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Water Droplet Simulation. Avneesh Sud. Problem. Realistic Animation of individual water droplets on surfaces Lot of work on ‘large’ water bodies (Napier-Stokes, Stam) Water droplets tougher Gravity Interfacial , surface tension Air resistance Accurate rendering

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  • Realistic Animation of individual water droplets on surfaces
    • Lot of work on ‘large’ water bodies (Napier-Stokes, Stam)
  • Water droplets tougher
    • Gravity
    • Interfacial , surface tension
    • Air resistance
    • Accurate rendering
  • Two Problems : Flow and Rendering
work presented
Work Presented
  • Kaneda93 : Water Droplets on Glass Plate
  • Kaneda96 : Droplets on a Curved Surface
flow of water droplets
Flow of Water Droplets
  • Physics studied by Janosi89
  • Droplet runs down glass plate if mass exceeds critical mass
  • Route of stream determined by impurities and presence of other droplets
  • Traces of water left behind on surface : “Wetting”
simulation of flow
Simulation of Flow
  • Surface divided into a nxn lattice
  • An affinity for water fi,jassigned to each lattice point
    • Depends on surface properties, impurities etc.
simulation of flow1
Simulation of Flow
  • When does droplet move?
  • Which direction does it move in?
  • What speed does it move with?
  • How much moves/left behind?
  • When does it stop?
critical mass
Critical Mass
  • Each lattice point associated with a mass mi,j
  • Droplet moves if

msc() is the static critical weight when inclination angle is 

direction of motion
Direction of Motion
  • From (i,j) to (i-1,j+1), (i,j+1) or (i+1,j+1)
  • If water exists in one of the 3 directions, then moves to that direction
    • If exists in more than 1 direction, then to (i,j+1)
    • If not exist in (i,j+1), then to direction with larger mass
  • If not exist in any direction, then tendency to move in direction (i+k,j+1) is

w1(,k) is the inclination weighting function

speed of water
Speed of water
  • Depends in wetness of new direction and inclination
  • Acceleration ai,j() can be dry acceleration ad() or wet acceleration aw(),

aw() > ad()

t is time from generation/collision

mass of moving water
Mass of Moving Water
  • Mass of remaining water m’i,jdepends on fi,j, mmin, mmax
  • Mass of water at new position
  • Conservation of mass and momentum
  • With no water ahead, decelerates and stops when mass is less than dynamic critical mass mdc()
  • Speed during deceleration given by
shape of droplet
Shape of Droplet
  • Shape of static droplet on glass plate determined by interfacial, surface tensions (de Gennes 85)
  • Dynamic droplets complicated – different contact angles at head & tail, several contact angles to minimize energy
shape of droplet1
Shape of Droplet
  • Approximated by a sphere
  • Radius of sphere dependent on mass
  • Background textures generated for environment mapping
    • Front face at higher resolution
  • Tracing reflected/refracted rays
    • Most rays either reflected or refracted : follow one principle direction
  • Determining pixel color using the background texture at the intersection point
curved surfaces
Curved Surfaces
  • Modeled as Bezier Patches
  • Discretized to a quad mesh – approximated by a plane
  • A more generic method that reduces discretization artifacts
critical mass1
Critical Mass
  • Movement Test : Sum of external (gravity, wind) forces greater than affinity force

Fi,j is the static critical force

s is degree of affinity coefficient

direction of motion1
Direction of Motion
  • “Roulette” of 8 adjacent meshes used
  • Probability assigned to each mesh
  • Using probabilities allows to simulate random ‘meandering’ of water
direction of motion3
Direction of Motion
  • Weight of each direction determined by
    • Newton’s Laws of Motion
    • Degree of affinity for water
    • Wetness of neighboring meshes
newton s laws
Newton’s Laws
  • Compute principle velocity vector VP from Newton's mechanics.

Solve to find position Pwhere droplet crosses boundary and the velocity VPat crossing point

newton s laws1
Newton’s Laws
  • Probabilities distributed between 2 nearest neighboring directions of VP (l, l+1)
  • Probability distributed to directions whose angle from VPis less than 90 deg

ckis degree of affinity in neighboring mesh

u(x) is unit step function

  • Probability distributed to directions whose angle from principle vector is less than 90 deg
    • Prevents a droplet from suddenly changing direction back to a wet spot

g(d*k) is a function to check wetness

determining direction
Determining direction
  • All 3 probabilities weighted and summed up

1 controls regularity, 2 controls meandering

  • Direction depends on generated random number r

p is the desired direction of movement

speed of travel
Speed of Travel
  • Project acceleration in direction of principle vector
  • Internal forces depend on affinity
mass of moving drop
Mass of moving drop
  • “Wetting” : Mass of remaining water

h(c) is a function for remaining water based on affinity

  • “Merging” : Follow conservation of mass, momentum
  • Make a discretized surface model, specify degree of affinity for each mesh element
  • Put new droplets at mesh points, specify weight and initial speed
  • Initialize timekeepers for all droplets to accumulate time taken for a droplet to travel from one mesh to another
  • If droplet moves, goto step (5) else repeat (4) for all droplets
  • Determine mesh droplet will visit next
  • Calculate time required for droplet to move to next mesh
  • Move the droplet to next mesh based on timekeeper value
  • Repeat steps (4)-(7) for all droplets till end of frame
  • Repeat (2)-(8) for duration of animation
  • Similar to glass plate –efficient bezier intersection tests used
  • Higher quality method based on metaballs
    • Efficient intersection between ray and metaball using bezier clipping
  • Janosi IM, Horvath VK Dynamics of Water Droplets on a Window Pane. Physical Review 40(9): 5232-5237 (1989)
  • De gennes PG. Wetting: Statucs and Dynamics. Rev. Mod. Phys. 57(3): 827-863 (1985)
  • Kaneda K, Kagawa T, Yamashita H. Animation of Wwater Droplets on a Glass Plate. Proc. Computer Animation’93: 177-189 (1993)
  • Kaneda K, Zuyama Y, Yamashita H, Nishita T. Animation of Water Droplet Flow on Curved Surfaces. Proc. PACIFIC GRAPHICS '96: 50-65 (1996).
  • Yu YJ, Jung HY, Cho HG. A New Rendering Techniques for Water Droplet using Metaball in the Gravitation Force. WCGS'98 (1998)