Illumination Models and Surface-Rendering Methods. Chapter 10

Transcription

1 Illumination Models and Surface-Rendering Methods Chapter 10

2 Illumination and Surface- Rendering Given scene specifications object positions, optical properties of the surface, viewer position, viewing direction, etc. Calculate the light intensity for each pixel viewer image plane light

3 Illumination and Surface- Rendering Illumination Model Calculate the color of an illuminated position on the surface of an object Surface-Rendering Method Use the color calculations from an illumination model to determine the pixel colors for all projected positions in a scene viewer image plane

4 Illumination Models (Lighting model, Shading model) Photorealism in computer graphics depends on Accurate representations of surface properties Good physical descriptions of the lighting effects Rendering needs a model of lighting Physically more correct model: the intensity reflected from every point depends on the intensity from every other points Global illumination Simplistic model: the intensity depends only on the direct illumination due to light sources Local illumination

5 Light Sources Point light sources Emitting radiant energy at a single point Specified with its position and the color of the emitted light Infinitely distant light sources A large light source, such as sun, that is very far from a scene Approximated as a point emitter, but little variation in its directional effects Specified with its color value and a fixed direction for the light rays Arjan Kok

6 Light Sources Radial intensity attenuation As radiant energy travels, its amplitude is attenuated by the 2 factor 1/ dl Sometimes, more realistic attenuation effects can be obtained with an inverse quadratic function of distance Point source at infinity all points in the scene are at a nearly equal distance from a faroff source f l,radatten = a a d 1 l + a 2 d 2 l if if source is at infinity source is local a 0,a 1,a 2 : adjustable for optimal attenuation effects

7 Light Sources Directional light sources Produces a directional beam of light Light vector direction and an angular limit θ l Spotlight effects Vobj Vlight = cosα cosα cosθ l : within the spot light cos α < cosθ l : outside the light cone

8 Light Sources Angular intensity attenuation For a directional light, we can attenuate the light intensity angularly as well as radially out from the point-source position A cone of light is most intense along the cone axis, with the intensity decreasing as moving farther from the cone axis fangatten ( φ) = cos The greater a l, the smaller the angularly attenuated intensity a l φ fl,angatten = 1.0, 0.0, (V obj V light ) a l if source is not a spotlight if V V = cosα < cosθ obj light, otherwise l

9 Surface Lighting Effects An illumination model computes the lighting effects for a surface using the various optical properties Degree of opacity, color reflectance, surface texture The local illumination model describes the way incident light reflects from an opaque surface ambient light, diffuse reflection, specular reflection Simple approximation of actual physical models This model is also known as: light reflection model Phong illumination model reflectance model

10 Ambient Light (Background Light) Multiple reflection of nearby objects (light-reflecting sources) yields a uniform illumination Ambient light is independent of light sources and viewer position Ambient illumination is constant for an object, without regard to directions of faces I = k I ambdiff a a I a : the incident ambient intensity k a : ambient reflection coefficient, the proportion reflected away from the surface Indirect illumination can be computed much better using other model such as radiosity

11 Diffuse Reflection (Rough or grainy) Surfaces tend to scatter the reflected light in all directions. Model diffuse reflection from very rough, matte surfaces that scatter incident light with equal intensity in all directions. The surfaces appear equally bright from any viewing angle. Such surfaces are called ideal diffuse reflectors (also referred to as Lambertian reflectors)

12 Diffuse Reflection Light intensity depends on the angle of incidence Light intensity is independent of the angle of reflection

13 Diffuse Reflection Light intensity depends on the angle of incidence Light intensity is independent of the angle of reflection I l, diff = kd Il cosθ = kd Il (N L) I l k d N L : the intensity of the light source : diffuse reflection coefficient : the surface normal (unit vector) : the direction of light source (unit vector)

14 Ambient + Diffuse I diff = k k a a I I a a +, k d I l (N L), if if N L N L > 0 0 Increasing k d Increasing k a

15 Specular Reflection Some of reflected light is concentrated into a highlight, or bright spot specular reflection An ideal reflector (perfect mirror) reflects incident light only in the sepcular-reflection direction Objects other than ideal reflectors Exhibit specular reflections over a finite range of viewing positions around R. Narrow specular reflection range Wide specular reflection range

16 Specular Reflection Phong specular-reflection model An empirical model developed by Phong Bui Tuong Note that N, L, and R are coplanar, but V may not be coplanar to the others I k I cos n l, spec = s l φ = s l k I (R V) s n s I l k s n : intensity of the incident light : color-independent specular-reflection coefficient : the gloss of the surface

17 Specular Reflection Glossiness of surfaces I V) n l, spec = ksil cos φ = ksil (R s n s

18 Specular Reflection Specular-reflection coefficient is a material property k s For some material, varies depending on θ k s I = φ V) n l, spec ksil cos = ksil (R s n s

19 Specular Reflection Calculating the reflection vector R R + L = ( 2N L) N R = (2N L) N L I = φ V) n l, spec ksil cos = ksil (R Simplified Phong model using the halfway vector H H is constant if both viewer and the light source are sufficiently far from the surface s n s H = V + L V + L I l,spec = k s I l cos n s φ = k s I l (R V) n s k s I l cos n s α = k s I l (N H) n s

20 Specular Reflection / Phong Increasing n s ns I k I cos k I (R V) l, spec = s l φ = s l n s Increasing k s

21 Specular Reflection / Phong Increasing k s ns I k I cos k I (R V) l, spec = s l φ = s l n s Increasing n s

22 Ambient+Diffuse+Specular Single light source I = k a I Multiple light sources I = k a I a a + + k n d l= 1 I I l l ( N L) + k I (N H) [ k d Surface light emissions and Intensity attenuation I = I surfemission + n l= 0 f + k a l,radatten I f a s (N L) + k l,angatten s l (N H) n s ( n + ) s k I (N L) k I (N H) d l n s ] s l

23 Only Emission and Ambient

24 Including Diffuse Reflection

25 Including Specular Reflection

26 Phong Illumination Model Ambient + Diffuse + Specular = Phong Illumination

27 RGB Color Considerations For RGB color description, each intensity specification is a three-element vector designating red, green, and blue components of that intensity I = I, I, I ) l ( lr lg lb k = k, k, k ) k = k, k, k ) k = k, k, k ) a ( ar ag ab d ( dr dg db s ( sr sg sb e.g. I = k (N L lb, diff db lb l I )

28 Parameter Choosing Tips I = k a I a + k d I l ( N L) + k I (R V) s l n s The sum of three reflectance coefficients is usually smaller than one: + kd + ks 1 Try n s in the range [0, 100] Use a small k a (~0.1) Example Metal: n s =90, k a =0.1, k d =0.2, k s =0.5 k a

29 Transparent Surfaces Transparent / Opaque Translucent Transmitted light is diffused in all directions (diffuse refraction) diffuse refraction Partially transparent object (e.g. frosted glass) penetrating light is diffused Decrease light intensity, spread intensity contribution of each point onto a finite area on the refracting surface Expensive, seldom used

30 Specular Refraction (Snell s law) η i, η r sin = θr ηi ηr sin θi : the index of refraction of each material The refraction shifts the incident light to a parallel path as it emerges from the material

31 Specular Refraction From Snell s law, we can obtain the unit transmission vector T in the direction r θ ηi ηi T = ( cosθi cosθr) N L ηr ηr The vector T Used to locate intersections of the refraction path with objects behind the transparent surface Considerable computations Accurate refraction effects using ray-tracing algorithms

32 Basic Transparency Model Path shifts are ignored for thin objects A simpler procedure for modeling transparent objects Ignore the path shifts due to refraction Calculation speed-up I = ( 1 k ) I k I t + 1 refl1 1 refl2 t 1 2 line of sight k : transmission coefficient t1 (0 for opaque objects, 1 for totally transparent objects)

33 Polygon Rendering Methods We could use an illumination model to determine the surface intensity at every projected pixel position Or, we could apply the illumination model to a few selected points and approximate the intensity at the other surface positions Curved surfaces are often approximated by polygonal surfaces. So, polygonal (piecewise planar) surfaces often need to be rendered as if they are smooth. Constant shading, Gouraud shading, Phong shading

34 Constant Shading Constant-intensity surface rendering or flat surface rendering The simplest method Determine the intensity at a single surface position, such as a vertex or the polygon centroid Assign the same color to all projected surface positions

35 Constant Shading Accurate surface display if all the followings are valid The polygon is not a section of curved-surface approximation mesh (N L) R) Infinitely distant light source constant diffuse reflection Infinitely distant viewpoint constant specular reflection (V Abrupt change in surface orientation of adjacent surfaces produce an unrealistic effect

36 Smooth Shading Two popular methods: Gouraud shading (Gouraud surface rendering) Phong shading (Phong surface rendering) Developed for rendering a curved surface approximated with a polygon mesh

37 Normal Vector of a Vertex Plane Normal n ( p p ) = 0 0 n = ( p1 p0) ( p2 p0) Vertex Normal N 2 N v = ( N N N N N N N N 4 4 ) N 3 N v N 1 N 4

38 Gouraud Shading Intensity-interpolation surface rendering Determine the average unit normal vector at each vertex of the polygon Apply an illumination model at each polygon vertex Linearly interpolate the vertex intensities over the projected area of the polygon I y y y y I y y y y I + = I x x x x I x x x x I p p p + =

39 Gouraud Shading Compute vertex illumination (color) before the projection transformation Shade interior pixels: color interpolation (normals are not needed) C1 for all scanlines Ca = lerp(c1, C2) Cb = lerp(c1, C3) C2 C3 lerp(ca, Cb) * lerp: linear interpolation

40 Gouraud Shading Problem Highlights on the surface are displayed with anomalous shapes Lighting in the polygon interior can be inaccurate

41 Gouraud Shading Problem Mach bands: bright or dark intensity streaks These Mach Bands are not physically there. Instead, they are illusions due to excitation and inhibition in our neural processing The bright bands at 45 degrees (and 135 degrees) are illusory. The intensity of each square is the same.

42 Mach Bands Effect

43 Gouraud Shading Problem To reduce the anomalous effects, Divide the surface into a greater number of polygon faces Use more precise intensity calculations

44 Phong Shading Normal-vector interpolation rendering Shades are computed at each point using the interpolated normal vector The shading computed by Phong shading is C 1 continuous. Fix the mach band effect : remove edge discontinuity

45 Phong Shading Normal interpolation N 3 N a = lerp(n 1, N 3 ) N b = lerp(n 2, N 3 ) N = y y 1 y y y y 2 1 N1 + N2 2 y1 y2 N 1 lerp(n a, N b ) N Slow not supported by OpenGL and most graphics hardware Modern programmable lighting hardware can implement full Phong shading (and much more!), but you have to do this yourself. N 2

46 Problems with Interpolated Shading Polygon silhouette Faceting effects Perspective distortion Orientation dependence Shared edges vertex normals not representing the surface geometry

47 Local vs. Global Illumination Models Local illumination models Object illuminations are independent No light scattering between objects No real shadows, reflection, transmission(refraction) Phong Illumination model Global illumination models Ray tracing (highlights, reflection, transmission) Radiosity (Surface inter-reflections) Photon mapping

48 Forward Ray Tracing Rays as paths of photons in world space Follow photon from light sources to viewer Problem Many rays will not contribute to image Recursion

49 Backward Ray Tracing Basic ray-tracing algorithm Trace rays backward from viewer to light sources One ray from center of projection through each pixel in image plane Ray casting Simplest form of ray tracing No recursion Visible surface detection Global reflection and transmission effects Shadow area identification Transparency effects Illumination effects from multiple light sources

50 Backward Ray Tracing Illumination Phong illumination Shadow rays primary ray Specular reflection Specular refraction Specular reflection and refraction are recursive secondary rays

51 Binary Ray-Tracing Tree Path termination conditions The ray intersects no surfaces The ray intersects a light source, not a reflecting surface The tree has been generated to its maximum depth

52 Shadow Rays If the ray hits an object, we want to know if that point on the object is in a shadow. So, when the ray hits an object, a secondary ray, called a "shadow" ray, is shot towards the light sources. If this shadow ray hits another object before it hits a light source, then the first intersection point is in the shadow of the second object. For a simple illumination model, this means that we only apply the ambient term for that light source

53 Recursive Ray Tracing Pros very high quality images fast for very complex scenes Cons slow complexity hinders hardware implementation

54 Distributed Ray Tracing Stochastic sampling method randomly distribute rays according to the various parameters More accurate modeling Surface gloss and transparency, finite light sources, motion-blur displays of moving objects Monte Carlo evaluation of the multiple integrals that occur in an accurate physical description of surface lighting

55 Distributed Ray Tracing Divide the pixel area (a unit square) into the 16 subareas Generate a random jitter position in each subarea The 16 ray intensities are then averaged for the overall pixel intensity

56 Distributed Ray Tracing Distribute reflection and transmission paths Divide the maximum spread about R into 16 angular zones Reflect each ray in a jittered position

57 Distributed Ray Tracing Finite light source Distribute a number of shadow rays over the area of the light source If some shadow rays intersect opaque objects a penumbra (partly illuminated region) If all shadow rays are blocked an umbra (completely dark region)

58 Distributed Ray Tracing Motion blur Distribute rays over time 16 rays per pixel

59 Distributed Ray Tracing Depth of Field Distribute rays over the circle of confusion

60 Depth of Field

61 Radiosity Ray tracing Global illumination Radiosity specular reflection & specular refraction Highly realistic, particularly when the scene contains shiny objects A solution to diffuse interaction At the expense of dividing the environment into largish elements (constant illumination) Ray tracing (global specular reflection) + Radiosity (global diffuse reflection)

62 Radiosity Radiosity Defined as the energy per unit area leaving a surface patch per unit time The sum of the emitted and the reflected energy + = k k kj k j j j j j da F B R da E da B + = k jk k j j j F B R E B = + = n k jk k j j j F B R E B 1 k kj j jk A F A F = (reciprocal relationship) (dividing by ) da j j j k j jk A A A A F space surrounding in the hemispherical directions in all radiative energy leaving surface directly that strikes radiative energy leaving surface = = n n nn n n n n n n E E E B B B F R F R F R F R F R F R R F R F R F

63 Radiosity

64 Photon Mapping Radiosity Accurate display of global illumination effects for simple scenes More difficult to apply as the scene complexity increases Regarding rendering time and storage requirements Photon mapping Used for modeling global illumination in complex scenes Efficient and accurate Two-pass global illumination algorithm 1. Rays from the light source and rays from the camera are traced independently until some termination criterion is met 2. They are connected in a second step to produce a radiance value

65 Photon Mapping

66 Texture Mapping Pattern Mapping Map patterns of color onto geometric description of an object for adding detail to the object. umbrella, background, beach ball, beach blanket

67 Texture Pattern Separate texture space and screen space Linear texture pattern: Surface texture pattern: Volume texture pattern: Parametric texture mapping T ( s), 0.0 s 1.0 T ( s, t), 0.0 s, t 1.0 T ( s, t, r), 0.0 s, t, r 1.0 s t

68 Texture Mapping Texture Space Texture- Surface Transformation Texture Scanning Object Space Viewing and Projection Transformation ( s, t) ( u, v, n) ( x, y) Inverse Scanning Image-Order Scanning Image Space

69 Texture Mapping Texture scanning Map from texture space to pixel space Disadv. A selected texture patch usually does not match up with pixel boundaries Calculations to determine the fractional area of pixel coverage Inverse scanning Map from pixel space to texture space Most commonly used method

70 Texture Mapping Inverse scanning Find pre-image of the current pixel in the texture space 1. Take the four pixel corner points 2. Invert the viewing and projection transformation 3. Invert the texture-surface transformation Object size decreases Pre-image of a pixel in texture space increases need anti-aliasing

71 Texture Aliasing Simple texture application At each pixel we calculate the correct texture coordinate And retrieve the corresponding texel Can lead to nasty aliasing A pixel is mapped to several (fractional) texels but we only select one of them to use in the pixel this kind of point sampling results in aliasing

72 Texture Aliasing Texture filtering Average all covered texels together Need to choose appropriate averaging method Reduce objectionable artifacts Very high frequency details just get smoothed over completely (e.g., gray on horizon) Drawbacks Averaging covered texels can be very expensive

73 Texture Aliasing pre-image pixel with pixel w/o anti-aliasing anti-aliasing pixel center

74 Texture Aliasing For efficiency, an image pyramid (MIP maps) multum in parvo, that is much on a small object Base of pyramid is the original image (level=0) Level 1: the image down-sampled by a factor of 2 Level 2: the image down-sampled by a factor of 4 Not too big: 4/3 the size of the original image

75 Antialiasing with MIP maps MIP maps Efficient averaging of large regions Each texel in upper level cover many base texels k k At level k, they are the average of 2 2 texels Can quickly assemble appropriate texels for averaging

76 Bump Mapping A method for modeling rough surface appearance E.g., Oranges, strawberries, and raisins Apply a perturbation function to the surface normal N = N + N Use the perturbed normal vector in the illumination calculations