CS5620 Intro to Computer Graphics

Transcription

1 CS560 Reminder - Pieline Polgon at [(,9), (5,7), (8,9)] Polgon at [ ] D Model Transformations Reminder - Pieline Object Camera Cli Normalied device Screen Inut: Polgons in normalied device Model-view Projection Persective division Viewort s s Outut: D image of rojected olgons containing onl visible ortions s s Algorithms Back face culling Back Face Culling Object Sace In a closed olhedron back faces are not visible Painter s algorithm (deth sort) Z-Buffer Scan-line Z-Buffer torus demo 5 6 Page

2 CS560 The Normal Vector Back Face Culling Determining back faces v n = (v v ) (v v ) v n = (v v ) (v v ) In a closed olhedron back faces are not visible Assume normals oint out face visible iff: π θ π iff cosθ 0 v n,, = n,, = n(,,) iff v n = v n cosθ Back Face culling When will it work? Closed, conve Oen Closed, non conve Back Face Culling Closed conve objects All back faces invisible All front faces visible Visibilit roblem solved Oen objects Back faces ossibl visible Closed non-conve objects Invisible back faces Front faces can be visible, invisible or artiall visible 9 0 Object sace Which color to draw? Draw everthing which order to draw? Sort olgons b deth values Paint back to front When will this fail? intersecting olgons cclic occlusion Page

3 CS560 Works in secial cases E.g. olgons with constant How do we fi it? Deth sort er olgon doesn t work Where do we have olgons with constant? Deth sort er iel Image sace algorithm Resolve visibilit at the iel level Store color + current er iel Image Sace Put new color onl if new < current The Z-Buffer 5 6 For ever iel (,) utz(,,maz) The Algorithm D Projected scene A B C For ever iel (,) utz(,,maz) The Algorithm D Projected scene A B C For each olgon P Q = roject(p) for each iel (,) in Q = deth(q,,) if < getz(,) utcolor(,,col(p)) utz(,,) Z buffer Image 0 For each olgon P Q = roject(p) for each iel (,) in Q = deth(q,,) if < getz(,) utcolor(,,col(p)) utz(,,) Z buffer Image 0 Page

4 CS560 For ever iel (,) utz(,,maz) The Algorithm For each olgon P Q = roject(p) for each iel (,) in Q = deth(q,,) if < getz(,) utcolor(,,col(p)) utz(,,) Projected scene Z buffer Image D A B C 0 Comuting deth(q,,) Have coordinate at vertices How do we comute at re-image of rojected oint? 0 Comuting deth(q,,) Comuting deth(q,,) We know D at vertices D at rojected vertices D at = (, ) We need D at v v Linear transformations reserve straight lines. Comute and. Eress with and. Comute in the same wa from and Inut: oints, values Linear Interolation On a line Outut: value at an oint on the line L(t) between them Comuting deth(q,,) Al linear interolation on a line twice: L t = t + t 0 t [0,] = t + t, f t = L t, f(t) 0, f 0 L 0 = 0 L = L 0.5 = 0 + t = 0 0, f, 0, f 0, = 0 = t t t = = t + t t = f = f t = tf + t f 0 Page

5 CS560 Z-Buffer deth(q,,) t ( t) t ( t) scanline Y= Rasterie using Bresenham algorithm (, ) deth( Q,, ) t ( t ) t, t, t deth( Q,, ) t ( t ) t ( t ( t ) ) ( t )( t ( t ) ) ( tt ( t ) t ) t ( t ) ( t )( t ) ; Inut: oints, values Linear Interolation On a triangle Outut: value at an oint in the triangle the oints san, f, f, f = α + α + α α + α + α = α i 0, f,, f,, f, f = f α, α, α = α f + α f + α f But α i =? 5 6 A i α i = A + A + A Barcentric Coordinates =(,, ) (,0,0) (0,0,) =(,, ) A A A =(,,) 7 =(,, ) (0,,0) Barcentric of = (,, ) B.C. are unique. B.C. of all interior oints are 0. Triangle centroid = (/,/,/). (-,,) Z-Buffer - Project(P) d d d( ) 0 0 d d d 0 0 / d 0 / d / d / d d d monotone with resect to use as deth to determine order 8 Image sace algorithm Data structure: Arra of deth values Imlemented in hardware due to simlicit Deth resolution of bits is common Scene ma be udated on the fl, adding new olgons 9 0 Page 5 5

6 6 CS560 Z Fighting Transarenc Z-Buffer How can we emulate transarent objects? When Z-buffer has low recision and/or is not chosen correctl Transarenc Z-Buffer The Grahics Pieline Etension to the basic Z-buffer algorithm Save all iel values At the have list of olgons & deths (order) for each iel Simulate transarenc b weighting the different list elements, in order Hardware imlementation of screen Z-buffer: Polgons sent through ieline one at a time Disla udated to reflect each new olgon Do we reall need to store all iel values? Geometr Processing (viewing transformations) Rasterier (scan-conversion Z-buffer) Scan-Line Scan-Line a d b c A={a,d} A={c,d,b} A={b} In software imlementations - amount of memor required for screen Z-buffer ma be rohibitive Scan-line Z-buffer algorithm: Rer the image one line at a time Take into account onl olgons affecting this line Combination of olgon scan-conversion & Z-buffer algorithms Onl Z-buffer the sie of scan-line is required. Entire scene must be available in advance Image cannot be udated incrementall 5 6 Page 6

7 CS560 Scan-Line ScanLineZBuffer(Scene) SceneD := Project(Scene); Sort SceneD into buckets of olgons P in increasing YMin(P) order; A := EmtSet; for := YMin(SceneD) to YMa(SceneD) do for each iel (, ) in scanline Y= do PutZ(, MaZ); A := A + {P in Scene : YMin(P)<=}; A := A - {P in A : YMa(P)<}; for each olgon P in A for each iel (, ) in P s san(s) on the scanline := Deth(P,, ); if (<GetZ()) then PutColor(,, Col(P)); PutZ(, ); ; ; ; ; 7 a d b c A={a,d} A={c,d,b} A={b} Line and Polgon Cliing Algorithms Cohen-Sutherland Sutherland-Hodgman Liang-Barks Crus-Beck 8 Page 7 7