Graphics Pipeline : Geometric Operations

Transcription

1 Graphics Pipeline : Geometric Operations Uniersit of Calgar GraphicsJungle Project CPSC page

2 Vieing transformation Tools for creating an manipulating a camera that prouces pictures of a 3D scene Vieing transformations an projections Perform culling or back-face elimination Uniersit of Calgar GraphicsJungle Project CPSC page 2

3 Local coorinate space Object efinition Worl coorinate space Moeling transformation 3D Renering Pipeline Compose scene Define ie reference Define lighting Vie space Vie transformation Projection Cull Clip to 3D ie olume 3D screen space Projection iie Hien surface remoal Rasteriation Shaing Displa space

4 Uniersit of Calgar GraphicsJungle Project CPSC page 4 Y Z X Compose scene Compose scene Define ie reference Define ie reference Worl coorinate space Vie space Moeling transformation Vie transformation ie T ( ) ( )

5 Uniersit of Calgar GraphicsJungle Project CPSC page 5 Vie plane ee V U -N RT T ie N evec V evec U evec T ( ) ( ) ee evec N N N V V V U U U R ie T Uniersit of Calgar GraphicsJungle Project CPSC page 5 Vieing transformation

6 Vieing Transforms R U V N U V N U V N Lemma: Where oes this matri come from: N e Ee Position g gae irection t ie up ector N V t g N g U t N t N V N U U e g Uniersit of Calgar GraphicsJungle Project CPSC page 6

7 Special Orthogonal Matrics See 453 slies Uniersit of Calgar GraphicsJungle Project CPSC page 7

8 Taonom of Projections Parallel Perspectie Uniersit of Calgar GraphicsJungle Project CPSC page 8

9 Uniersit of Calgar GraphicsJungle Project CPSC page 9 / T T pers proj obs: is N in the picture Perspectie Projections Perspectie Projections Z Y X

10 Uniersit of Calgar GraphicsJungle Project CPSC page T proj T ort Parallel Projections (orthographic) Parallel Projections (orthographic)

11 Perspectie Diie Y Worl coorinate space ( ) Moeling transformation Z X Vie space ( ) Compose scene Define ie reference Projection Vie transformation 3D screen space ( X Y Z W ) ( ) s s s Projection Diie Uniersit of Calgar GraphicsJungle Project CPSC page

12 Perspectie Diie Perspectie s s s X Y Z here X Y Z Parallel (orthographic) s s s Uniersit of Calgar GraphicsJungle Project CPSC page 2

13 Perspectie Diie See 453 slies for ramifications of iie b W Uniersit of Calgar GraphicsJungle Project CPSC page 3

14 Vie Volume Uniersit of Calgar GraphicsJungle Project CPSC page 4

15 We specif it! V U Vie olume ee Y -N Vie plane ino What appears on the screen: projection of part of the scene containe ithin the ie olume X Z Uniersit of Calgar GraphicsJungle Project CPSC page 5

16 ee Vie olume Uniersit of Calgar GraphicsJungle Project CPSC Vie plane ino page 6

17 ol h h h f f h h

18 Uniersit of Calgar GraphicsJungle Project CPSC page 8 ( ) ( ) f f f f h h T pers Scaling (/h in an ) Truncate prami into a Regular prami Regular prami into a bo Perspectie Matri Perspectie Matri

19 Uniersit of Calgar GraphicsJungle Project CPSC page 9 ( ) ( ) f f f f h h T pers

20 Uniersit of Calgar GraphicsJungle Project CPSC page 2 Z Y X s s s ( ) ( ) f f f f Z h Y h X here ( ) ( ) f f f f h h T pers

21 OpenGL: Vieing Process, Graphics Pipeline Scales an shifts each erte so that all of them that lie insie the ie olume ill lie insie a stanar cube Proies the CT Combines to effects: Moeling transformations applie to objects + Transformation that orients an positions the camera in space Uniersit of Calgar GraphicsJungle Project CPSC page 2

22 Uniersit of Calgar GraphicsJungle Project CPSC page 22

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24 OpenGL: Positioning an Aiming the Camera Vie plane V U ee -N glmatrimoe (GL_MODELVIEW) glloaientit(); gllookat (ee., ee., ee., look., look., look., up., up., up.);

25 OpenGL: Setting the Camera (Parallel Projection) glmatrimoe (GL_PROJECTION) glloaientit(); glortho (left, right, bottom, top, near, far); Uniersit of Calgar GraphicsJungle Project CPSC page 25

26 OpenGL: Setting the Camera (Perspectie Projection) glmatrimoe (GL_PROJECTION) glloaientit(); glfrustum (left, right, bottom, top, near, far); or more intuitie gluperspectie (ieangle,, aspect, near, far); Uniersit of Calgar GraphicsJungle Project CPSC page 26

27 Local coorinate space 3D Renering Pipeline Object efinition Worl coorinate space Moeling transformation. INTRODUCTION 2. IMAGING Compose scene Define ie reference Define lighting Vie transformation Vie space Projection Cull Clip to 3D ie olume 3D screen space Projection iie Hien surface remoal Rasteriation Shaing 3. 3D RENDERING OVERVIEW 4. MODELING () shapes an transformations 5. RENDERING (, 2, 3, 4). Graphics Pipeline : Geometric Operations 6. MODELING (2) Representation an Moeling 7. ANIMATION 8. TOPICS Displa space

28 Y Z X Compose scene Compose scene Define ie reference Define ie reference Worl coorinate space Vie space Moeling transformation Vie transformation ie T ( ) ( )

29 Vie plane V U Culling (back-face remoal) ee -N F is back face if ( P ee) ot > mf

30 n i i i Dot Prouct Angle beteen To Vectors cos ( θ ) b c Sign an Perpenicularit perpenicular orthogonal normal

31 Normal to a Plane

32 Fining the Normal Vectors V Flat Face: m V V 2 3 m ( V V ) ( V ) 2 3 V2 To Problems: V V 3 V 2 Vectors nearl parallel, the cross prouct ill be er small, Numerical inaccuracies ma result Polgon is not perfect planar

33 Fining the Normal Vectors V m V V 2 3 Robust Metho (Neell): m m m N i N i N i ( ) i net() i i + net() i ( ) ( ) i net() i i + net() i ( ) ( ) i net() i i + net() i ( )

34 Verte an Face Table Each face lists erte references Share ertices Still no topolog information (, ), (, ) 2 2, (, ) 2 3 3, F F 2 F 3 3 (, ) 5 5, (, ) 4 4, 4 5 VERTEX TABLE V V 2 V 3 V 4 V 5 (, ), ( 2, 2, 2 ) ( 3, 3, 3) (, ) 4 4, 4 (, ) 5 5, 5 FACE TABLE F F 2 F 2 V V 2 V 3 V 3 V 2 V 4 V 3 V 4 V 5

35 Mesh pt norm numverts Point3,, numnormals Vector3 face numfaces Face ert,, nverts VerteID ertine normine

36 Vie plane V U Culling (back-face remoal) ee -N F is back face if ( P ee) ot > mf

37 oi Mesh :: ra () { for (int f ; f < numfaces; f++) { glbegin (GL_POLYGON) for (int ; < face[f].nverts; ++) { int i face[f].ert[].ertine; glverte3f(pt[i]., pt[i]., pt[i].); } glen(); } }

38 oi Mesh :: ra () { for (int f ; f < numfaces; f++) { } } If ( isbackface ( f, ee ) ) continue; glbegin (GL_POLYGON) for (int ; < face[f].nverts; ++) { int i face[f].ert[].ertine; glverte3f(pt[i]., pt[i]., pt[i].); } glen();