Graphics' Dependencies

• Basic mathematics
  • Linear algebra, calculus, statistics
• Basic physics
  • Optics, Mechanics
• Misc
  • Signal processing
  • Numerical analysis
• And a bit of aesthetics

This Course

• More dependent on Linear Algebra
  • Vectors (dot products, cross products, …)
  • Matrices (matrix-matrix, matrix-vector mult., …)
• For example,
  • A point is a vector (?)
  • An operation like translating or rotating objects can be matrix-vector multiplication

An Example of Rotation

Vectors

• Usually written as $\vec{a}$ or in bold $\mathbf{a}$
• Or using start and end points $\overrightarrow{AB} = B - A$
• Direction and length
• No absolute starting position

Vector Normalization

• Magnitude (length) of a vector written as $\left\lVert \vec{a} \right\rVert$
• Unit vector
  • A vector with magnitude of 1
  • Finding the unit vector of a vector (normalization): $\hat{a} = \vec{a} / \left\lVert\vec{a}\right\rVert$
  • Used to represent directions

Vector Addition

• Geometrically: Parallelogram law & Triangle law
• Algebraically: Simply add coordinates