# Introduction. Lighting model Light reflection model Local illumination model Reflectance model BRDF

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2 Introduction Affine transformations help us to place objects into a scene. Before creating images of these objects, we ll look at models for how light interacts with their surfaces. Such a model is called a shading model. Other names: Lighting model Light reflection model Local illumination model Reflectance model BRDF

3 An abundance of photons Properly determining the right color is really hard. Look around the room. Each light source has different characteristics. Trillions of photons are pouring out every second. These photons can: interact with the atmosphere, or with things in the atmosphere strike a surface and be absorbed be reflected (scattered) cause fluorescence or phosphorescence. interact in a wavelength-dependent manner generally bounce around and around University of Texas at Austin CS354 - Computer Graphics Don Fussell #

4 Break problem into two parts Part 1: What happens when photons interact with a particular point on a surface? Local illumination model Part 2: How do photons bounce between surfaces? And, what is the final result of all of this bouncing? Global illumination model Today we re going to focus on Part 1.

5 Strategy for today We re going to build up to an approximation of reality called the Phong illumination model. It has the following characteristics: not physically based gives a first-order approximation to physical light reflection very fast widely used We will assume local illumination, i.e., light goes: light source -> surface -> viewer. No interreflections, no shadows.

6 Setup Given: a point P on a surface visible through pixel p The normal N at P The lighting direction, L, and intensity, I l,at P The viewing direction, V, at P The shading coefficients (material properties) at P Compute the color, I, of pixel p. Assume that the direction vectors are normalized: N = L = V = 1

7 Iteration zero The simplest thing you can do is Assign each polygon a single color: where I is the resulting intensity k e is the emissivity or intrinsic shade associated with the object This has some special-purpose uses, but not really good for drawing a scene. [Note: k e is omitted in Watt.] I = k e

8 Iteration one Let s make the color at least dependent on the overall quantity of light available in the scene: I = k e + k a I a k a is the ambient reflection coefficient. really the reflectance of ambient light ambient light is assumed to be equal in all directions I a is the ambient intensity. Physically, what is ambient light?

9 Wavelength dependence Really, k e, k a, and I a are functions over all wavelengths λ. Ideally, we would do the calculation on these functions. We would start with: I(λ) = k e (λ) + k a (λ)i a (λ) then we would find good RGB values to represent the spectrum I(λ). Traditionally, though, k e, k a and I a are represented as RGB triples, and the computation is performed on each color channel separately: I R = k e,r + k a,r I a,r I G = k e,g + k a,g I a,g I B = k e,b + k a,b I a,b

10 Diffuse reflectors Diffuse reflection occurs from dull, matte surfaces, like latex paint, or chalk. These diffuse or Lambertian reflectors reradiate light equally in all directions. Picture a rough surface with lots of tiny microfacets.

11 Diffuse reflectors or picture a surface with little pigment particles embedded beneath the surface (neglect reflection at the surface for the moment): The microfacets and pigments distribute light rays in all directions. Embedded pigments are responsible for the coloration of diffusely reflected light in plastics and paints. Note: the figures above are intuitive, but not strictly (physically) correct.

12 Diffuse reflectors, cont. The reflected intensity from a diffuse surface does not depend on the direction of the viewer. The incoming light, though, does depend on the direction of the light source:

13 Iteration two The incoming energy is proportional to cos(θ), giving the diffuse reflection equations: I = k e + k a I a + k d I l cos(θ) + = k e + k a I a + k d I l (N L) + where: k d is the diffuse reflection coefficient I l is the intensity of the light source N is the normal to the surface (unit vector) L is the direction to the light source (unit vector) (x) + means max {0, x} [Note: Watt uses I i instead of I l.]

14 Specular reflection Specular reflection accounts for the highlight that you see on some objects. It is particularly important for smooth, shiny surfaces, such as: metal polished stone plastics apples skin Properties: Specular reflection depends on the viewing direction V. For non-metals, the color is determined solely by the color of the light. For metals, the color may be altered (e.g., brass)

15 Specular reflection derivation For a perfect mirror reflector, light is reflected about N, so! Il if V = R I = " # 0 otherwise For a near-perfect reflector, you might expect the highlight to fall off quickly with increasing angle φ. Also known as: rough specular reflection directional diffuse reflection glossy reflection

16 Derivation, cont. cos n s φ ns = 1 N 1.0 L R V ns = φ One way to get this effect is to take (R V), raised to a power n s. As n s gets larger, the dropoff becomes {more,less} gradual gives a {larger,smaller} highlight simulates a {more,less} mirror-like surface

17 Iteration three The next update to the Phong shading model is then: I = k e + k a I a + k d I l (N L) + + k s I l (R V) + n s where: k s is the specular reflection coefficient n s is the specular exponent or shininess R is the reflection of the light about the normal (unit vector) V is viewing direction (unit vector) [Note: Watt uses n instead of n s.]

18 What is incoming light intensity? So far we ve just been considering what happens at the surface itself. How does incoming light intensity change as light moves further away?

19 Intensity drop-off with distance OpenGL supports different kinds of lights: point, directional, and spot. For point light sources, the laws of physics state that the intensity of a point light source must drop off inversely with the square of the distance. We can incorporate this effect by multiplying I by 1/d 2 l. Sometimes, this distance-squared dropoff is considered too harsh. A common alternative is: f atten (d) = 1 a + bd + cd 2 with user-supplied constants for a, b, and c. [Note: not discussed in Watt.]

20 Iteration four Since light is additive, we can handle multiple lights by taking the sum over every light. Our equation is now: I = k e + k a I a + j f atten (d j )I l j [ n k d (N L j ) + + k s (R j V) s ] + This is the Phong illumination model.

21 Choosing the parameters Experiment with different parameter settings. To get you started, here are a few suggestions: Try n s in the range [0,100] Try k a + k d + k s < 1 Use a small k a (~0.1) Metal Plastic n s k d k s Small, Large, large color of color of metal metal medium Medium, color of plastic Planet 0 varying 0 Medium, white

22 BRDF The Phong illumination model is really a function that maps light from incoming (light) directions to outgoing (viewing) directions: f r (ω in,ω out ) This function is called the Bi-directional Reflectance Distribution Function (BRDF). Here s a plot with ω in held constant: Physically valid BRDF s obey Helmholtz reciprocity: f r (ω in,ω out ) = f r (ω out,ω in ) and should conserve energy (no light amplification).

23 f r (ω in,ω out ) = f r (L,V) How do we express Phong model using explicit BRDF? I = k e + k a I a + j f atten (d j )I l j [ n k d (N L j ) + + k s (R j V) s ] +

24 More sophisticated BRDF s Cook and Torrance, 1982 Westin, Arvo, Torrance 1992

25 Summary Local vs. Global Illumination Models Local Illumination Models: - Phong Physically inspired, but not truly physically correct. - Arbitrary BRDFs In applying the Phong model, we assumed unshadowed point light sources.

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