Illumination & Reflectance

1. Illumination & Reflectance Dr. Amy Zhang

2. Outline • Illumination and Reflectance • The Phong Reflectance Model • Shading in OpenGL

3. Two Components of Illumination • Light sources with: • Emittance spectrum (color) • Geometry (position and direction) • Directional attenuation (falloff) • Surface properties with: • Reflectance spectrum (color) • Geometry (position, orientation, and micro-structure) • Absorption

4. Computer Graphics Jargon • Illumination: the transport of energy from light sources between points via direct and indirect paths • Lighting: the process of computing the light intensity reflected from a specific 3‐D point • Shading: the process of assigning a color to a pixel based on the illumination in the scene

5. Direct and Global Illumination • Direct illumination: A surface point receives light directly from all light sources in the scene • Computed by the local illumination model • Determine which light sources are visible • Global illumination: A surface point receives light after the light rays interact with other objects in the scene I = Idirect + Ireflected + Itransmitted

6. Directional Light Sources • All of the rays from a directional light source have a common direction (parallel) • The direction is a constant at every point in the scene • It is as if the light source was infinitely far away from the surface that it is illuminating

7. Point Light Sources • The rays emitted from a point light radially diverge from the source • Direction to the light changes at each point

8. Other Light Sources • Spotlights • Area light sources • Light source occupies a 2D area (polygon) • Generates soft shadows.

9. Linearity of Light = + + Paul Haeberli, Grafica Obscura

11. Outline • Illumination and Reflectance • The Phong Reflectance Model • Shading in OpenGL

12. OpenGL Reflectance Model • A simple model that can be computed rapidly • Has three components • Diffuse • Specular • Ambient • Uses four vectors • To source • To viewer • Normal • Perfect reflector

13. Ideal Diffuse Reflectance • Surface reflects light equally in all directions • • Why? Examples?

14. Lambert’s Cosine Law • Diffuse reflectance scales with cosine of angle

15. Ideal Diffuse Reflectance • Lambertian reflection model • IL: The incoming light intensity • kd: The diffuse reflection coefficient • N: Surface normal • cosqi = N· L if vectors normalized • There are also three coefficients, kdr, kdg, kdb that show how much of each color component is reflected

16. Ideal Specular Reflectance • Normal is determined by local orientation • Angle of incidence = angle of reflection • The three vectors must be coplanar • Ideal Specular Reflectance • Surface reflects light only at mirror angle

17. Reflection Vector R • The vector R can be computed from the incident ray direction L and the surface normal N • Note that all vectors have unit length

18. How much light is seen? Depends on: • Angle of incident light • Angle to the viewer • ks is the absorption coef

19. Non-ideal Reflectors • Real materials tend to deviate significantly from ideal mirror reflectors • Introduce an empirical model that is consistent with our experience • The amount of reflected light is greatest in the direction of the perfect mirror reflection • The reflected light forms a “beam” pattern around this mirror direction

20. Phong Specular Reflection • Phong proposed using a term that dropped off as the angle between the viewer and the ideal reflection increased. n is the shininess coefficient • The cosine lobe gets more narrow with increasing n. • Values of a between 100 and 200 correspond to metals • Values between 5 and 10 give surface that look like plastic

21. Blinn & Torrance Variation • The specular term in the Phong model is problematic because it requires the calculation of R and V for each vertex • Blinn suggested an more efficient approximation using the halfway vector halfway vector H between L and V • H is the normal to the (imaginary) surface that maximally reflects light in the V direction

22. No need to compute reflection vector R at every point • Is is a function only of N, if: • the viewer is very far away and V does not change for all points on the object (e.g., orthographic projection) • L does not change for all points on the object (e.g., directional lights) • Resulting model is known as the modified Phong or Blinn lighting model • Specified in OpenGL standard

23. Ambient Light • Ambient light is the result of multiple interactions between (large) light sources and the objects in the environment • It represents the reflection of all indirect illumination • Amount and color depend on both the color of the light(s) and the material properties of the object • Add ka Ia to diffuse and specular terms reflection coef intensity of ambient light

24. 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/(a + bd +cd2) to the diffuse and specular terms • The constant and linear terms soften the effect of the point source

25. The Phong Illumination Model • Sum of three components: diffuse reflection + specular reflection + ambient • Ambient represents the reflection of all indirect illumination

27. 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 • Idr, Idg, Idb, Isr, Isg, Isb, Iar, Iag, Iab • Material properties match light source properties • Nine absorption coefficients • kdr, kdg, kdb, ksr, ksg, ksb, kar, kag, kab • Shininess coefficient a

28. Phong Reflectance Model

29. Phong Examples • The direction of the light source and the n are varied

30. The Plastic Look • The Phong illumination model is an approximation of a surface with a specular and a diffuse layer • E.g., shiny plastic, varnished wood, gloss paint

31. Phong Reflectance Model • Single light source:

32. Phong Reflectance Model • Multiple light sources:

33. Computation of Vectors • L and V are specified by the application • Can compute R from L and N • Problem is determining N • OpenGL leaves determination of normal to application • Exception for GLU quadrics and Bezier surfaces

34. Plane Normals • Equation of plane: ax+by+cz+d = 0 • we know that plane is determined by three points p0, p1, p2 or normal n and p0 • Normal can be obtained by p2 n = (p1-p0) × (p2-p0) p0 p1

35. Normal to Sphere • Surface implicit function f(x, y, z) = 0 • Normal given by gradient vector • Unit sphere f(p)=p·p-1 • n = [∂f/∂x, ∂f/∂y, ∂f/∂z]T=p

36. Parametric Form • For unit sphere • Tangent plane determined by vectors • Normal given by cross product x=x(u,v)=cos u cos v y=y(u,v)=cos u sin 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

37. General Case • We can compute parametric normals for other simple cases • Quadrics • Parametric polynomial surfaces • Bezier surface patches

38. Outline • Illumination and Reflectance • The Phong Reflectance Model • Shading in OpenGL

39. Objectives • Introduce the OpenGL shading functions • Discuss polygonal shading • Flat • Smooth • Gouraud

40. Steps in OpenGL shading • Specify normals • Enable shading and select model • Specify lights • Specify material properties

41. Normals • In OpenGL the normal vector is part of the state • Set byglNormal*() • glNormal3f(x, y, z); • glNormal3fv(p); • Usually we want to set the normal to have unit length so cosine calculations are correct • Length can be affected by transformations • Note that scaling does not preserved length • glEnable(GL_NORMALIZE) allows for autonormalization at a performance penalty

42. Normal for Triangle p1 n p2 planen·(p - p0 ) = 0 n = (p2 - p0 ) ×(p1 - p0 ) p p0 normalizen  n/ |n| Note that right-hand rule determines outward face

43. Enabling Shading • Shading calculations are enabled by • glEnable(GL_LIGHTING) • Once lighting is enabled, glColor() ignored • Must enable each light source individually • glEnable(GL_LIGHTi) i=0,1….. At least 8 light sources • Can choose light model parameters • glLightModeli(parameter, GL_TRUE) • GL_LIGHT_MODEL_LOCAL_VIEWER do not use simplifying distant viewer assumption in calculation • GL_LIGHT_MODEL_TWO_SIDED shades both sides of polygons independently • Time consuming

44. Defining a Point Light Source • For each light source, we can set an RGBA for the diffuse, specular, and ambient components, and for the position GL float diffuse0[]={1.0, 0.0, 0.0, 1.0}; GL float ambient0[]={1.0, 0.0, 0.0, 1.0}; GL float specular0[]={1.0, 0.0, 0.0, 1.0}; Glfloat light0_pos[]={1.0, 2.0, 3,0, 1.0}; glEnable(GL_LIGHTING); glEnable(GL_LIGHT0); glLightv(GL_LIGHT0, GL_POSITION, light0_pos); glLightv(GL_LIGHT0, GL_AMBIENT, ambient0); glLightv(GL_LIGHT0, GL_DIFFUSE, diffuse0); glLightv(GL_LIGHT0, GL_SPECULAR, specular0);

45. Distance and Direction • The source colors are specified in RGBA • The position is given in homogeneous coordinates • If w =1.0, a finite location • If w =0.0, a parallel source with the given direction vector • The coefficients in the distance terms (1/(a+bd+cd2)) • by default a=1.0 (GL_CONSTANT_ATTENUATION), • b=c=0.0 (GL_LINEAR_ATTENUATION, GL_QUADRATIC_ATTENUATION ). Change by a= 0.80; glLightf(GL_LIGHT0, GL_CONSTANT_ATTENUATION, a);

46. Spotlights • Use glLightv to set • Direction GL_SPOT_DIRECTION • Cutoff GL_SPOT_CUTOFF • Attenuation GL_SPOT_EXPONENT • Proportional to cosaf f q -q

47. Global Ambient Light • Ambient light depends on color of light sources • A red light in a white room will cause a red ambient term that disappears when the light is turned off • OpenGL also allows a global ambient term that is often helpful for testing • glLightModelfv(GL_LIGHT_MODEL_AMBIENT, global_ambient)

48. Moving Light Sources • Light sources are geometric objects whose positions or directions are affected by the model-view matrix • Depending on where we place the position (direction) setting function, we can • Move the light source(s) with the object(s) • Fix the object(s) and move the light source(s) • Fix the light source(s) and move the object(s) • Move the light source(s) and object(s) independently

49. Material Properties • Material properties are also part of the OpenGL state and match the terms in the modified Phong model • Set by glMaterialv() GLfloat ambient[] = {0.2, 0.2, 0.2, 1.0}; GLfloat diffuse[] = {1.0, 0.8, 0.0, 1.0}; GLfloat specular[] = {1.0, 1.0, 1.0, 1.0}; GLfloat shine = 100.0 glMaterialf(GL_FRONT, GL_AMBIENT, ambient); glMaterialf(GL_FRONT, GL_DIFFUSE, diffuse); glMaterialf(GL_FRONT, GL_SPECULAR, specular); glMaterialf(GL_FRONT, GL_SHININESS, shine);

50. Front and Back Faces • The default is shade only front faces which works correctly for convex objects • If we set two sided lighting, OpenGL will shade both sides of a surface • Each side can have its own properties which are set by using GL_FRONT, GL_BACK, or GL_FRONT_AND_BACK in glMaterialf back faces not visible back faces visible