기본 수학

Dot Product ( Inner Product )

• result = ( Ax*Bx, Ay*By )
• |result| = |A|*|B|*cos(theta)

 

Cross Product ( Outer Product )

• |result| = |A|*|B|*sin(theta) (평행사변형넓이)
• dir(result) = A와B가 이루는 면의 normal vector ( 오른손법칙 )
• result = ( Ay*Bz-Az*By, Az*Bx - Ax*Bz, Ax*By - Ay*Bx )

 

Interpolation

Linear Inter. ( lerp ) : p(α) = p0 + α(p1 -p0)

Sphere Lerp ( Slerp ) : p(α) = ( qrt p0 ^  ( α ) ) * ( qrt p1 ^ ( 1 - α ) )

 

Affine Transform ( object basis - u, v, n )

SRT matrix ( scaling - rotation - translation ) for object space

Scaling / Rotation / Translation

만들땐 회전행렬 x3

역계산(값산출) 할떈 상위의 규칙에 따라 역행렬 산출-적용

( u*v = 0,  v*n = 0, n*u = 0 )

 

PreAttribute = position, normal

 

• [R | t] ( rigid motion )
  • pre-post 합동