Computer Modelling Of Fallen Snow Paul Fearing University of British Columbia Vancouver, Canada

Goal

Introduction Related Work Snow Accumulation Snow Stability Implicit Function Validation Future Work Conclusion

Decomposition of Gravity

Global of the Snow Model Snow Location Snow Stability Snow Surface Wind

Snow Location Snow bridge across gaps Cornice and Overhang

Snow Location

Related Work Snows –Metaballs Stochastic Motion Snow Shadows Flow and Change Dust Accumulation

Related Work Three Major Models –Volume-based model –Surface-based model –Hybrid-based model

Volume-based model

Surface-based model

Hybrid-based model

Contribution Accumulation Model Stability Model

snow pipeline Overview of the snow pipeline Commercial software –Alias Wavefront 96 (Shader libraries, Rendering)

Entities World –Sky, Ground, wind, Original input model and allocated snow Model –The set of input polygons –Connected and Non-connected component Face –Primary structure

Entities Launch site Subdivision area (or Launch area)

Entities Edge group Drops

Entities Snow planes –Top snow planes (Triangular ) –Edge snow planes (Quadrilateral ) Avalanche Avalanche Flake –When an avalanche hits a drop, it is converted into a number of particles.

Snow Accumulation Occlusion Boundary –The “ Flake Flutter ” effect eventually produces an occlusion boundary between completely blocked and unblocked areas. Influence –Amount of snow –Closeness of the occlusion to the ground –Fluttering effect (wind )

Launch sites Shoot particles –This approach allow launch sites on each surface to emit a series of particles aimed upwards towards a sky bounding plane.

Launch sites –Whenever a launch site has a sufficiently different sky occlusion from an adjacent neighbor, a new launch site is added at the perturbed midpoint to be refine the transition. –Likewise, launch sites can be merged whenever all surrounding neighbors have identical sky occlusions.

Launch sites There is no stability in this example

Occlusion Boundary Transition Zone

Importance Ordering Resolution –How many launch sites the face needs. –How many particles each site should shoot. Determination –Order of site testing –Improve the resolution

Importance Ordering Completeness –Global approximation Area –To prevent missing occlusion, large area may need more particles per launch site and more initial sites. Neighborhoods –Add or remove the launch site.

Importance Ordering Limits –Prevent launch sites from increasing very complex occlusion boundaries. Steepness –Launch sites that are too steep to support much snow.

Importance Ordering Camera –Sites closer to the camera receive more particles, greater refinement and accuracy. User –“ Boring ” –“ Interesting ”

Launch Site Meshing Launch site surfaces are represented as triangles. (the original base models) All upwards-facing triangles are initially allocated at least one launch site. Additional launch sites are allocated base on the importance ordering of the surface.

Launch Site Meshing Launch sites are connected in the Delaunay triangulation, where each launch site is responsible for its own immediately surrounding Voronoi area.

Launch Site Meshing In practice, many surface are small and isolated (such as pine needle) Significant meshing occurs on large, connected surface (such as the ground)

Edge Groups Edge groups are primarily used for –Avalanche –Denoting sharp boundary –Snow may slide off from one edge group to another

Edge Groups Drops Bordered by XY silhouette edge (in red)

Edge Groups This graph show a model (knot ) that our meshing algorithm considers hard.

Initial Particle Distribution Final mesh Initial launch sites Final mesh Final launch sites

Snowflake Motion Have no experimental data –How flakes of various sizes and shapes move when dropped from a significant height. Provide some parameters to simulate snowflake motion.

Snowflake Motion Circumference (swirl) Radius (wiggle) Z step resolution

Snowflake Motion Changing a flake ’ s Z incremental test change the flake ’ s direction.

Snowflake Motion At each step –The value of is randomly chosen from a normal distribution. –“ Area of effect ” increases from 1 cm to 4 cm to 7 cm from left to right. = 1 cm

Wind The “ wind influence ” is essentially a velocity vector for every point x, y, z in space.

Intersection Bucketing Dividing the XY plane into a regular grid of buckets.

Locating Particles in the Sky

Writing in the Sky

Snow Stability All launch sites are initially stored by Z height plus accumulation. Angle of Repose (AOR) Fresh snow => 90 o Slush snow => 15 o

Stability Test 1. Compute AOR between s and all neighbors n i lower than s. 2. For each i with an AOR to steep to support snow, perform an obstacle test between s and n i. 3. Evenly shift snow from s to all neighbors n i. 4. Repeat steps 1 to 3 until no unstable neighbors left, or s is bare of snow.

Moving Snow over Edges

Implicit Function Each snow volume is converted into one of several different implicit function types. –Gap bridging, Edge bulges, Wind cornices

Implicit Function

Validation Validation of snow-covered scenes is hard. –Uncontrollable –Unknown environmental factors

Future Work Physically realistic Animation Time –Large model

Result