Effects of Wind on Virtual Plants in Animation

Algorithm 2

The general algorithm for growth and movement of one leaf.

Global Initialize: 𝑡=0,𝑠₀=1,𝜃₀=0,ℎ₀=1,𝑑₀=1

       Choose a random type of leaf motion 𝑟∈{1,2,3}

Input: Time 𝑡, old leaf parameters (𝜃_𝑡−1,𝛽_𝑡−1,𝜓_𝑡−1,𝜑_𝑡−1), wind speed 𝑤

Output: New leaf parameters (𝜃_𝑡,𝛽_𝑡,𝜓_𝑡,𝜑_𝑡), thickness (ℎ_𝑡), and radius (𝑑_𝑡)

 If 𝑤>𝑐_𝑝𝑡_𝑝 or 𝑤>𝑐_𝑏𝑡_𝑏, that is, if the wind exceeds the maximum tensile strengths of the

 petiole (𝑡_𝑝) or blade (𝑡_𝑏), then exit because the leaf is no longer attached.

 𝜃_𝑡=𝜃_𝑡−1, 𝛽_𝑡=𝛽_𝑡−1, 𝜓_𝑡=𝜓_𝑡−1, and 𝜑_𝑡=𝜑_𝑡−1

 If 𝑟=1

   If 𝑡_𝑝 ≤ 𝑡_𝑏,

     Bend the petiole at the petiole center of rotation

     (See (10) and (11))

   else

     Bend the leaf blade at the leaf center of rotation

     𝛽_𝑡=𝛽_𝑡−1+𝑠_𝑡𝑤𝑐_𝛽Δ𝑡 ((11) with β instead of θ)

 else if 𝑟=2

   Twist the leaf (see (12) and (13))

 else if 𝑟=3

   Vibrate the leaf at the leaf center of rotation (see (14) and (15))

 Calculate the leaf thickness (see (16))

 Calculate the leaf radius (see (17))