Schedule

Outlined below is the schedule for the course, including lecture topics and assignment due dates. The specific dates of different topics are subject to change based on the pace at which we go through the course.

The assigned textbook for the course covers most of the topics we will go over in the class, but I will sometimes add external links to other resources if I feel the textbook is lacking in a particular area, particularly for WebGL/GLSL topics. At times, I will even write my own little web pages to describe a concept (e.g. for scene graphs).

Lecture	Date	Lectures (click for notes)	Readings/Links	Assignments/Deliverables
Geometric Primitives The course will start with an overview of some important mathematical concepts from linear algebra and vector geometry to get everyone on the same page. These are the basic building blocks that will be used again and again in the rest of the course. The pace at which we go through this section will adapt to the background knowledge of the students. We will have two small individual programming assignments in this section to get everyone used to programming with geometry in Javascript. Big Concepts And Questions: What is numerical geometry? How does the quadratic formulat help is with ray object intersections? What trick can we use to incorporate both linear operations and translations into a single matrix? Why do we want to do this?
1	Mon 8/26/2019	Course Sneak Preview, Beginning Vectors	S/M Chapter 1	Submit Personal Survey on Microsoft Teams
2	Wed 8/28/2019	Vectors, Dot Products, Javascript Crash Course	Math Resources: S/M 2.3, 2.4 Calculus Blue 4.1 - 4.3, 5.1 - 5.3, 6.1 - 6.3 Javascript Resources Princeton Javascript for Graphics Crash Course Mozilla Javascript tutorial http://www.json.org/ glMatrix library documentation Google Javascript Style Guide (for what it's worth)	Mini Assignment 1: Geometric Primitives Out
3	Mon 9/2/2019	Projection, Normals, Lines, And Planes	Calculus Blue Parameterized Lines in 3D
4	Wed 9/4/2019	Ray/Sphere Intersections	S/M 4.4.1	Mini Assignment 1: Geometric Primitives Part 1 Due
	Fri 9/6/2019			Last day to add courses
5	Mon 9/9/2019	Barycentric Coordinates, Triangle Interior Point Testing, Begin 2D Matrix Transformations	S/M 2.7 S/M 6.1 - 6.4 (skip SVD) Prof. Tralie's 2D Matrix Transformation Demo Widget
6	Wed 9/11/2019	Homogenous Coordinates, Composition of Transformations, Inverses	S/M 6.1-6.4 2D Homogenous Coordinates Reactive Demo
	Fri 9/13/2019			Mini Assignment 1: Geometric Primitives Part 2 due
3D Rendering In this part of the course, we discuss how to use a computer to generate images of 3D geometric scenes, a process known as "3D rendering." The ultimate goal of such techniques is to make photorealistic images that look like what a camera might take in the real world, though, as we will see, this is quite challenging. In the process of attempting to meet this goal, we will think about how light bounces around in the real world and how humans see that light, and we will discuss algorithms that attempt to mimic this. To this end, students will start off implementing a ray tracer, which is a non-realtime rendering technique, but which allows for visually stunning effects with reflection, refraction, and shadows. We will then talk about the more traditional rendering pipeline, which leads to visually inferior but interactive images. Students will learn the basics of the WebGL / GLSL Javascript API, which implements this rendering pipeline. Big Concepts And Questions: What are local coordinates, and what are world coordinates? What are we modeling in a "scene" of 3D geometry? What kinds of visual effects emerge as light bounces around? What can be accomplished with ray tracing that's difficult to accomplish with real time rendering pipelines? What kinds of approximations make WebGL rendering fast? What challenges emerge in virtual reality compared to monocular rendering?
7	Mon 9/16/2019	3D Matrix Transformations, Normal Transformations, Scene Graphs	S/M 6.1-6.4, 6.5, 12.2 3D Transformations Slides Scene Viewer
	Tue 9/17/2019			Mini Assignment 2: Scene Graphs Out
8	Wed 9/18/2019	Scene Graphs Continued	Scene Viewer
9	Mon 9/23/2019	Shaders And GLSL	S/M Chapter 18 Slides from today Code we wrote today GLSL Programming WikiBook shadertoy.com
	Tue 9/24/2019			Mini Assignment 2: Scene Graphs Due
10	Wed 9/25/2019	Fractals, Texture Maps, Lambertian/Phong Illumination, Gouraud/Per-Fragment Shading	S/M 4.5, 8.2.4 - 8.2.6, 10.1, 10.2, 11.2, 11.3 Wikipedia Page on L-Systems John Bell's Notes on fractals in computer graphics Mozilla developer notes on WebGL Texture Mapping WebGL Fundamentals Notes on Texture Maps And Mipmapping Alec Jacobson's WebGL Illumination/Shading Demo	Mini Assignment 3: Shaders/GLSL Out
11	Mon 9/30/2019	GLSL Working Session
12	Wed 10/2/2019	3D Perspectives, Ray Tracing Overview, Ray Instancing	S/M 4.1 - 4.3, 13.2	Mini Assignment 3: Shaders/GLSL Due
13	Mon 10/7/2019	Continuing Ray Instancing, Global Illumination (Including Multiple Lights/Shadows)	S/M 4.7	Large Scale Assignment 1: Ray Tracing Out
14	Wed 10/9/2019	Finish Global Illumination (Specular Reflections, Refraction/Transmission), Begin Object-First Viewing	S/M 4.8, 13.1, 7.1 gluLookAt documentation	Viewing Matrices Class Exercise
--	Mon 10/14/2019	Fall Break		Enjoy!
15	Wed 10/16/2019	Perspective Viewing, Hidden Surface Removal / Depth Sorting, Culling, Begin Cel (Toon) Shading	S/M Chapter 7.2, 7.3, 8.2.2, 8.2.3, 8.4, 10.3 Wikipedia Page on Cel Shading RPI Final Project on Ray Tracing Cel Shading	Cel Shading Class Exercise
	Fri 10/18/2019			Large Scale Assignment 1: Ray Tracing Checkin
16	Mon 10/21/2019	Finish Cel Shading Exercise / Bump Maps, Displacement Maps, Shadow Maps	S/M 11.4, 11.5, 11.7
3D Shape Representations Now that we are comfortable rendering basic shapes, we will discuss data structures for representing more complicated custom shapes, which form the backbone of modern CAD and 3D modeling applications. The first of these is the triangle mesh, which is a discrete approximation of a smooth 2D manifold surface consisting of a collection of triangles connected to each other at a common edge. We will then discuss continuous representations, including subdivision surfaces and splines. We will conclude this unit with implicit surfaces, which are volumetric descriptions of surfaces which allow for easy boolean operations and natural design of neat shapes such as water drops. And as we will see, implicit surfaces lead to a very particular, smooth aesthetic via "metaballs" (not "meatballs"!). Big Concepts And Questions: What is the difference between a discrete and continuous data structure for surfaces? What are geometric properties of a triangle mesh, and what are topological properties of a triangle mesh? What are the strengths and limitations of different shape representations? How many metaballs does one need to design a human head?
17	Wed 10/23/2019	Triangle Mesh Topology: Manifold, Boundary, Euler Characteristic	S/M 12.1.1 - 12.1.3	Last day to drop courses with a W
	Fri 10/25/2019			Ray Tracing Hackathon 4PM - 12AM, IDC 114
18	Mon 10/28/2019	Mesh Orientation, Mesh Storage Requirements, Basic Mesh Data Structures	S/M 12.1.2 - 12.1.3 Additional Reading on Mesh Data Structures
19	Wed 10/30/2019	The Half Edge Data Structure, Per-Vertex Normals, Truncation	S/M 12.1.4 Kalle Rutanen's Half Edge Tutorial Per-vertex normals notes	Large Scale Assignment 1: Ray Tracing Due
	Thu 10/31/2019			Large Scale Assignment 2: Mesh Processing Out
	Fri 11/1/2019			Midterm Cel Shading Art Contest Due
20	Mon 11/4/2019	Subdivision Surfaces (Guest lecture by Dr. Nick Scoville)	SIGGRAPH 2000 Subdivision Surface Notes
21	Wed 11/6/2019	Intermezzo: Video Game Design Q&A (Guest Lecture by Steven Espinosa)	Unity videos on your first game, https://www.gamedesigning.org/ Bill Gates Talking About Windows 95 And The Original Doom
22	Mon 11/11/2019	Curves And Splines, Bidirectional Reflectance Distribution Functions (BRDFs)	S/M Chapter 15 (skim)
23	Wed 11/13/2019	Implicit Surfaces/ Marching Cubes	S/M 2.5.3-2.5.5, 16.1.1-16.1.3 Code from class Implicit human minus ellipsoid
3D Animation In this section, we will cover some of the basics of 3D animation at a surface level. This is an incredibly broad field, so we will focus primarily on the math underlying a subset of professional animation tools such as Blender and Maya, rather than the tools themselves. Big Concepts And Questions: Explain why "inverse kinematics" are named as such How does skinning work, and what are its shortcomings? What is Gimbal Lock, and what animation scenarios does it adversely impact and how?
24	Mon 11/18/2019	Animation Overview, The Animation Loop, Begin Collision Detection, Final Project Discussion	S/M 17.1	Final Project Out / Form Groups
25	Wed 11/20/2019	Collision Response, Convex Hulls/The Separating Axis Theorem, Begin Euler Angles		Large Scale Assignment 2: Mesh Processing Due Mini Assignment 4: Euler Angles And Gimbal Lock Out
	Sun 11/24/2019			Mini Assignment 4: Euler Angles And Gimbal Lock Due
26	Mon 11/25/2019	Finish Euler Angles, Rodrigues' Rotation Formula, Quaternions/SLERP	Quaternion SLERP Visualization App Wikipedia Derivation of Quaternion Axis/Angle Identity
	Tue 11/26/2019			Final Project Progress Mini Report Due
--	Wed 11/27/2019	Thanksgiving		Enjoy!
27	Mon 12/2/2019	Character Animation: Inverse Kinematics, MOCAP, Skinning	S/M 17.4 Forward Kinematics Demo FABRIK Paper FABRIK Demo CMU MOCAP Database Javascript MOCAP Visualizer
28	Wed 12/4/2019	Course Wrap-Up / Raffle	Raffle Prizes
--	Wed 12/11/2019			Final Project Prototype/Video Due
--	Sat 12/14/2019			Final Project Feedback Due

Geometric Primitives

3D Rendering

3D Shape Representations

3D Animation