2-D Raster Graphics. Graphics Pipeline. Conversion to. Conversion. to Pixel Values. Pixel Values

Transcription

1 -D Raste Gahics Gahics Pielie Data Objects Covesio Covesio to to Piel Values Piel Values Disla Device Geometic Vecto Fields Chaacte Pojectio Illumiatio Shadig Deflect Beam Active Phosho -D Raste Gahics Cotiuous Real Coodiates Discete Itege Coodiates Rasteizatio - Covesio of cotiuous, eal valued, data to itege iel values

2 Lie Dawig Lie Equatios Sloe - Itecet Equatio Imlicit Equatio Paametic Vecto Equatio Bleded Iteolatio Equatio m b A B C P P P P t P P t P t 3 Lie Dawig Algoithms Bute Foce Solutio Give:, ad, as edoits Comute sloe: m Comute -itecet: {,,3,... } b m Least Effective / Efficiet Eo Accumulatio m b i it.5 j it.5 4

3 Lie Dawig Algoithms Basic Icemetal Aoach m m b whee m b m b m m whe Digital Dfeece Aalze DDA b 5 Lie Dawig Algoithms m b, m,, it.5,it m.5 6 3

4 Lie Dawig Algoithms Midoit Checkig Miimize Eos 8 7 m b ene ee 3 4 Beseham Algoithm 7 Lie Dawig Algoithms Comute Eo at Each Potetial Piel, Coodiates of Cuet iel ene ee Eo at NothEast iel whee a oit o the lie m b Eo at East iel m b 8 4

5 Lie Dawig Algoithms If ene < en SetPiel else SetPiel,, 8 7 m b ene ee Lie Dawig Algoithms e E Defie Decisio Paamete, Based o Dfeece of Eo Tems ee ene { m b } { m b} ene m b b 5

6 6 Lie Dawig Algoithms Set Piel Based o the Sig of { } { }, SetPiel else, SetPiel If N < < E NE NE E e e e e C b b C Note: C is Ideedet of Cuet Positio Lie Dawig Algoithms C Iteative Calculatio fo Decisio Paamete NE was chose Piel E was chose Piel whee <

7 Lie Dawig Algoithms Beseham Lie Dawig Algoithm m <. Ete Edoits: stat, stat,sto, sto. ComuteCostats: sto stat, sto,, 3.Plot, 4. Fo L If < Plot, Else Plot, stat, Lie Dawig Algoithms Beseham Eamle Edoits:,, 3,8, 8, 6, 6, 6-4,,, 3, 4, 3 5, , 6-4 6, 7, 8, 9, 3,, 4 7

8 Lie Dawig Algoithms Lie Dawig Algoithms Lie Dawig Issues Edoit Ode Covetio fo Sloe > Secial Cases Hoizotal Vetical Diagoal 6 8

9 Cicle Dawig Algoithms Bute Foce Solutio No-Uom Samles M Cicle Dawig Algoithms Tigoometic Solutio cosθ siθ Samle Sacig Deeds o Disla Device θ Comutatioall Eesive 8 9

10 Cicle Dawig Algoithms Cicula Smmet,,,, 45,,,, Comute i d Octat to 9 Cicle Dawig Algoithms Midoit Checkig Defie Cicle Fuctio f, f, < > Poit is ON the cicle Poit is INSIDE the cicle Poit is OUTSIDE the cicle

11 Cicle Dawig Algoithms Comute Decisio Paamete at Midoit Midoit, Cicle Dawig Algoithms f, < > Midoit INSIDE cicle, choose Midoit ON cicle, choose - Midoit OUTSIDE cicle,choose -

12 3 [ ] < whee, f Iteative Calculatio fo Decisio Paamete Cicle Dawig Algoithms 4 Cicle Dawig Algoithms < 3 ] [ ] [ < 5 3 < whee

13 3 5 Cicle Dawig Algoithms Iitializig the Decisio Paamete, f,, f f 4 5 4,, 6 Cicle Dawig Algoithms Siml Calculatios With Itege Aithmetic Chage of Vaiables i Iteative Equatios 4 q q 4 5 Decisio Paamete Becomes < < < q q Sice q stats as a it ad is icemeted b it s

14 Cicle Dawig Algoithms Midoit Cicle Algoithm. Ete Cete ad Radius : c, c,. Iitialize Paametes:,,, q 3. DetemieSmmet Poits,-,,, -, 4. Taslate Poits to Cicle Cete c, c ad Plot 5. While If q < q q 3 Else q q 5 DetemieSmmet Poits Taslate Poits to Cicle Cete c,c ad Plot Edwhile 7 Polgo Fillig A Fist Look At Sca Covesio Simle Oveview Fo each scalie... Fo stat to ed Colo Iteio Piels Potetial Poblem Aeas Comutig Itesectios Detemiig Iteio Secial Cases Itesectios at a Vete Hoizotal Lies 8 4

15 Polgo Fillig Comutig Itesectios,, m m 9 Polgo Fillig Soted Edge Table Sot All Edges Based o mi of each edge Liked list fo each scalie bucket Odeed b iceasig Each Et i Liked List Cotais: ma -itecet at mi vete icemet /m Pocess Scalie Liked Lists 3 5

16 Polgo Fillig Detemiig Iteio Piels Pait Rule Iitialize ait to eve Each itesectio ivets ait bit Daw iel whe ait is odd Do t daw whe ait is eve Aoachig a Itesectio If iside, oud dow If outside oud u 3 Polgo Fillig Shaed Vete Iclude i ait cout vete is a mi fo the edge Hoizotal Edges Do t iclude i ait cout C B E D A 3 6