1. 1 Shading I Shandong University Software College Instructor: Zhou Yuanfeng E-mail: yuanfeng.zhou@gmail.com

2. 2 Objectives Learn to shade objects so their images appear three-dimensional Introduce the types of light-material interactions Build a simple reflection model---the Phong model--- that can be used with real time graphics hardware

3. Simple Lighting model With Specular lighting Gouraud shading Wireframe Polygon Why we need shading 3 With shadow With Texture

4. 4 Why we need shading Suppose we build a scene using many polygons and color it with glColor. We get something like Which is the best?

5. 5 Shading Why does the image of a real sphere look like Light-material interactions cause each point to have a different color or shade Need to consider ­Light sources ­Material properties ­Location of viewer ­Surface orientation Why?

6. 6 Scattering Light strikes A ­Some scattered ­Some absorbed Some of scattered light strikes B ­Some scattered ­Some absorbed Some of this scattered light strikes A and so on

7. 7 Rendering Equation The infinite scattering and absorption of light can be described by the rendering equation ­Cannot be solved in general ways ­Ray tracing is a special case for perfectly reflecting surfaces Rendering equation is global and includes ­Shadows ­Multiple scattering from object to object

8. 8 Global Effects translucent surface shadow multiple reflection

9. 9 Local vs Global Rendering Correct shading requires a global calculation involving all objects and light sources ­Incompatible with pipeline model which shades each polygon independently (local rendering) However, in computer graphics, especially real time graphics, we are happy if things “look right” ­Exist many techniques for approximating global effects

10. 10 Light-Material Interaction Light that strikes an object is partially absorbed and partially scattered (reflected) The amount reflected determines the color and brightness of the object ­A surface appears red under white light because the red component of the light is reflected and the rest is absorbed The reflected light is scattered in a manner that depends on the smoothness and orientation of the surface

11. 11 Light Sources General light sources are difficult to work with because we must integrate light coming from all points on the source Light color : I = [Ir, Ig, Ib], RGB mode, CMY mode

12. 12 Simple Light Sources Point source ­Model with position and color ­Distant source = infinite distance away (parallel) ­I(p0) = [Ir(p0), Ig(p0), Ib(p0)]

13. Simple Light Sources Easy to use (in computer) Realistic is poor: Image contrast is high, some parts are bright and others are dark; In real world, the lights will be large. We can add ambient light to solve this problem. 13 umbra penumbra

14. Simple Light Sources Spotlight ­Restrict light from ideal point source 14 Why use cos function?

15. Simple Light Sources Infinite light: Sun light - Just know the light direction; - The intensity is constant. Ambient light ­Same amount of light everywhere in scene ­Can model contribution of many sources and reflecting surfaces 15 I a = [I ar, I ag, I ab ] the same value at each point on surfaces

16. 16 Surface Types The smoother a surface, the more reflected light is concentrated in the direction a perfect mirror would reflected the light A very rough surface scatters light in all directions smooth surfacerough surface Such as mirrors Such as a wall translucent surface Such as water

17. 17 Phong Model A simple model that can be computed rapidly Has three components ­Diffuse ­Specular ­Ambient Uses four vectors ­To light source ­To viewer ­Normal ­Perfect reflector

18. 18 Ambient Light Ambient light is the result of multiple interactions between (large) light sources and the objects in the environment Amount and color depend on both the color of the light(s) and the material properties of the object Add k a I a to diffuse and specular terms reflection coef intensity of ambient light =

19. 19 Diffuse Reflection An ideal diffuse surface is, at the microscopic level, a very rough surface. Chalk is a good approximation to an ideal diffuse surface. Because of the microscopic variations in the surface, an incoming ray of light is equally likely to be reflected in any direction over the hemisphere.

20. 20 Lambertian Surface( 朗伯面 ) Perfectly diffuse reflector Light scattered equally in all directions Amount of light reflected is proportional to the vertical component of incoming light ­reflected light ~ cos  i ­cos  i = l · n if vectors normalized ­There are also three coefficients, k r, k b, k g that show how much of each color component is reflected, related with the materials

21. 21 Lambert's Cosine Law Lambert's law determines how much of the incident light energy is reflected. Remember that the amount of energy that is reflected in any one direction is constant in this model. In other words, the reflected intensity is independent of the viewing direction. I pd I pd cos   C A B =

22. 22 Illumination effects Shaded using a diffuse-reflection model ， from left to right k d =0.4, 0.55, 0.77, 0.85, 1.0. Shaded using a ambient and diffuse-reflection model ， I a =I light = 1.0, k d = 0.4. From left to right k a =0.0, 0.15, 0.30, 0.45, 0.60

23. 23 Specular Surfaces Most surfaces are neither ideal diffusers nor perfectly specular (ideal reflectors) Smooth surfaces show specular highlights due to incoming light being reflected in directions concentrated close to the direction of a perfect reflection specular highlight

24. 24 Ideal Reflector Normal is determined by local orientation Angle of incidence = angle of relection The three vectors must be coplanar r = 2 (l · n ) n - l r l How to compute r n l i v

25. 25 Modeling Specular Relections Phong proposed using a term that dropped off as the angle between the viewer and the ideal reflection increased  I r ~ k s I cos   shininess coef absorption coef incoming intensity reflected intensity

26. 26 The Shininess Coefficient Values of  between 100 and 200 correspond to metals Values between 5 and 10 give surface that look like plastic cos    90 -90

27. 27 Spheres shaded using phong illumination model

28. Refract light Snell law ηt, ηi are the refract factors 28

29. Refract factor 29

30. 30 Distance Terms The light from a point source that reaches a surface is inversely proportional to the square of the distance between them We can add a factor of the form 1/(c 1 +c 2 d L +c 3 d L 2 ) to the diffuse and specular terms The constant and linear terms soften the effect of the point source

31. 31 Light source attenuation( 衰减 ) I = I a k a +f att I light k d (N. L) ­f att =1/d L 2 ­f att = (1/min((c 1 +c 2 d L +c 3 d L 2 ), 1)); Distance 1 1.375 1.75 2.125 2.5 C 0 0 1.25.25.5 010

32. 32 Light Sources In the Phong Model, we add the results from each light source Each light source has separate diffuse, specular, and ambient terms to allow for maximum flexibility even though this form does not have a physical justification Separate red, green and blue components Hence, 9 coefficients for each point source ­I dr, I dg, I db, I sr, I sg, I sb, I ar, I ag, I ab

33. 33 Material Properties Material properties match light source properties ­Nine absorbtion coefficients k dr, k dg, k db, k sr, k sg, k sb, k ar, k ag, k ab ­Shininess coefficient 

34. 34 Adding up the Components For each light source and each color component, the Phong model can be written (without the distance terms) as I = k d I d l · n + k s I s ( v · r )  + k a I a For each color component we add contributions from all sources

35. Phong light model 35

36. 36 Modified Phong Model The specular term in the Phong model is problematic because it requires the calculation of a new reflection vector and view vector for each vertex Blinn suggested an approximation using the halfway vector( 分向量 ) that is more efficient

37. 37 Calculating the reflection vector R =Ncosq + S =Ncosq + Ncosq - L =2N (N.L) - L Calculating N. H instead of R. V, in which H = (L+V)/|L+V| 2*b=a

38. 38 Using the halfway angle Replace ( v · r )  by ( n · h )   is chosen to match shineness Note that halfway angle is half of angle between r and v if vectors are coplanar Resulting model is known as the modified Phong or Blinn lighting model ­Specified in OpenGL standard

39. 39 Example Only differences in these teapots are the parameters in the modified Phong model

40. 40 Computation of Vectors l and v are specified by the application Can computer r from l and n Problem is determining n For simple surfaces, it can be determined but how we determine n differs depending on underlying representation of surface OpenGL leaves determination of normal to application ­Exception for GLU quadrics and Bezier surfaces (Chapter 11)

41. 41 Plane Normals Equation of plane: ax+by+cz+d = 0 From Chapter 4 we know that plane is determined by three points p 0, p 2, p 3 or normal n and p 0 Normal can be obtained by n = (p 2 -p 0 ) × (p 1 -p 0 ) p1p1 p0p0 p2p2

42. 42 Normal to Sphere Implicit function f(x,y.z)=0 Normal given by gradient Sphere f(p)=x 2 + y 2 + z 2 -1=0 n = [ ∂ f/ ∂ x, ∂ f /∂ y, ∂ f/ ∂ z] T = p

43. 43 Parametric Form For sphere Tangent plane determined by vectors Normal given by cross product x=x(u,v)=cos u sin v y=y(u,v)=cos u cos v z= z(u,v)=sin u ∂p/∂u = [∂x/∂u, ∂y/∂u, ∂z/∂u] T ∂p/∂v = [∂x/∂v, ∂y/∂v, ∂z/∂v] T n = ∂p/∂u × ∂p/∂v

44. 44 General Case We can compute parametric normals for other simple cases ­Quadrics ­Parameteric polynomial surfaces Bezier surface patches (Chapter 11)

45. 45 Polygonal Shading Shading calculations are done for each vertex ­Vertex colors become vertex shades By default, vertex shades are interpolated across the polygon: ­glShadeModel(GL_SMOOTH); If we use glShadeModel(GL_FLAT); the color at the first vertex will determine the shade of the whole polygon

46. Flat shading Normal is same in each polygon; Infinite viewer; Infinite light; For flat shading, we only need compute the color of one point in this polygon. 46

47. 47 Polygon Normals Polygons have a single normal ­Shades at the vertices as computed by the Phong model can be almost same ­Identical for a distant viewer (default) or if there is no specular component ­Infinite viewer and light Consider model of sphere Want different normal at each vertex even though this concept is not quite correct mathematically

48. Characteristic It’s bad for polygon approximate smooth surface. The color in polygons is different. 48

49. View of human Mach band How to avoid this band? We should use smooth shading. 49

50. 50 Smooth Shading We can set a new normal at each vertex Easy for sphere model ­If centered at origin n = p Now smooth shading works Note silhouette edge

51. 51 Mesh Shading The previous example is not general because we knew the normal at each vertex analytically For polygonal models, Gouraud proposed we use the average of the normals around a mesh vertex n = (n 1 +n 2 +n 3 +n 4 )/ |n 1 +n 2 +n 3 +n 4 |

52. Data structure for polygon Search adjacent polygons for each vertex. 52

53. 53 Shading models for Polygons

54. 54 Two interpolated shading Gouraud shading ­Cheap but gives poor highlights Phong shading ­Slightly more expensive, but gives high quality highlights Flat GouraudPhone

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58. 58 Gouraud V.S. Phong

59. 59

60. 60 Gouraud and Phong Shading Gouraud Shading ­Find average normal at each vertex (vertex normals) ­Apply modified Phong model at each vertex ­Interpolate vertex shades across each polygon Phong shading ­Find vertex normals ­Interpolate vertex normals across edges ­Interpolate edge normals across polygon ­Apply modified Phong model at each fragment

61. 61 Unrepresentative vertex normals

62. Sphere subdivision 62

63. 63 Comparison If the polygon mesh approximates surfaces with a high curvatures, Phong shading may look smooth while Gouraud shading may show edges Phong shading requires much more work than Gouraud shading ­Until recently not available in real time systems ­Now can be done using fragment shaders (see Chapter 9) Both need data structures to represent meshes so we can obtain vertex normals