Physical Simulation of Tree Motion CS 658 BYU

Skip Right to the Branch Dynamics: Wind effect on branches Njoint = moment of the joint (ie torque applied to the joint) Lbranch = length of the branch Mjoint = mass of joint Awind = acceleration due to wind (stay tuned for details) Rjoint = elastic coefficient of the joint torque = length from rotation point cross perpendicular force. Akagi and Kitajima, “Computer Animation of swaying trees based on physical simulation” in Computers and Graphics 2006

Branch effect on other branches “this force is added to the wind forces applied directly to the joints of that parent branch” All the joints of the parent branch or just the one where it’s connected? Akagi and Kitajima, “Computer Animation of swaying trees based on physical simulation” in Computers and Graphics 2006

Branch structure Use 6 joints and 7 segments. Segments are stiff, joints rotate. Akagi and Kitajima, “Computer Animation of swaying trees based on physical simulation” in Computers and Graphics 2006

Acceleration due to wind A = “acceleration of the wind” I think that’s the acceleration of the branch due to wind. where A = F/M and F due to wind is given by the aerodynamic drag equation. F = ½ rho u^2 C A rho = air density u = velocity of object relative to fluid C = drag coefficient A = aerodynamic cross section In fluid simulation, this is conceptually easy to apply. In complex situations, that’s fairly complex to apply. So they approximate it.

Branches in the wind Akagi and Kitajima, “Computer Animation of swaying trees based on physical simulation” in Computers and Graphics 2006

Branches moving in wind Akagi and Kitajima, “Computer Animation of swaying trees based on physical simulation” in Computers and Graphics 2006

Branches moving in wind Akagi and Kitajima, “Computer Animation of swaying trees based on physical simulation” in Computers and Graphics 2006

Branches moving in wind Akagi and Kitajima, “Computer Animation of swaying trees based on physical simulation” in Computers and Graphics 2006

Global wind effect Akagi and Kitajima, “Computer Animation of swaying trees based on physical simulation” in Computers and Graphics 2006