Transcript L07A_Forces
Forces - basic physics Springs (Hooke’s law) Damping Gravity Friction - static and kinetic Viscosity Rick Parent - CIS682 Basic Physics f ma Accumulate forces, calculate acceleration f a m v' v a * dt Implicit assumption is constant acceleration over time slice p' p v * dt Rick Parent - CIS682 Integration For arbitrary function, f f (t 1) f (t ) f ' (t ) * dt We know the derivative (acceleration). We need to update the function based on derivative information Accuracy v. time slice Much mathematics about how to update f based on its derivative – Runga-Kutta integration – Implicit Euler integration – Etc. Rick Parent - CIS682 Springs (Hooke’s law) Spring’s rest length: exerts zero force Fspring kspring(x x rest ) x xrest F x F Rick Parent - CIS682 Spring Mesh Edges => springs Internal springs to stabilize shape Rick Parent - CIS682 Damping Calm down spring oscillations Fdamping kdampingv F (x x rest )kspring vkdamping Rick Parent - CIS682 Mass-Spring-Damper System Define point masses postion velocity mass force fixed? Define springs point 1 point 2 rest length kspring kdamper Multiple time samples per frame? Rick Parent - CIS682 Mass-Spring-Damper System For each point Initialize force with wind For each spring Calculate spring-damper force spring.point1.force += force spring.point2.force -= force For each point acc = gravity acc += mass/force newVel = velocity + acc*dt position += dt*(velocity+newVelocity)/2 velocity = newVelocity Rick Parent - CIS682 Randomize Controlled randomness adds more interest To initial values (positions, velocities) To force fields (wind direction, wind speed) To spring constants, masses To joint angles Proximal joints: lower amplitude Distal joints: higher amplitude Coordinate frequence and phase Rick Parent - CIS682 Angular Springs 1) Use dot product of normals (cosine) 2) Take inverse cosine and use angle 3) Place a linear spring between ends of triangles Rick Parent - CIS682 Constrain Forces (soft constraints) Create temporary restoring forces (springs) when constraint violated F F F Non-penetration Fix to surface Rick Parent - CIS682 Friction Supporting object Resting contact Fs F FN Normal force Static friction Fs usFN Rick Parent - CIS682 Friction Supporting object Resting contact Fk F FN Normal force Static friction Kinetic friction v Fs usFN Fk uk FN Rick Parent - CIS682 Gravity Gm1m2 Fgravity r2 aobject F mobject Gmearth 2 2 32 ft /s 9.8m /s rearth2 Rick Parent - CIS682 Viscosity Fv kv nv kv - depends on shape of object n - depends on properties of liquid For spherical object: kv 6r Terminal velocity - viscosity and gravity balance E.g., for sphere: mg 6rnv Rick Parent - CIS682