5.1 si31_2001 SI31 Advanced Computer Graphics AGR Lecture 5 A Simple Reflection Model

5.2 si31_2001 What is a Reflection Model? reflection modellighting illumination n A reflection model (also called lighting or illumination model) describes the interaction between light and a surface, in terms of: – surface properties – nature of incident light n Computer graphics uses a simplification of accurate physical models – objective is to mimic reality to an acceptable degree

5.3 si31_2001 Phong Reflection Model n The most common reflection model in computer graphics is due to Bui-Tuong Phong - in 1975 n Has proved an acceptable compromise between simplicity and accuracy n Largely empirical

5.4 si31_2001 Diffuse Reflection and Specular Reflection - Phong Approach microscopic view white light specular reflection (white) diffuse reflection (yellow) yellow pigment particles Some light reflected directly from surface. Other light passes into material. Particles of pigment absorb certain wavelengths from the incident light, but also scatter the light through multiple reflections - some light emerges back through surface as diffuse reflection.

5.5 si31_2001 Ambient Reflection ambient n In addition to diffuse and specular reflection, a scene will also include ambient reflection n This is caused by light falling on an object after reflection off other surfaces – eg in a room with a light above a table, the floor below the table will not be totally black, despite having no direct illumination - this is reflection of ambient light

5.6 si31_2001 Reflection Model - Ambient Light surface I ( )= K a ( )I a ( ) I a = Intensity of ambient light K a = Ambient-reflection coefficient I = Reflected intensity = wavelength of light hemisphere of ambient light P

5.7 si31_2001 Ambient Lighting

5.8 si31_2001 Reflection Model - Diffuse Reflection Light reflected equally in all directions - intensity dependent on angle between light source and surface normal Lamberts cosine law: I = I* cos where I* is intensity of light source P light source P light source light source N L surface

5.9 si31_2001 Reflection Model - Diffuse Reflection I = K d ( cos ) I* I* = Intensity of light source N = Surface normal L = Direction of light source K d = Diffuse-reflection coefficient I = Reflected intensity light source N L surface Light reflected equally in all directions, with intensity depending on angle between light and surface normal:

5.10 si31_2001 Reflection Model - Diffuse Reflection The angle between two vectors is given by their dot product: cos = L. N (assume L, N are unit length) The coefficient K d depends on the wavelength of the incoming light light source N L surface I ( ) = K d ( ) ( L. N ) I*( )

5.11 si31_2001 Ambient and Diffuse

5.12 si31_2001 Reflection Model - Specular Reflection In perfect specular reflection, light is only reflected along the unique direction symmetric to the incoming light P light source N R

5.13 si31_2001 Reflection Model - Specular Reflection P light source N R In practice, light is reflected within a small angle of the perfect reflection direction - the intensity of the reflection tails off at the outside of the cone. This gives a narrow highlight for shiny surfaces, and a broad highlight for dull surfaces.

5.14 si31_2001 Reflection Model - Specular Reflection Thus we want to model intensity, I, as a function of angle between viewer and R, say, like this: I with a sharper peak for shinier surfaces, and broader peak for dull surfaces.

5.15 si31_2001 Reflection Model - Specular Reflection n Phong realised this effect can be modelled by: (cos ) n with a sharper peak for larger n I n=1 n=10

5.16 si31_2001 Reflection Model - Specular Reflection I = K s ( cos ) n I* I* = Intensity of light source V = View direction R = Direction of perfect reflected light K s = Specular-reflection coefficient I = Reflected intensity n varies with material large n : shiny small n : dull Intensity depends on angle between eye and reflected light ray: V light source N L R eye surface

5.17 si31_2001 Reflection Model - Specular Reflection V light source N L R eye surface Using cos = R. V (R, V unit vectors), we have: I ( ) = K s ( R. V ) n I( )* Note: K s does not depend on the wavelength - hence colour of highlight is same as source Note: intensity forms ellipse shape

5.18 si31_2001 Ambient, Diffuse and Specular

5.19 si31_2001 Reflection Model - Ambient, Diffuse and Specular Reflection Model - Ambient, Diffuse and Specular light source I( ) = K a ( )I a ( ) + ( K d ( )( L. N ) + K s ( R. V ) n ) I*( ) N L R V eye surface

5.20 si31_2001 Example - Ambient Reflection

5.21 si31_2001 Example - Ambient and Diffuse

5.22 si31_2001 Ambient, Diffuse and Specular

5.23 si31_2001 Reflection Model - Effect of Distance light source surface d The intensity of light reaching a surface decreases with distance - so we use typically: I* K 1 + K 2 *d + K 3 *d 2 K 1, K 2, K 3 constant - often K 2 =1, K 3 =0

5.24 si31_2001 Final Reflection Model light source N L R V eye surface d I( ) = K a ( )I a ( ) + ( K d ( )( L. N ) + K s ( R. V ) n ) I*( ) K 1 + K 2 *d + K 3 *d 2 This needs to be applied for every light source in the scene

5.25 si31_2001 Phong illumination model: Ks 0.0 to 1.0, Kd 0.0 to 1.0 (Ka = 0.7, n = 10.0) Ks Kd

5.26 si31_2001 Phong Illumination Model: Ks 0.0 to 1.0; n = 10.0 to (Ka = 0.7, Kd = 1.0) n Ks

5.27 si31_2001 Phong Model in Practice n In practice, some simplifications are made to the model for sake of efficiency n For example, ambient light is sometimes assumed to be a constant n Other simplifications are: – lights at infinity – simple colour model

5.28 si31_2001 Practicalities - Effect of Distance n There are advantages in assuming light source and viewer are at infinity – L and V are then fixed for whole scene and calculations become simpler directional n Lights at infinity are called directional lights positional point n Lights at a specified position are called positional, or point, lights

5.29 si31_2001 Practicalities - Calculating R n R + L = 2 ( N.L ) N hence R = 2 ( N.L )N - L n In practice, implementations often compute H = ( L + V ) / 2 and replace (R.V) with (H.N) – these are not the same, but compensation is made with choice of n (angle between N and H is half angle between R and V - if vectors coplanar) N LR R L V R H N

5.30 si31_2001 Practicalities - Calculating R n As noted, if viewer and light source both sufficiently far from surface, then V and L are constant over scene - and so H = (L+V)/2 just needs to be calculated once n H is often called the halfway vector

5.31 si31_2001 Practicalities - Effect of Colour The Phong reflection model gives reflection for each wavelength in visible spectrum n In practice, we assume light to be composed as a mixture of RGB (red, green, blue) components - and reflection model is applied for each component n Coefficients of ambient-reflection (K a ) and diffuse-reflection (K d ) have separate components for RGB n Coefficient of specular-reflection (K s ) is independent of colour

5.32 si31_2001 Acknowledgements n Thanks to Alan Watt for the images