Parallelized%20Real-Time%20Dynamic%20Simulation%20of%20Long%20Hair%20over%20Arbitrary%20Meshes

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Parallelized Real-TimeDynamic Simulation of Long
Hair over Arbitrary Meshes

• Stuart Golodetz

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What is hair simulation?

• Hair simulation is about physically modelling
  hair and seeing what happens when it is perturbed
  (by wind, for example).
• It involves three distinct activities hair
  shape modelling, hair rendering and hair
  dynamics.
• Hair shape modelling is concerned with how to
  model hair so that it has the right shape (e.g.
  short vs. long, straight vs. curly). The other
  two are self-explanatory.

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Why model hair?

• Two separate questions we want to model hair
  both because its inherently interesting and
  because it has similarities to strings, ropes and
  fibres.
• We want to model hair because without an
  appropriate underlying physical representation,
  rendered hair looks good but cant do anything
  interesting.

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State Of The Art (1)

• Modelling (particularly rendering) of short hair
  and fur is getting better all the time (see
  right).

• Modelling of longer hair remains a research
  problem.

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State Of The Art (2)

• Current research tends to produce impressive
  results in specific areas whilst avoiding dealing
  with others.
• There are documented approaches based on
  level-of-detail (LOD) ideas, computational fluid
  dynamics (CFD) and thin shell volumes (TSVs).
  Each method has different strengths and
  weaknesses.

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Aims

• Blue-skies research! The aim is to simulate as
  much hair as possible, with the greatest possible
  accuracy and speed.
• We want to see what happens when the hair is
  perturbed (e.g. by wind).
• We want to be able to specify properties of the
  hair, e.g. length, number density, etc.
• We want our implementation to be generic and
  flexible.

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Basic Design Physics

• We start with the physics kernel. Its purpose is
  to simulate a number of objects by applying
  type-specific numerical schemes to update their
  properties (e.g. position, velocity) from one
  time-step to the next.
• The physics kernel does not (and should not)
  worry about collision detection and response
  (CDR), which is application-specific and must be
  dealt with at a higher level.

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Basic Design Physics

• Each object in our system has a number of key
  points to which forces (which may vary with the
  system state) can be applied.
• The numerical schemes use these forces when
  calculating how to update the objects.
• In this design, springs are considered to be
  force appliers, that is, things which add forces
  to objects. (Disconnecting a spring would mean
  removing forces in this context.)

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Basic Design Hair Representation

• The hairs in our simulation are represented as
  chains of point masses, connected using linear
  and angular springs as shown.
• Linear springs apply a force (along their line of
  action) to each of the two objects they connect,
  calculated using Hookes Law.

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Basic Design Hair Representation

• Angular springs are used to prevent the hairs
  bending too much.
• They exert forces on points i-1 and i1 which
  have a restoring effect on the angle at point i.

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Basic Design Forces

• We model gravity, wind and (velocity-dependent)
  air resistance in the obvious way, by applying
  the relevant forces to each of the point masses
  which make up the hairs. The air resistance
  constant was determined empirically.
• There are (at most) seven forces acting on any
  one point mass gravity, wind, air resistance,
  two linear spring forces and two angular spring
  forces.

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Basic Design Hair Bases

• We introduce the concept of a hair base, which
  generalises heads, meshes, etc.
• The roots of the hairs are represented as key
  points on the hair base. A hair is connected to
  the hair base by connecting the closest point
  mass to the hair root with a linear spring.

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In Detail The Head Hair BaseRepresentation and
Coordinate Systems (1)

• The head is represented as an ellipsoid.
• In turn, we represent an ellipsoid as an
  orthogonal coordinate system, with its centre
  being the origin of that system.
• In the case of the head hair base, we call that
  system the heads local coordinate system.

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In Detail The Head Hair BaseRepresentation and
Coordinate Systems (2)

• We also define a polar coordinate system (f, ?)
  for distributing hair roots.
• This goes from f 0 at the top of the head, to f
  p at the bottom, and from ? 0 at the right of
  the head to ? p at the left.
• The point (f, ?) in polar coordinates corresponds
  to the local coordinate system point (cos ? sin
  f, sin ? sin f, cos f).

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In Detail The Head Hair BaseHair Root
Distribution

• To distribute the hair roots over the head, users
  specify intervals flow, fhigh and ?low,
  ?high over which hair should be distributed
  (this allows us to cover the back but not the
  front of the head, for instance).
• A uniform grid is generated and then random
  points are chosen in each grid square according
  to a user-specified number density function ?(f,
  ?).

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In Detail The Head Hair BaseHair Properties

• Hair properties such as length, colour, etc. can
  be specified as functions of the hair root
  position (f, ?).
• In practice, we tend to borrow an idea from the
  literature and interpolate user-specified values
  at the top, bottom, left, right, front and back
  of the head.

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In Detail The Head Hair BaseCollision Detection

• Since we have to simulate large numbers of hairs
  in real-time, collision detection and response
  needs to be cheap.
• We can get acceptable results by simply testing
  the individual point masses against a slightly
  expanded head. By keeping the points outside of
  this, we generally manage to avoid the hairs
  penetrating the actual head. Using more points
  provides better accuracy but carries a
  computational cost.

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In Detail The Head Hair BaseCollision Response

• When a collision is detected, we simply move the
  point away from the centre of the head until its
  outside the expanded head.
• This is unsophisticated, but fast.
• Our CDR approach provides reasonable results for
  a stationary head, but if the head can move then
  a better scheme is required.

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In Detail The Mesh Hair Base

• Many of our ideas generalise to arbitrary meshes.
• In particular, I have been simulating a
  long-haired penguin as a proof-of-concept.
• Collision detection and response requires
  additional work, as will be described shortly.

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In Detail The Mesh Hair BaseHair Root
Distribution and Properties

• The mesh for the penguin was constructed using
  Blender.
• The hair root distribution is specified by
  applying a special material to parts of the mesh
  which should have hair attached.
• Hair properties are specified by varying which
  material is applied.

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In Detail The Mesh Hair BaseCollision Detection

• We expand the penguin mesh using Blender to form
  a collision mesh (this can be less detailed).
• This mesh is then used to construct a BSP tree
  which we use for collision detection.

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In Detail The Mesh Hair BaseCollision Detection

• BSP trees (binary space partitioning trees)
  recursively divide space in two

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In Detail The Mesh Hair BaseCollision Detection

• We do our collision detection by recursively
  testing each hair point object against the BSP
  tree.
• Those objects that end up in a solid leaf of the
  tree (and are therefore inside the penguin) are
  then subjected to collision response.

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In Detail The Mesh Hair BaseCollision Response

• There is a BSP raycasting algorithm that allows
  us to find the point at which we first transition
  from solid to empty space (or vice-versa). We use
  this to move our penetrating point outside the
  mesh again.
• What ray direction to use is non-obvious. The
  negation of the objects velocity doesnt work
  well. In practice, we try several directions and
  pick the one which induces the smallest change in
  position.

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In Detail The Mesh Hair BaseCollision Response

• We dont want our collision response to change
  the length of the hair.
• That would change the sizes of the spring forces
  being applied and cause instability.
• We thus apply length constraints to maintain the
  hair length over collision response.

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Rendering Details

• We render the hairs as cubic splines. To do this,
  we have to interpolate the point objects at each
  frame. The interpolation process involves a
  matrix inversion, but we can cache the inverted
  matrix for each hair to speed things up.
• We use OpenGL Shading Language (GLSL) vertex and
  fragment shaders to get our Phong lighting
  effects.

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HairPen BendCoding for the Cell BE

• IBM are running a student competition to write
  code for the new Cell BE architecture, which is
  finding use in Sonys PS3.
• It has 1 primary and 8 secondary processors
  running in parallel. This makes it good for
  parallelizing simulation code.
• I am currently in the process of porting the Java
  code to C for my competition entry.

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Future Work

• The collision detection and response could do
  with more work.
• Accommodating hair base movement remains a
  challenge with this approach.
• In practice, Im planning to spend the rest of my
  DPhil on kidney cancer work, but hair modelling
  has been really interesting.