Turn on the Lights: Reflectance

Transcription

1 Turn on the Lights: Reflectance Part 2: Shading Tuesday, October Lecture #14 Goal of Shading Model simple light sources Point light sources Extended light sources Ambient lighting Model lighting geometry Angle between light ray and surface normal Angle between surface normal and viewing ray Model surface reflections Diffuse (Lambertian) reflections Specular reflections Phong reflectance 2

2 Reflectance - 3 Kinds Ambient reflection. Models perfectly even illumination. Lambertian reflection. Matte surfaces, dull rather than shiny. Specular reflection. Bright highlights seen on polished surfaces. Slide 3 Reflectance - Geometry Reflectance functions are defined in terms of: The position of a (point) light source The orientation of the reflecting surface The viewing position. angle of incidence viewing angle surface normal 4

3 Reflectance Functions (III) Light rays, surface normals, and colors are expressed using vectors Light often described as illumination I Three components to illumination: Ir I = Ig Ib 10/10/13 Ross Beveridge Bruce Draper, CSU CS 410 Slide 5 Lambertian Reflection. The moon is cited as a good example of lambertion reflection Image by Dmitry, dzz at Morgefile. Maybe not such a great example large dark patches. 10/10/13 Ross Beveridge Bruce Draper, CSU CS 410 Slide 6

4 Lambertion Reflection Consider a point light source and a Diffuse (Lambertian) Surface. Diffuse surfaces reflect light with equal intensity in all directions. L R 7 A Touch of Physics Light per unit area arriving depends upon angle to light source. Light leaves in all directions, reflected off micro surfaces. 8

5 Diffuse Reflection Illumination/area drops when tilted from a point light source. I = I p1 K d cos K is a (usually diagonal) 3x3 matrix of reflectance parameters (material property) L N 9 Material Properties A full-blown diffuse reflectance matrix looks like:! # K = # # " # k rr k gr k br k rg k gg k bg k rb k gb k bb $ % Most surfaces reflect red light as red, etc.:! # K = # # "# k rr k gg k bb $ % For example, k gr modulates the percentage of incoming green light reflected back as red light. 10

6 Material Properties (II) There are some pragmatic constraints: No term in K may exceed 1.0 No term in K may be negative No column may have a sum exceeding 1 But, These constraints are not always enforced There is an art to lighting a scene! 11 Diffuse Reflection (III) The final term in diffuse reflection is cos(). This is the angle between the incoming light ray L and the surface normal N L = (P pos S)/ (P pos S), where P pos is the position of the light source. S is the position of the surface point. N = E 1 E 2 / E 1 E 2 for two surface edges Remember, the surface is planar. Avoid parallel edges! cos() = N L 12

7 Surface Normals - Sphere What about the surface normal for a sphere? N circlecenteredat P C surface point onsphere S S P C N = S P C S P C 13 Diffuse Reflection (IV) For a single point light source p1: I = I p1 K d ( N L ) p1 For many point light sources I = I p K ( d N L ) p p 14

8 Ambient Reflection Ambient reflection is just diffuse reflection of light from the ambient light source Ambient light models background light It is the same intensity everywhere It is the same color everywhere It comes from every angle So I = I a K d 15 Specular Reflection Most surfaces do more. Consider two extremes: a diffuse surface, and a Mirror. Specular reflection component Mirrors are extreme Mirrors reflect around an angle Metals, for example, combine Diffuse and specular components. 16

9 Only Skin Deep Diffuse models light deep reflection Enters through micro-holes in the surface Bounced from facet to facet, changing color Exits at a random angle Specular reflection is surface reflection Light hits a single surface facet, skips off. The color of the light is unchanged. The exit angle depends on the entry angles. 17 Limiting Case - Mirror The angle of incidence equals the angle of reflection. Idealized form only applies to mirrors. L N R 18

10 Mirrors are hard. Thinking about mirrors helps. One place difference between polygon pipelines and ray tracing differ greatly! For example: Return only when the viewing angle equals the angle of reflection. Generally, need to think about: What is the angle of reflection R? What is the viewing ray V? 19 Reflection and Viewer V is the unit vector from the surface point to the camera: V = (C Q)/ C Q Calculating R is more involved L S N S R V C Q 20

11 Reflection Vector Let N L be the projection of L onto N Assume N is a unit vector N L = (L N)N S is defined as S = N L L = (L N)N L R is L + 2S ( ) = 2 L N R = L + 2 ( L N)N L ( )N L 21 Back to Perfect (for now) If V R, there is no (pure) specular reflection. If V = R, then I = I p1 k s Note that k s is a scalar, measuring the percent of light reflected specularly. Color reflected is that of the light source. 22

12 Close Counts - Phong In Phong s model, reflection strongest in the direction of the angle of reflection Drops off with the cosine of the deviation from the angle of reflection L S N S R 23 Phong Specular Highlights I = I p1 k s ( cosφ) α Φ is the angle between the viewing ray and the angle of reflection. α is the so-called Phong constant, expressing how shiny an object is Mirrors: α = 200 Dull objects: α =

13 Phong - The Algebra cos(φ) = V R = V (2(L N)N L) I = I p1 k s ( V R) α I = I p1 k ( s V ( 2( L N) N L) ) α 25 Total Reflectance Reflectance off a surface point is the sum of: Diffuse reflection from the ambient light Diffuse reflection off of every point light Specular reflection off of every point light ( ) + I p k s ( V R p ) p lights( α ) I = I a K d + I p K d L p N 26