Tools Engineer: Core Game Development - Math

Numbers

• Radix (2: binary, 10: decimal, 16: hexadecimal)

Alegbra

• Polynomials
• Conic sections

Linear Algebra

• Matrices for representing systems of equations
• The determinant and what it tells you about a matrix

Linear Algebra

• All the trigonometric functions
• How each trig function relates to coordinate components on the unit circle

ℝ3 and affine transformations:

• Fundamental vector operations: addition, subtraction, dot product, cross product
• Vectors that are "normalized," "orthogonal," and "ortho-normalized"
• Basis vectors of a matrix
• Row-major vs. column-major notation
• The plane equation, and its related to the dot product
• Affine transform composition: scale, rotation, translation
• Affine transform concatenation: global/parent/object space
• Affine transform inversion
• Affine transform decomposition

Rotations

• Euler angles, axis-angle, quaternion, rotation matrices
• 3-by-3 Rotation matrices (matrices, normal and non-normal, orthogonal and non-orthogonal)"
• How euler angles are short-hand for rotation matrices
• How to intuit a rotation from a 3-by-3 ortho-normalized matrix
• Euler angle static and rotating frame conventions