Geometric Interpretation of Hermite-Coons curves If we make the following substitutions R O R(1)=a1t(1) where t(a) is the unit tangent of the curve, the following observations can be made from Figure 4.5, relating the coefficients ao and an to the shape of the curve const= bias towards t(O) ·a1↑,ao= const→ bias towards t(1) a0,a1↑→ increase fullness ao, a1 both LARGE cusp forms(R(u)=0) or self-intersection occurs ao Increasing t(1) R(0) R(1) a0, a1 Increasing simultaneously R(1) R(0) t(1) Figure 4.5: Fullness of a Hermite-Coons curve Due to the importance of choosing ao and an appropriately, the Hermite-Coons represen- tation can be difficult for designers to use efficiently, but is much easier to understand than the Ferguson or monomial fornGeometric Interpretation of Hermite-Coons curves. If we make the following substitutions: R˙ (0) = α0t(0) R˙ (1) = α1t(1) where t(u) is the unit tangent of the curve, the following observations can be made from Figure 4.5, relating the coefficients α0 and α1 to the shape of the curve: • α0 ↑, α1 = const ⇒ bias towards t(0) • α1 ↑, α0 = const ⇒ bias towards t(1) • α0, α1 ↑ ⇒ increase fullness • α0, α1 both LARGE ⇒ cusp forms (R˙ (u ∗ ) = 0) or self-intersection occurs R(1) t(0) R(0) t(1) simultaneously α0, α1 increasing α1 constant α0 increasing t(1) t(0) R(0) R(1) Figure 4.5: Fullness of a Hermite-Coons curve. Due to the importance of choosing α0 and α1 appropriately, the Hermite-Coons represen￾tation can be difficult for designers to use efficiently, but is much easier to understand than the Ferguson or monomial form. 6