Paper Summaries Any takers? Rendering Assignments Projects - PDF document

Paper Summaries • Any takers? Rendering Assignments Projects • Approx 17 projects • Checkpoint 3 • Listing of projects now on Web – Still grading • Presentation schedule • Checkpoint 4 – Presentations (20 min max) – Due Tuesday – Last 3 classes (week 10 + finals week) • Renderman – Sign up • Email me with 1 st , 2 nd , 3 rd choices – Due Nov 4 th • First come first served. – Getting distributions on mycourses • Mid-quarter report due next Thursday Today’s Class Computer Graphics as Virtual Photography • Rendering real camera photo Photographic Photography: scene (captures processing print – What it is light) – Techniques for solving processing • Local Illumination • Global Illumination – The Rendering Equation camera Computer 3D synthetic tone model Graphics: models reproduction image (focuses simulated lighting) 1

Rendering Render • See Render • (v.) To make visible the final result. • Aka Shading. Shading Shading Models • Computing the light that leaves a point • Illumination vs. Shading Models • Shading point - point under investigation – Each of the illumination models given last class could be applied by either a local or global • Illumination model - function or algorithm shading algorithm used to describe the reflective characteristics of a given surface. – The illumination models are not global vs. • Shading model – algorithm for using an local, the illumination algorithms are. illumination model to determine the color of • Shading models are examples of local illumination a point on a surface. algorithms. Shading Rasterization • Goal: Determine the color at each pixel • Visible Surface Determination – Determine what is rendered where – Done in 2D camera space – Image precision vs object precision • Image Precision – determine for each pixel, which object is visible at the pixel • Object Precision – determine for each object, which part of the object is potentially visible. 2

Object Precision – BEFORE projection Image Precision AFTER Projection For each pixel in image { For each object in scene { O = object that is closest determine which parts of object not obscured draw pixel with appropriate color from O shade these parts } } Z-buffer Z-buffer • Basic algorithm • Visible surface algorithm to determine what Initialize frame buffer (to background) object appears on a given pixel Initialize Z-buffer (to 0) – Image Precision Algorithm – Two frame buffers For each polygon P { For each pixel p in polygon’s projection { • One contains colors z = P’s z at pixel p • One contains depth values (Z-buffer) if (z > Zbuffer at that pixel) { – Basic idea zBuffer at pixel = z Frame buffer at pixel = calcColor() • Only calculate shading on object if depth is closer to } value at z-buffer } Z-buffer List Priority Algorithms • Applet • Object precision and image-precision – Sort polygons by z http://www.cs.technion.ac.il/%7Ecs234325/Homepage/A pplets/applets/zbuffer/GermanApplet.html – Rasterize each polygon in order – Problems: • Polygons must not overlap in z • If they do, they must be split 3

Shading models Shading Models Interpolation • Direct Shading Models p1 – Only consider direct lighting from light sources Scan line – Flat (constant) shading – Gouraud Shading p2 – Phong Shading p3 Phong Illumination Model Shading Models • Geometry N V H viewer normal Half-way R S reflection source ∑ ∑ = + • + • k L ( V ) k L k L ( S N) k L ( R V) e a a d i i s i i i i ambient diffuse specular Note: L n are radiance terms, include both light and material info Shading Models Shading Models • Flat shading • Flat Shading – Illumination model applied once per polygon. – Constant color for entire polygon – Assumes normal vector is constant across the entire polygon Hwang 4

Shading Models Shading Models • Gouraud Shading – finding the normal • Gouraud Shading – Illumination is interpolated across each polygon – Normals required at each polygon vertex, calculated as an average of the normals of each face that shares that vertex – Illumination is calculated for each polygon vertex – Interior points interpolated from endpoint illumination intensities Gouraud Rendering Pipeline Shading Model with Z Buffer • Gouraud Shading Database Model Lighting Culling traversal transform Viewing Clipping Projection Rasterization transform Display Hwang Shading Models Shading Models • Phong Shading • Phong Shading – Normal vectors are interpolated across each polygon – Averaged normal (per Gouraud required at each polygon vertex) – Illumination is calculated for each polygon interior point by applying illumination model directly using interpolated normal Hwang 5

Phong Rendering Pipeline Shading models with Z-Buffer • Phong vs. Gouraud Trivial Database Model View Accept / traversal transform transform Reject Rasterization Display Clipping Projection and lighting Shading Models To summarize – Comparison • Rasterization – Scan conversion / Interpolation in 2D – Z-buffer • Local Illumination models – Only considers first reflection of light with object – No shadows (unless you add them) • Shading vs. Illumination Models – A shading model can use any illumination model – Phong was a busy guy! Flat Gouraud Phong The Rendering Equation The Rendering Equation • General form [ ] ∫ • Kajiya: 1986 ′ = ′ ε ′ + ρ ′ ′ ′ ′ ′ ′ ′ ′ I ( x , x ) g ( x , x ) ( x , x ) ( x , x , x ) I ( x , x ) d x S • “Unified context for viewing rendering algorithms as more or less accurate approximations to the solution of a single equation” • Expresses the quantity of light transferred from one point x’ to another x , summed over all points. Ashdown 6

The Rendering Equation The Rendering Equation • Transport Intensity • Geometry term [ ] [ ] ∫ ∫ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ = ε + ρ = ε + ρ I ( x , x ) g ( x , x ) ( x , x ) ( x , x , x ) I ( x , x ) d x I ( x , x ) g ( x , x ) ( x , x ) ( x , x , x ) I ( x , x ) d x S S I(x, x’) = Transport energy or intensity of light g(x, x’) = geometry term passing from point x’ to point x (unoccluded two = 0, if x is not visible from x’ point transport) = 1/d 2 otherwise The Rendering Equation The Rendering Equation • Emittance • Scattering [ ] ∫ [ ] ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ = ε + ρ I ( x , x ) g ( x , x ) ( x , x ) ( x , x , x ) I ( x , x ) d x ∫ ′ = ′ ε ′ + ρ ′ ′ ′ ′ ′ ′ ′ ′ S I ( x , x ) g ( x , x ) ( x , x ) ( x , x , x ) I ( x , x ) d x S ρ (x, x ′ , x ′′ ) = light energy reflected off ε (x, x ′ ) = light energy emitted from point x ′ point x’ towards point x from light coming from x ′′ towards x . The Rendering Equation The Rendering Equation • Incoming = direct + indirect (scattered) [ ] ′ ′ ′ ∫ ′ ′ ′ ′ ′ ′ ′ ′ = ε + ρ I ( x , x ) g ( x , x ) ( x , x ) ( x , x , x ) I ( x , x ) d x S = ε + I g gR ( I ) direct indirect ρ (x, x’, x’’) = light energy reflected from point x’ towards point x from light coming from x’’, i.e. BRDF 7

The Rendering Equation The Rendering Equation • In short… – The transport of light from point x’ to point x is equal to the sum of • the light emitted from x’ in the direction of x and • the total light scattered from x’ towards x due to light from all other surfaces in the scene. The Rendering Equation The Rendering Equation • This can be expanded using the Neuman series for • Why is this important? implementation purposes: = ε + ε + ε + ε + … 2 3 I g g ( Rg ) g ( Rg ) g ( Rg ) = ε + ε + ε + ε + … 2 3 I g g ( Rg ) g ( Rg ) g ( Rg ) direct 1st scattering 2nd scattering 3rd scattering or Rendering methods can be ∞ ∑ = ε i characterized by the number of I g ( Rg ) scatterings considered = i 0 The Rendering Equation The Rendering Equation • Local vs Global Illumination Models • Local Illumination = ε + ε + ε + ε + … = ε 2 3 ( ) ( ) ( ) I g g Rg g Rg g Rg I g direct 1st scattering 2nd scattering 3rd scattering direct Local illumination - only considers direct component Only object’s first contact with light is considered. Lighting “simulated” by illumination model used. Global illumination - also considers other scattered component NOTE: Kajiya does not include ambient light! 8