure 6.34 I = I E + K I A AL + ( K D ( N L ) I + K S n ( V R ) I ) 4

5 Polygon Shadng 25 Polygon Shadng Algorthms 26 Can take advantage of spatal coherence ο Illumnaton calculatons for pxels covered by same prmtve are related to each other Flat Shadng Gouraud Shadng Phong Shadng I = I E + K I A AL + ( K D ( N L ) I + K S n ( V R ) I ) Polygon Shadng Algorthms 27 Flat Shadng 28 Flat Shadng Gouraud Shadng Phong Shadng What f a faceted object s llumnated only by drectonal lght sources and s ether dffuse or vewed from nfntely far away I = I E + K I A AL + ( K D ( N L ) I + K S n ( V R ) I ) Flat Shadng One llumnaton calculaton per polygon ο Assgn all pxels nsde each polygon the same color 29 Flat Shadng Objects look lke they are composed of polygons ο OK for polyhedral objects ο Not so good for ones wth smooth surfaces 30 N 5

6 31 Polygon Shadng Algorthms Flat Shadng 32 Gouraud Shadng What f smooth surface s represented by polygonal mesh wth a normal at each vertex? Gouraud Shadng Phong Shadng Watt Plate 7 I = I E + K A I AL + ( K D ( N L ) I + K S (V R ) n I ) 33 Gouraud Shadng Method 1: One lghtng calculaton per vertex Blnearly nterpolate colors at vertces down and across scan lnes ο Assgn pxels nsde polygon by nterpolatng colors computed at vertces Gouraud Shadng 34 Gouraud Shadng 35 Smooth shadng over adjacent polygons 36 Gouraud Shadng Produces smoothly shaded polygonal mesh ο Curved surfaces ο Illumnaton hghlghts ο Soft shadows ο Pecewse lnear approxmaton ο Need fne mesh to capture subtle lghtng effects Flat Shadng Gouraud Shadng Mesh wth shared normals at vertces Watt Plate 7 6

7 Polygon Shadng Algorthms Flat Shadng Gouraud Shadng Phong Shadng 37 Phong Shadng What f polygonal mesh s too coarse to capture llumnaton effects n polygon nterors? 38 I = I E + K I A AL + ( K D ( N L ) I + K S n ( V R ) I ) Phong Shadng Method 2: One lghtng calculaton per pxel ο Approxmate surface normals for ponts nsde polygons by blnear nterpolaton of normals from vertces 39 Phong Shadng Blnearly nterpolate surface normals at vertces down and across scan lnes 40 Polygon Shadng Algorthms Wreframe Flat 41 Shadng Issues Problems wth nterpolated shadng: ο Polygonal slhouettes ο Perspectve dstorton ο Orentaton dependence (due to blnear nterpolaton) ο Problems at T-vertces ο Problems computng shared vertex normals 42 Gouraud Phong Watt Plate 7 7

8 Summary 43 2D polygon scan converson ο Pant pxels nsde prmtve ο Sweep-lne algorthm for polygons Polygon Shadng Algorthms ο Flat ο Gouraud ο Phong ο Ray castng Key deas: ο Samplng and reconstructon ο Spatal coherence Less expensve More accurate 8

Scan Conversion & Shading

Scan Conversion & Shading Scan Converson & Shadng Thomas Funkhouser Prnceton Unversty C0S 426, Fall 1999 3D Renderng Ppelne (for drect llumnaton) 3D Prmtves 3D Modelng Coordnates Modelng Transformaton 3D World Coordnates Lghtng

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