Computer Graphics Lighting Outline Lighting models Ambient Diffuse

Computer Graphics Lighting

Outline • Lighting models • Ambient • Diffuse • Specular • Surface Rendering Methods

What we know • We already know how to render the world from a viewpoint.

“Lighting” • Two components: – Lighting Model or Shading Model - how we calculate the intensity at a point on the surface – Surface Rendering Method - How we calculate the intensity at each pixel

Jargon • Illumination - the transport of light from a source to a point via direct and indirect paths • Lighting - computing the luminous intensity for a specified 3 D point, given a viewpoint • Shading - assigning colors to pixels • Illumination Models: – Empirical - approximations to observed light properties – Physically based - applying physics properties of light and its interactions with matter

The lighting problem… • What are we trying to solve? • Global illumination – the transport of light within a scene. • What factors play a part in how an object is “lit”? • Let’s examine different items here…

Two components • Light Source Properties – Color (Wavelength(s) of light) – Shape – Direction • Object Properties – Material – Geometry – Absorption

Global Effects shadow multiple reflection translucent surface 8 Angel: Interactive Computer Graphics 5 E © Addison-Wesley 2009

Local vs Global Rendering • Correct shading requires a global calculation involving all objects and light sources – Incompatible with pipeline model which shades each polygon independently (local rendering) • However, in computer graphics, especially real time graphics, we are happy if things “look right” – Exist many techniques for approximating global effects 9 Angel: Interactive Computer Graphics 5 E © Addison-Wesley 2009

Light Source Properties • Color – We usually assume the light has one wavelength • Shape – point light source - approximate the light source as a 3 D point in space. Light rays emanate in all directions. • good for small light sources (compared to the scene) • far away light sources?

Distributed Lights • Light Source Shape continued – distributed light source (not supported natively in Open. GL) - approximating the light source as a 3 D object. Light rays usually emanate in specific directions • good for larger light sources • area light sources

Light Source Direction • In computer graphics, we usually treat lights as rays emanating from a source. The direction of these rays can either be: – Omni-directional (point light source) – Directional angle (spotlights) – Directional (parallel rays)

Light Position • We can specify the position of a light with an x, y, and z coordinate. – What are some examples? – These lights are called positional lights • Q: Are there types of lights that we can simplify? A: Yep! Think about the sun. If a light is significantly far away, we can represent the light with only a direction vector. These are called directional lights. How does this help?

Contributions from lights • We will breakdown what a light does to an object into three different components. This APPROXIMATES what a light does. To actually compute the rays is too expensive to do in real-time. – Light at a pixel from a light = Ambient + Diffuse + Specular contributions. – Ilight = Iambient + Idiffuse + Ispecular

Ambient Term - Background Light • The ambient term is a HACK! • It represents the approximate contribution of the light to the general scene, regardless of location of light and object • Indirect reflections that are too complex to completely and accurately compute • Iambient = color

Diffuse Term • Contribution that a light has on the surface, regardless of viewing direction. • Diffuse surfaces, on a microscopic level, are very rough. This means that a ray of light coming in has an equal chance of being reflected in any direction. • What are some ideal diffuse surfaces?

Lambert’s Cosine Law • Diffuse surfaces follow Lambert’s Cosine Law • Lambert’s Cosine Law - reflected energy from a small surface area in a particular direction is proportional to the cosine of the angle between that direction and the surface normal. • Think about surface area and # of rays

Diffuse Term • To determine how much of a diffuse contribution a light supplies to the surface, we need the surface normal and the direction on the incoming ray • What is the angle between these two vectors? • Idiffuse = kd. Ilightcos = kd. Ilight(N. L) • Ilight = diffuse (intensity) of light • kd [0. . 1] = surface diffuse reflectivity • What CS are L and N in? • How expensive is it?

Example • What are the possible values for theta (and thus the dot product? ) http: //graphics. lcs. mit. edu/classes/6. 837/F 98/ Lecture 18/Slide 11. html

Normal for Triangle n plane n ·(p - p 0 ) = 0 p 1 n = (p 1 - p 0 ) × (p 2 - p 0 ) normalize n n/ |n| p p 2 p 0 Note that right-hand rule determines outward face (programatically: ‘winding’ or order of vertices) 20 Angel: Interactive Computer Graphics 5 E © Addison-Wesley 2009 X

Specular Reflection • Specular contribution can be thought of as the “shiny highlight” of a plastic object. • On a microscopic level, the surface is very smooth. Almost all light is reflected. • What is an ideal purely specular reflector? • What does this term depend on? Viewing Direction Normal of the Surface

Snell’s Law • Specular reflection applies Snell’s Law. · We assume l = r

Snell’s Law is for IDEAL surfaces • Most surfaces are not ideal. • Think about the amount of light reflected at different angles. N R L V

Different for shiny vs. dull objects

Snell’s Law is for IDEAL surfaces • Think about the amount of light reflected at different angles. N R L V

Phong Model Phong Reflection Model • An approximation: set the intensity of specular reflection proportional to (cos )shininess • What are the possible values of cos ? • What does the value of shininess mean? • How do we represent shinny or dull surfaces using the Phong model? • Ispecular = ks. Ilight (cos )shininess = ks. Ilight (V. R)shininess

The Shininess Coefficient • Values of a between 100 and 200 correspond to metals • Values between 5 and 10 give surface that look like plastic cosa -90 27 90 Angel: Interactive Computer Graphics 5 E © Addison-Wesley 2009

How do we compute R? • N*(N. L) • R+L=2 N(N. L) • R = 2 N(N. L)-L L N R N(N. L) L V

Simplify this • Instead of R, we compute halfway H between L and V. • We call this vector the halfway vector, H. N L R V

Combining the terms • Ambient - the combination of light reflections from various surfaces to produce a uniform illumination. Background light. • Diffuse - uniform light scattering of light rays on a surface. Proportional to the “amount of light” that hits the surface. Depends on the surface normal and light vector. • Sepecular - light that gets reflected. Depends on the light ray, the viewing angle, and the surface normal.

Ambient + Diffuse + Specular

Lighting Equation Ilambient = light source l’s ambient component Ildiffuse = light source l’s diffuse component Ilspecular = light source l’s specular component kambient = surface material ambient reflectivity N R L kdiffuse = surface material diffuse reflectivity kspecular = surface material specular reflectivity shininess = specular reflection parameter (1 -> dull, 100+ -> very shiny) V

Attenuation • One factor we have yet to take into account is that a light source contributes a higher incident intensity to closer surfaces. • What happens if we don’t do this?

Subtleties • What’s wrong with: What’s a good fix?

Full Illumination Model Run demo

Steps in Open. GL lighting 1. 2. 3. 4. Enable lighting and select model Specify normals Specify material properties Specify lights 36 Angel: Interactive Computer Graphics 5 E © Addison-Wesley 2009

Normal for Triangle n plane n ·(p - p 0 ) = 0 p 1 n = (p 1 - p 0 ) × (p 2 - p 0 ) normalize n n/ |n| p p 2 p 0 Note that right-hand rule determines outward face (programatically: ‘winding’ or order of vertices) 37 Angel: Interactive Computer Graphics 5 E © Addison-Wesley 2009 X

Normals • In Open. GL the normal vector is part of the state • Set by gl. Normal*() – gl. Normal 3 f(x, y, z); – gl. Normal 3 fv(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 – gl. Enable(GL_NORMALIZE) allows for autonormalization at a performance penalty 38 Angel: Interactive Computer Graphics 5 E © Addison-Wesley 2009

Shading • Shading is how we “color” a triangle. • Constant Shading • Gouraud Shading

Constant Shading • • • Constant Intensity or Flat Shading One color for the entire triangle Fast Good for some objects What happens if triangles are small? Sudden intensity changes at borders

Gouraud Shading • Intensity Interpolation Shading • Calculate lighting at the vertices. Then interpolate the colors

Gouraud Shading • • • Relatively fast, only do three calculations No sudden intensity changes What can it not do? What are some approaches to fix this? Question, what is the normal at a vertex?

Enabling Shading • Shading calculations are enabled by – gl. Enable(GL_LIGHTING) – Once lighting is enabled, gl. Color() ignored • Must enable each light source individually – gl. Enable(GL_LIGHTi) i=0, 1…. . • Can choose light model parameters – gl. Light. Modeli(parameter, GL_TRUE) 43 • 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 Angel: Interactive Computer Graphics 5 E © Addison-Wesley 2009

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 diffuse 0[]={1. 0, 0. 0, 1. 0}; GL float ambient 0[]={1. 0, 0. 0, 1. 0}; GL float specular 0[]={1. 0, 0. 0, 1. 0}; Glfloat light 0_pos[]={1. 0, 2. 0, 3, 0, 1. 0}; gl. Enable(GL_LIGHTING); gl. Enable(GL_LIGHT 0); gl. Lightv(GL_LIGHT 0, GL_POSITION, light 0_pos); gl. Lightv(GL_LIGHT 0, GL_AMBIENT, ambient 0); gl. Lightv(GL_LIGHT 0, GL_DIFFUSE, diffuse 0); gl. Lightv(GL_LIGHT 0, GL_SPECULAR, specular 0); 44 Angel: Interactive Computer Graphics 5 E © Addison-Wesley 2009

Distance and Direction • The source colors are specified in RGBA • The position is given in homogeneous coordinates – If w =1. 0, we are specifying a finite location – If w =0. 0, we are specifying a parallel source with the given direction vector • The coefficients in the distance terms are by default a=1. 0 (constant terms), b=c=0. 0 (linear and quadratic terms). Change by a= 0. 80; gl. Lightf(GL_LIGHT 0, GLCONSTANT_ATTENUATION, a); 45 Angel: Interactive Computer Graphics 5 E © Addison-Wesley 2009

Spotlights • Use gl. Lightv to set – Direction GL_SPOT_DIRECTION – Cutoff GL_SPOT_CUTOFF – Attenuation GL_SPOT_EXPONENT • Proportional to cosa - 46 Angel: Interactive Computer Graphics 5 E © Addison-Wesley 2009

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 • Open. GL also allows a global ambient term that is often helpful for testing – gl. Light. Modelfv(GL_LIGHT_MODEL_AMBIENT, global_ambient) 47 Angel: Interactive Computer Graphics 5 E © Addison-Wesley 2009

Moving Light Sources • Light sources are geometric objects whose positions or directions are affected by the modelview 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 48 Angel: Interactive Computer Graphics 5 E © Addison-Wesley 2009

Material Properties • Material properties are also part of the Open. GL state and match the terms in the modified Phong model • Set by gl. Materialv() GLfloat ambient[] = {0. 2, 1. 0}; GLfloat diffuse[] = {1. 0, 0. 8, 0. 0, 1. 0}; GLfloat specular[] = {1. 0, 1. 0}; GLfloat shine = 100. 0 gl. Materialf(GL_FRONT, GL_AMBIENT, ambient); gl. Materialf(GL_FRONT, GL_DIFFUSE, diffuse); gl. Materialf(GL_FRONT, GL_SPECULAR, specular); gl. Materialf(GL_FRONT, GL_SHININESS, shine); 49 Angel: Interactive Computer Graphics 5 E © Addison-Wesley 2009

Front and Back Faces • The default is shade only front faces which works correctly for convex objects • If we set two sided lighting, Open. GL 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 gl. Materialf back faces not visible 50 back faces visible Angel: Interactive Computer Graphics 5 E © Addison-Wesley 2009

Emissive Term • We can simulate a light source in Open. GL by giving a material an emissive component • This component is unaffected by any sources or transformations GLfloat emission[] = 0. 0, 0. 3, 1. 0); gl. Materialf(GL_FRONT, GL_EMISSION, emission); 51 Angel: Interactive Computer Graphics 5 E © Addison-Wesley 2009