PowerPoint Presentation
18. Review
Dr. Hamish Carr
COMP 5812M: Foundations of Modelling & Rendering
1. Mathematics of Surfaces
Function Notation
Graphs of Functions
Multi-dimensional Calculus
Mathematics of Surfaces & Manifolds
Meshes & Attributes
The Euler Formula
COMP 5812M: Foundations of Modelling & Rendering
COMP 5812M: Foundations of Modelling & Rendering
2. Quaternions
Fundamental maths for rotations
Used very heavily in animation
Gimbal locks, great circles
Complex numbers & transformations
Action of a Quaternion
Conversion to/from matrix
Arcball controller
COMP 5812M: Foundations of Modelling & Rendering
COMP 5812M: Foundations of Modelling & Rendering
3. Mesh Data Structures
Requirements
Operations
Smooth Normal Calculation
Trap Tables / POD Loophole
Face, Indexed Face, Fans, Strips, Arrays, VBOs
Winged Edge, Half Edge, Directed Edge
COMP 5812M: Foundations of Modelling & Rendering
COMP 5812M: Foundations of Modelling & Rendering
4. Homogeneous Coords
Projective Nature of Homogeneous Coords
Conversion to/from Cartesian Coords
Rotation Matrices
Translation Matrices
Rotation around Arbitrary Point
Orthogonal & Perspective Projection
Speed Advantages
COMP 5812M: Foundations of Modelling & Rendering
COMP 5812M: Foundations of Modelling & Rendering
5. Barycentric Interpolation
Normal & Parametric Forms of a Line
Linear Interpolation
Definition of Triangle
Raster Scan Algorithm
Half-Plane Test
Barycentric Coordinates
Relationship to Distance
Interpolation
COMP 5812M: Foundations of Modelling & Rendering
COMP 5812M: Foundations of Modelling & Rendering
6. Projective Rendering
Standard Coordinate Systems
Projective Rendering
Painter’s Algorithm
Depth (Z-) Buffer
Projective Pipeline
Geometry / Raster / Fragment Stages
COMP 5812M: Foundations of Modelling & Rendering
COMP 5812M: Foundations of Modelling & Rendering
7. Physics of Light
Photons: Orbitals, Absorption, Emission
Wave-Particle Duality
Diffraction, Polarisation, Reflection, Refraction
Integrating Radiance (5-deep integral)
Angular Dependence
Lambertian Reflectance
COMP 5812M: Foundations of Modelling & Rendering
COMP 5812M: Foundations of Modelling & Rendering
8. Colour & Perception
Spectral Distribution
Rods & Cones
Luminance
Tri-Stimulus Theory
Gamma Encoding
Colour Spaces
COMP 5812M: Foundations of Modelling & Rendering
COMP 5812M: Foundations of Modelling & Rendering
9. Blinn-Phong Model
Local vs. Global Illumination
Specular (Glossy, not Mirror)
Diffuse (Lambertian)
Ambient (approximates Local Illumination)
Emissive
Debugging Graphics Code
COMP 5812M: Foundations of Modelling & Rendering
COMP 5812M: Foundations of Modelling & Rendering
7. Texture Mapping
Mapping From Manifold to Surface
Forwards (u,v -> x,y,z)
Backwards (x,y,z -> u,v)
Bilinear Interpolation
Replacement vs. Modulation
Mipmaps
Uses & Construction
COMP 5812M: Foundations of Modelling & Rendering
COMP 5812M: Foundations of Modelling & Rendering
11. Filtering & Scaling
Continuous vs. Discrete Images
Reconstruction, Aliasing & Filtering
Convolution
Blurring
Fourier Analysis
Frequency Filtering
Scaling Down / Up
COMP 5812M: Foundations of Modelling & Rendering
COMP 5812M: Foundations of Modelling & Rendering
12. Raytracing / Intersection
Ray Casting & Visibility
Shadow Rays
Geometric Intersections
Line-Sphere
Line-Plane
Line-Triangle
Triangle-Triangle
COMP 5812M: Foundations of Modelling & Rendering
COMP 5812M: Foundations of Modelling & Rendering
13. Materials & Scattering
Scattering Functions (BSDFs)
Finding Surface Frames
Sources of BSDFs
Blinn-Phong Shading
Add Specular Reflection / Refraction
Replace Ambient
Translucency & Opacity
COMP 5812M: Foundations of Modelling & Rendering
COMP 5812M: Foundations of Modelling & Rendering
14. Light Transport
Rendering Equation
Basic Path Tracer
Direct Point Lights
Indirect Point Lights
Recursive Scattering
Transmissive Terms
COMP 5812M: Foundations of Modelling & Rendering
COMP 5812M: Foundations of Modelling & Rendering
15. Monte Carlo Sampling
Random Numbers
Mean, Variance & Standard Deviation
Importance Sampling
Monte Carlo Sampling
Weighting Sampling Directions
COMP 5812M: Foundations of Modelling & Rendering
COMP 5812M: Foundations of Modelling & Rendering
16. Practical Raytracing
Recursive Path Tracer
Emissive Term for Area Lights
Direct Term for Point Lights
Direct Monte Carlo Term for Area Lights
Impulse Scatter for Reflection/Transmission
Indirect Light for Everything Else
Randomised Direction & Extinction Factor
COMP 5812M: Foundations of Modelling & Rendering
COMP 5812M: Foundations of Modelling & Rendering
17. Rendering Solutions
Radiosity
Path Tracing (Kajiya)
Bidirectional Path Tracing
Metropolis Light Transport
Photon Mapping
Image-Space Photon Mapping
All of the stuff we don’t use
COMP 5812M: Foundations of Modelling & Rendering
COMP 5812M: Foundations of Modelling & Rendering
18. NPR
Style, Intent, Message, Abstraction
Role of Strokes
Simplify, Factorise, Schematise
Silhouette Detection from Normals
Curvature Lines
Cel (Toon) Shading
COMP 5812M: Foundations of Modelling & Rendering
COMP 5812M: Foundations of Modelling & Rendering
19. Volume Rendering
Volumetric Functions
Meshes & Interpolation
Isosurfaces
Normal Vectors & Central Differencing
Volume Rendering Integral
Transfer Functions
Pseudocode
COMP 5812M: Foundations of Modelling & Rendering
COMP 5812M: Foundations of Modelling & Rendering
20. OpenGL in Qt
Projective Pipeline
Input, Geometry, Raster, Texture, Fragment
Coordinate Systems (Modelview)
Intro to GL functions
Model-View-Controller (MVC)
initializeGL(), paintGL(), resizeGL()
Example
COMP 5812M: Foundations of Modelling & Rendering
COMP 5812M: Foundations of Modelling & Rendering
What’s on the Exam?
2 Questions (25 marks each)
1 on Modelling
1 on Rendering
Each with 3-4 subparts
Different from last two years
But I’ll upload them anyway
COMP 5812M: Foundations of Modelling & Rendering
COMP 5812M: Foundations of Modelling & Rendering