[Computer Animation] Catmull-Rom Spline

Catmull-Rom Spline

Without tangent vectors?

 

τ(타우)는 보통 0.5로 설정해준다.

 

Cubic Splines

 

• τ(타우) 값에 따른 그래프의 변화

 

Catmull-Rom Spline Properties

• Variation Diminishing
  • the curve in 2D space does not oscillate about any straight line more often than the control point polygon.
• $C^{1}$-continuity
• Local Controllability

 

Question

• Find a catmull-rom cubic spline interpolating the four key points with $\tau = 0.5$
• $p(t) = L_{0}(t)p_{0} + L_{1}(t)p_{1} + L_{2}(t)p_{2} + L_{3}(t)p_{3}$
  • $p_{0} = (0, 0)$
  • $p_{1} = (10, 10)$
  • $p_{2} = (15, 5)$
  • $p_{3} = (20, 15)$

 

Solution