Q1: Graphics depends on knowledge

Basic Mathematics: Linear Algebra, Calculus, Statistics Basic Physics:…. A little aesthetics

Q2: Vector related introduction

The most important two properties of a vector: the direction and the length are equal after translation, and they don’t care about the absolute starting position

Vector length representation Unit vector calculation: read A Hat Unit vector is used to indicate direction

Two algorithms for geometric vector addition:

Method one: you start at one vertex and you shift two vectors to a parallelogram method two: you put all the vectors end to end, and you get the result from the beginning to the end

Mathematical representation

Vector calculation: dot product, cross product

The calculation rules of vectors are commutative law, associative law and distribution rate

Calculation rules in the coordinate system

Dot (dot product) :

Maximum effect of dot product:

  • Find the Angle between the two vectors

  • Find one vector to project to another (projection pronounced B perp

The dot product tells us that the direction between two vectors, >0 in the same direction, <0 in the opposite direction, is equal to 0 perpendicular

The cross product:

The third vector, c, is perpendicular to a and B, so it must not be in the same plane as AB and C can be computed using the right hand helical rule does not satisfy the commutative law

The vector cross itself, you get the 0 vector, because the Angle between sine theta is 0

What about the cross product

Vector cross product action:

  1. You can figure out whether one vector is to the left or the right of the other
  2. Vector AB cross AP, vector BC cross BP, and vector CA cross CP are all in the same direction, so P is inside the triangle formed by ABC, and vice versa

Define a frame, and put any vector in a frame

matrix

Matrix is defined

Matrix multiplication

Matrix algorithm (does not satisfy commutative law)

Transposed matrix

Identity matrix (used to compute inverse matrices)

Matrix representation of dot and cross products (A*b is the adjoint matrix)