Graphics Pipeline: Transformation, Shading/Lighting, Projection, Texturing, and more!

Transcription

1 Graphics Pipeline: Transformation, Shading/Lighting, Projection, Texturing, and more! Fall 2015 Daniel G. Aliaga Department of Computer Science Purdue University

2 Computer Graphics Pipeline Geometry Modeling Transformation Lighting Viewing Transformation Clipping Projection Scan Conversion Transform into 3D world coordinate system Simulate illumination and reflectance Transform into 3D camera coordinate system Clip primitives outside camera s view Transform into 2D camera coordinate system Draw pixels (incl. texturing, hidden surface ) Image

3 Computer Graphics Pipeline Geometry Modeling Transformation Lighting Viewing Transformation Clipping Projection Scan Conversion Transform into 3D world coordinate system Simulate illumination and reflectance Transform into 3D camera coordinate system Clip primitives outside camera s view Transform into 2D camera coordinate system Draw pixels (incl. texturing, hidden surface ) Image

4 Modeling Transformations Most popular transformations in graphics Translation Rotation Scale Projection In order to use a single matrix for all, we use homogeneous coordinates

5 Modeling Transformations

6 Modeling Transformations And many more

7 Computer Graphics Pipeline Geometry Modeling Transformation Lighting Viewing Transformation Clipping Projection Scan Conversion Transform into 3D world coordinate system Simulate illumination and reflectance Transform into 3D camera coordinate system Clip primitives outside camera s view Transform into 2D camera coordinate system Draw pixels (incl. texturing, hidden surface ) Image

8 Diffuse (mostly)

9 Specular++

10 Environment Mapping

11 Subsurface Scatterring

12 Others Transparency Radiosity Ambient occlusion

13 Others

14 Lighting and Shading Light sources Point light Models an omnidirectional light source (e.g., a bulb) Directional light Models an omnidirectional light source at infinity Spot light Models a point light with direction Light model Ambient light Diffuse reflection Specular reflection

15 Lighting and Shading Diffuse reflection Lambertian model

16 Lighting and Shading Diffuse reflection Lambertian model

17 Lighting and Shading Diffuse reflection Lambertian model

18 Lighting and Shading Specular reflection Phong model

19 Lighting and Shading Specular reflection Phong model

20 Lighting and Shading Specular reflection Phong model

21 Computer Graphics Pipeline Geometry Modeling Transformation Lighting Viewing Transformation Clipping Projection Scan Conversion Transform into 3D world coordinate system Simulate illumination and reflectance Transform into 3D camera coordinate system Clip primitives outside camera s view Transform into 2D camera coordinate system Draw pixels (incl. texturing, hidden surface ) Image

22 Viewing Transformation ~ x c ~ x c ~ R( X C) RX ~ RC t ~ x c World-to-camera matrix M R 0 X t Y 1 Z 1 R R t x R y R z 3x3 rotation matrices t x t y t T z translation vector

23 Computer Graphics Pipeline Geometry Modeling Transformation Lighting Viewing Transformation Clipping Projection Scan Conversion Transform into 3D world coordinate system Simulate illumination and reflectance Transform into 3D camera coordinate system Clip primitives outside camera s view Transform into 2D camera coordinate system Draw pixels (incl. texturing, hidden surface ) Image

24 Computer Graphics Pipeline Geometry Modeling Transformation Lighting Viewing Transformation Clipping Projection Scan Conversion Transform into 3D world coordinate system Simulate illumination and reflectance Transform into 3D camera coordinate system Clip primitives outside camera s view Transform into 2D camera coordinate system Draw pixels (incl. texturing, hidden surface ) Image

25 Perspective projection eye/viewpoint f Z z (x, y) y? image plane (X, Y, Z) Y optical axis y = Y f Z y = f Y Z & x = f X Z

26 Perspective Projection Z Y X f f Z fy fx Z fy Z fx / / y x

27 Projection Transformations void glfrustum(gldouble left, GLdouble right, GLdouble bottom, GLdouble top, GLdouble near, GLdouble far);

28 Projection Transformations void gluperspective(gldouble fovy, GLdouble aspect, GLdouble near, GLdouble far);

29 Projection Transformations void glortho(gldouble left, GLdouble right, GLdouble bottom, GLdouble top, GLdouble near, GLdouble far); void gluortho2d(gldouble left, GLdouble right, GLdouble bottom, GLdouble top);

30 Computer Graphics Pipeline Geometry Modeling Transformation Lighting Viewing Transformation Clipping Projection Scan Conversion Transform into 3D world coordinate system Simulate illumination and reflectance Transform into 3D camera coordinate system Clip primitives outside camera s view Transform into 2D camera coordinate system Draw pixels (incl. texturing, hidden surface ) Image

31 Scan Conversion/Rasterization Determine which fragments get generated Interpolate parameters (colors, textures, normals, etc.)

32 Scan Conversion/Rasterization Determine which fragments get generated Interpolate parameters (colors, textures, normals, etc.)

33 Scan Conversion/Rasterization Determine which fragments get generated Interpolate parameters (colors, textures, normals, etc.) How?

34 Scan Conversion/Rasterization Determine which fragments get generated Interpolate parameters (colors, textures, normals, etc.) Barycentric coords amongst many other ways

35 Barycentric coordinates p 1 q p 3 p 2 q = αp 1 + βp 2 + γp 3 If [α + β + γ = 1 and α, β, γ 0], then q inside triangle (p 1, p 2, p 3 ) Can also write: q = αp 1 + βp 2 + (1 α β)p 3

36 Barycentric coordinates p 1 q p 3 p 2 How to solve for α and β in q = αp 1 + βp α β p 3? Two equations, two unknowns: use 2x2 matrix inversion

37 Additional concept: Texture mapping Model surface-detail with images wrap object with photograph(s) graphics object itself is a simpler model but looks more complex 37

38 Texture mapping Model surface-detail with images wrap object with photograph(s) graphics object itself is a simpler model but looks more complex 38

39 Texture mapping bark Generic image to represent material e.g., tile pattern veneer bricks 39

40 Tiling Repeat pattern 40

41 Tiling Repeat pattern 41

42 Tiling Repeat pattern How can we improve? 42

43 Tiling Repeat pattern reduce seems by mirroring 43

44 Tiling Repeat pattern reduce seems by mirroring 44

45 Tiling Repeat pattern reduce seems by mirroring 45

46 Tiling Repeat pattern reduce seems by mirroring How we can further improve? 46

47 Tiling Repeat pattern reduce seems by mirroring reduce seems by choosing tile that covers one period of repeated texture 47

48 Tiling 48

49 Texture mapping limitations do exist 49

50 Bricks are similar not identical 50

51 Solution? 51

52 Solution: Texture synthesis 52

53 Texture coordinates Mechanism for attaching the texture map to the surface modeled a pair of floats (s, t) for each triangle vertex corners of the image are (0, 0), (0, 1), (1, 1), and (1, 0) tiling indicated with tex. coords. > 1 texels color samples in texture maps 53

54 Texture coordinates P 2 (0, 0) P 1 (1, 0) P 3 (0, 1) P 4 (1, 1) y O x z 54

55 Texture mapping P 2 (0, 0) P 1 (1, 0) a P 3 (0, 1) y c P 2 P 1 P 4 (1, 1) z O x C P 3 b 55

56 Texels: texture elements P 1 (u 1, v 1, s 1, t 1 ) P (u, v, s, t) P 3 (u 3, v 3, s 3, t 3 ) P 2 (u 2, v 2, s 2, t 2 ) 56

57 Texture mapping Problem: how to compute the texture coordinates for an interior pixel? a P 2 (s 2, t 2 ) P (s, t) P 1 (s 1, t 1 ) y c P 2 P P 1 P 3 (s 3, t 3 ) z O x C P 3 b 57

58 Texture mapping Solution: interpolate vertex texture coordinates P 2 (s 2, t 2 ) P (s, t) P 1 (s 1, t 1 ) a y c P 2 P P 1 P 3 (s 3, t 3 ) z O x C P 3 b 58

59 Parameter Interpolation Texture coordinates, colors, normals, etc. How? Again, use barycentric coordinates

60 Level of detail problem aliasing anti-aliased If curious, you can read more on this subject! 60