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Instructor

Crane He Chen

Email: h.chen1@northeastern.edu

Teaching Assistants

Abhijeet Chowdhury

Email: chowdhury.ab@northeastern.edu

Office Hour: Thursday, 2:30PM-3:30PM

Taiwei Cui

Email: cui.ta@northeastern.edu

Office Hour: Tuesday, 12PM-1PM

Suggested Reading And Playground

Course Information

This course provides a fundamental introduction to computer graphics with hands-on opportunities. We cover four main subfields of graphics in the lectures, including rendering, geometry, animation, and simulation. The focus is geometry. We begin our journey from image processing, spend time studying the rendering of three-dimensional scenes using ray-tracing techniques, adding texture to surfaces, exploring the tessellation problem on Euclidean plane with wallpaper groups, and looking into how to animate an animal in an industrial pipeline. During the lectures, there will be a short break every 45 minutes, because super long didactic lectures are unhelpful for focusing. During the break, we will be watching either two SIGGRAPH technical paper trailers from the past 10 years or a classical short computer animation movie.

Course Objectives

By the end of this course, you will be ready to

Prerequisites

Rubric (it is possible to earn more than 100%)

Course Policies

Intended Course Roadmap

Week Num. Lecture Slides Keywords In-Class Coding Practice Assigned Reading
Week 0 Welcome
  • What is Computer Graphics?
  • N/A
    Week 1 Math Preliminary
    • Vector
    • Vector Field, Scalar Field
    • Gradient, Divergence, Curl, Laplacian
    • Solving a Linear System
    • Poisson Surface Reconstruction
    Week 2 Software Tools
    • CMake
    • Modern C++
    • C++ in The Wild for Computer Graphics
    Week 3
    • Image Acquisition Methods
    • What is Diffusion?
    • Representations of Digital Images
    • Digital Half Toning
    • Beier-Neeley Morfing
    Week 4
    • Transformation Matrices
    • Homogeneous Coordinates
    • Interpolating Transformations
    • SLERP
    • Linear Blend Skinning
    Week 5,6
    • Direct Illumination
    • Indirect Illumination
    Week 7
    • Quotient
    • Orbifold
    • Cone Points
    • Embedding
    • Tutte Embedding
    • Surface Parametrization
    • Criterions of Good Surface Parametrization
  • Practice 701: Orbifold Tutte Embeddings
  • Practice 702: Hyperbolic Orbifold Tutte Embeddings
  • Practice 703: Spherical Orbifold Tutte Embeddings
  • Week 8
    • Growth Rules of Plant-like Curves
    • SDS Loss
    • Symmetry Groups
    Week 9
    • What is a Mesh?
    • Data Structure of Meshes
    • Pipeline and Tasks of Digital Geometry Processing
    • Delaunay Triangulation
    • Curvature
    Week 10
    • What is Mesh Deformation?
    • Cage-based Deformation
    • Intuition of the Three Terms in Elastic Potential Energy
    • What is Kelvinlets?
    • Strengths of Kelvinlets
    Week 11
    • What is Dynamic Kelvinlets?
    • Elastic Wave Equation
    • Helmholtz Decomposition
    Week 12
    • Intuition of Navier-Stokes Equations
    • Lagrangian Method
    • Eulerian Method
    • Neural Style Transfer of Volumes
    • N/A
    Week 13
    • Standard Form of Optimization
    • Feasibility of Optimization
    • PDE VS. ODE
    • Intuition of Laplace Equation, Heat Equation, Wave Equation
    • Numerical Solve of Laplace Equation
    • Prescribing Boundary Conditions
    • N/A

    Reference

    I did not grow the knowledge out of the ground. The knowledge did not fall out of the sky either. My own insights were injected, but I have also put existing things together for a lot of parts. In alphabetical order, I have stolen contents from: