3D Viewing Pipeline. Instructor Stephen J. Guy

Transcription

1 3D Viewing Pipeline Instructor Stephen J. Guy 1

2 Overview Review Linear s & Homogeneous coordinates Scene Graph 3D Polygon rendering Graphics Pipeline Viewing 2

3 Overview Review Linear s & Homogeneous coordinates Scene Graph 3D Polygon rendering Graphics Pipeline Viewing 3

4 Reviewing Transforms Linear s Scale Rotate Shear Mirror 4

5 Review Homogeneous Coordinates Use 3 coordinates for a 2D point (4 coord. for 3D point) (x,y,w) represents (x,y,0) represents (0,0,0) a point at (x/w, y/w) a point at infinity not allowed! (2,1,1) or (4,2,2,) or (6,3,3) 5

6 Review Translating and More Basic 2D s as 3x3 6

7 Review 3D Transforms Homogenous coordinates (x,y,z,w) 4x4 transformation matrix 7

8 Review Basic 3D Transforms 8

9 Review 3D Rotations 9

10 Review Hierarchies Successively applied matrixes Stored in a DAG == Scene Graph Examples Robot Arm Articulated Characters Complex Scenes 10

11 Transform Example - Robot Arms 11

12 Example Humanoid Character 12

13 Example Complex Scenes 13

14 Example Complex Scene Graph 14

15 Ray Casting with Hierarchies 15

16 Overview Review Linear s & Homogeneous coordinates Scene Graph 3D Polygon rendering Graphics Pipeline Viewing 16

17 3D Polygon Rendering Many applications make use if 3D polygons with direct illumination 17

18 3D Polygon Rendering - Examples 18 Quake II (Id Software)

19 3D Polygon Rendering - Examples Architectural Walkthrough 19

20 Ray Casting Revisiting For each sample Construct ray though pixel Find first surface intersected by ray through pixel Compute color of sample based on surface radiance More Efficient Algorithms Utilize Spatial Coherence! 20

21 3D Polygon Rendering What steps are necessary to utilize spatial coherence while drawing polygons on a 2D image? 21

22 3D Rendering Pipeline (direct illumination only) 3D Geometric Primitives Modeling Lighting Viewing A pipelined sequence of operations to draw a 3D primitive onto a 2D image Projection Clipping Scan Conversion 22 Image

23 OpenGL Example Modeling Lighting Viewing Projection Clipping Scan Conversion glbegin(gl_polygon); glvertex3f(0.0, 0.0, 0.0); glvertex3f(1.0, 0.0, 0.0); glvertex3f(1.0, 1.0, 1.0); glvertex3f(0.0, 1.0, 1.0); glend(); OpenGL runs the 3D rendering pipeline for each polygon 23 Image

24 3D Rendering Pipeline (direct illumination only) 3D Geometric Primitives Modeling Transform in 3D word coordinate system Lighting Viewing Projection Clipping Scan Conversion 24 Image

25 3D Rendering Pipeline (direct illumination only) 3D Geometric Primitives Modeling Lighting Transform in 3D word coordinate system Illuminate according to lighting and reflectance Viewing Projection Clipping Scan Conversion 25 Image

26 3D Rendering Pipeline (direct illumination only) 3D Geometric Primitives Modeling Lighting Viewing Transform in 3D word coordinate system Illuminate according to lighting and reflectance Transform into 3D camera coordinate system Projection Clipping Scan Conversion 26 Image

27 3D Rendering Pipeline (direct illumination only) 3D Geometric Primitives Modeling Lighting Viewing Projection Transform in 3D word coordinate system Illuminate according to lighting and reflectance Transform into 3D camera coordinate system Transform into 2D screen coordinate system Clipping Scan Conversion 27 Image

28 3D Rendering Pipeline (direct illumination only) 3D Geometric Primitives Modeling Lighting Viewing Projection Transform in 3D word coordinate system Illuminate according to lighting and reflectance Transform into 3D camera coordinate system Transform into 2D screen coordinate system Clipping Clip primitives outside camera s view Scan Conversion 28 Image

29 3D Rendering Pipeline (direct illumination only) 3D Geometric Primitives Modeling Lighting Viewing Projection Transform in 3D word coordinate system Illuminate according to lighting and reflectance Transform into 3D camera coordinate system Transform into 2D screen coordinate system Clipping Scan Conversion Clip primitives outside camera s view Draw Pixels (also texturing, hidden surface, ) 29 Image

30 3D Rendering Pipeline (direct illumination only) 3D Geometric Primitives Modeling Lighting Viewing Projection Transform in 3D word coordinate system Illuminate according to lighting and reflectance Transform into 3D camera coordinate system Transform into 2D screen coordinate system Clipping Scan Conversion Clip primitives outside camera s view Draw Pixels (also texturing, hidden surface, ) 30 Image

31 3D Rendering Pipeline (direct illumination only) 3D Geometric Primitives Modeling Lighting Viewing Projection Transform in 3D word coordinate system Illuminate according to lighting and reflectance Transform into 3D camera coordinate system Transform into 2D screen coordinate system Clipping Scan Conversion Clip primitives outside camera s view Draw Pixels (also texturing, hidden surface, ) 31 Image

32 s p(x,y,z) Modeling 3D World Coordinates Viewing Projection Window-to-Viewport 32 p'(x,y ) 3D Object Coordinates 3D Camera Coordinates 2D Screen Coordinates 2D Image Coordinates s map points from one coordinate system to another 3D World Coordinates 3D Camera Coordinates 3D Object Coordinates

33 Viewing s p(x,y,z) 3D Object Coordinates Modeling 3D World Coordinates Viewing Projection Window-to-Viewport 33 p'(x,y ) 3D Camera Coordinates 2D Screen Coordinates 2D Image Coordinates Viewing s

34 Camera Coordinates Canonical coordinate system Convention is right-handed (looking down z-axis) Convenient for projection, clipping, etc 34

35 Viewing Mapping from world to camera coordinates Eye position maps to origin Right vector maps to X-axis Up vector maps to Y-axis Back vector maps to Z-axis 35

36 Finding the Viewing We have the camera (in world coordinates) We want T taking objects from world to camera P c = T * P W Trick: Find T-1 taking objects from camera to world P W = T * P c 36

37 Finding the Viewing 37

38 Viewing s p(x,y,z) 3D Object Coordinates Modeling 3D World Coordinates Viewing Projection Window-to-Viewport 38 p'(x,y ) 3D Camera Coordinates 2D Screen Coordinates 2D Image Coordinates Viewing s

39 Projection General definition: Transform points in n-space to m-space (m<n) In computer graphics Map 3D camera coordinates to 2D screen coordinates 39

40 Taxonomy of Projections 40

41 Taxonomy of Projections 41

42 Parallel Projection Center of projection is at infinity Direction of Projection (DOP) is same for all points 42

43 Orthographic Projection DOP Parallel to View Plane 43

44 Oblique Projection DOP not perpendicular to view plane 44

45 Oblique Projection Examples Oblique Cabinet Cavalier Fortification Diagrams 45

46 Orthographic Perspective in Games Common in pre-hardware card Graphics 46

47 Parallel Projection View Volume 47

48 Orthographic Project Matrix Straight on projection throw away Z What does the matrix look like? 48

49 Parallel Projection Matrix 49

50 Taxonomy of Projections 50

51 Perspective Projection 51

52 Perspective View Volume 52

53 Camera to Screen Remember: Object -> Camera -> Screen Just like raytracer screen is the z=d plane for some constant d Origin of screen coordinate is (0,0,d) Its x and y axes are parallel to the x and y axes of the eye coordinate system All these coordinates are in camera space 53

54 Overhead view of our screen 54

55 The Perspective Matrix This division by z can be accomplished by a 4x4 matrix too! What happens to the point (x,y,z,1) What s this in non-homogenous coordinates? 55

56 What s Next? 3D Geometric Primitives Modeling Lighting Viewing Projection Transform in 3D word coordinate system Illuminate according to lighting and reflectance Transform into 3D camera coordinate system Transform into 2D screen coordinate system Clipping Scan Conversion Clip primitives outside camera s view Draw Pixels (also texturing, hidden surface, ) 56 Image

57 What s Next? 3D Geometric Primitives Modeling Lighting Viewing Projection Transform in 3D word coordinate system Illuminate according to lighting and reflectance Transform into 3D camera coordinate system Transform into 2D screen coordinate system Clipping Scan Conversion Clip primitives outside camera s view Draw Pixels (also texturing, hidden surface, ) 57 Image