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A Simple Method for Extracting the Natural Beauty of Hair. Ken-ichi Anjyo, Yoshiaki Usami, Tsuneya Kurihara Presented by Chris Lutz. “How many roads must a man walk down…”. Presentation Overview. The “Dr. B” presentation style:

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a simple method for extracting the natural beauty of hair

A Simple Method for Extracting the Natural Beauty of Hair

Ken-ichi Anjyo, Yoshiaki Usami, Tsuneya Kurihara

Presented by Chris Lutz

“How many roads must a man

walk down…”

presentation overview
Presentation Overview
  • The “Dr. B” presentation style:
    • I’ll just read the first sentence of each paragraph and try to wing it.
    • Next, I’ll write some vocab on the board.
    • Finally, I’ll scribble down some incomplete matrices and run out of time.
  • (I’m assuming Dave can take a joke.)
  • Man, it’s late. Wow.
real presentation overview
Real Presentation Overview

(It’s not all that much better, really)

  • How hair is actually represented and how it is allowed to move
    • WHAM! Whole lotta math comin’ atchya
  • Dynamic behaviors
    • Coordinate system
    • Inertia and force fields
  • Rendering Techniques & Results
philosophy and caveats
Philosophy and Caveats
  • This paper is concerned (oddly enough) with the “natural beauty” of hair.
  • To that end, the authors sacrifice some realism:
    • Physically-based simulation
    • Collision detection between hair & body as well as hair & other hair
    • Shadowing of hair onto itself
  • In a sense, they’re after pretty pictures
modeling process overview
Modeling Process Overview
  • 1. Create a model of a head
  • 2. Define an ellipsoidal hull
    • A rough approximation, yes, but not too bad
    • It’s faster for collisions & pore placement
  • 3. Calculate hair bending (cantilever beam)
  • 4. Cut and style as desired
    • Essentially, “blow-dry” the hair by applying various directional forces
not so touchably soft
Not So Touchably Soft
  • Hair is modeled as a series of segments connected at bending points
  • Apply some force to the beam and watch it deform
  • d2y/dx2 = -M/(E*I)
    • E: Young’s Modulus
    • I: 2nd momentum of area
get volume through math
Get Volume Through Math
  • Bending by “sequentially averaged concentrated loads”
  • Mi = -||g||d(1k-i+1p + 1k-ip)/2 = -||g||d(k-i+1)2/2
    • g: force on the hair
    • 1..k: number of segments in the hair
    • d: segment length
  • Displacement of node yi = (-1/2)*(Mi/E*I)*d2
  • 2D: define a new vector ei of magnitude yi
    • ei = pi-2pi-1 + yi
    • pi = (d/||ei||)ei + pi-1
  • New node pi = (d/||ei||)ei + pi-1
3d bending
3D Bending
  • Set up coordinate system
  • Use 2D deformation formulas along both a0 (x) and a2 (z) axes
  • The deflectional vector is is then just y1a1 + y2a2
avoiding the issue of hair piercing the skull
Avoiding the Issue of Hair Piercing the Skull
  • Since collision detection using the actual head model is hard, revert to using an ellipsoidal representation
  • Check every new pi for collision
    • If the new pi collides with the head, move it to a “close” point on the plane defined by pi-2, pi-1, and pi
    • Which way do you move it?
the taming of the do
The Taming of the ’Do
  • (a) Initial conditions: zero-g bed-head
  • (b) Gravity kicks in
  • (c) Apply external forces (blow-dry) the hair & cut (define y-threshold and pore location)
  • (d) Paul Mitchel would be proud
the answer my friend
The Answer, My Friend...
  • So we want to add wind; that means keeping track of inertia and applied forces
  • Again, some realism issues:
    • Hair is modeled as rigid segments connected with flexible joints
    • Hair-to-hair collisions & friction is not modeled in a physically correct manner
  • Use a pseudo force-field and solve differential equations
single hair dynamics
Single Hair Dynamics
  • Set up an initial polar coordinate system like the one to the right
  • Track the projection of the hair onto the  and  planes
more math stuff
More Math Stuff
  • i(t) = d2i/dt2 = ci ui F
  • i(t) = d2i/dt2 = ci vi F
  • Variables:
    • ci: reciprocal number of the inertia moment of si
    • ui: (1/2)||si||
    • vi: half of segment si projected onto  plane
    • F &F: the respective force components
still more math stuff
Still More Math Stuff
  • Given in-1 and in
  • in+1 = in+1-2in+in-1 = (t)2ciuiF
  • Similar thing for in+1
    • Outer loop is segment number I
    • Inner loop is time loop n
  • By selectively manipulating the ci’s, you can simulate frictional effects
  • You can also manipulate joint stiffness
hey look a dab of reality
Hey Look! A Dab of Reality!
  • We should try and keep track of the inertia moment of hair
    • kd: length of hair (k segments of length d)
    • : line density
  • IS = (1/3)(kd)2
  • Ii = (/3i)k3d2
  • Putting this in for (t)2ciui results in (3(t)2i) / (2k3d)
a bouncy hold all day long
A Bouncy Hold All Day Long
  • (a) 10,000 hairs of length <= 18
  • (b) F = (-200, 0, 0), 10th frame
  • (c) F = (-20, -250, 0), 15th frame
  • (d) 20th frame shows the effects of the force (wind) shift
pseudo force fields
Pseudo-Force Fields
  • Again, hairs could pierce the skull (bad)
  • Define a pseudo-force field to replace the specified force for hairs close to the head
  • Make this PsFF ellipsoidal to make it easier
pseudo force field definition
Pseudo-Force Field Definition
  • F: original user-specified force (wind)
  • Di: segment direction of si defined in terms of the ellipsoid
    • E(p): Di = (Ex(pi), Ey(pi), Ez(pi))
    • Ex, Ey, Ez: partial derivatives of polynomial
  • For some value (|| <= 1):
    • If (Di, F) < ||Di||||F|| then si is facing “into” F
    • If si is near the head, replace F with iF
    • (near pore) 0 <= i <= 1 (end of hair)
  • Ellipsoidal representation won’t always look good
lighting silky shiny
Lighting: Silky & Shiny
  • Diffuse term is neglected
  • Instead of polylines, assume the hair is cylindrical
  • s(P) = ks(1-(T,H)2)n/2
    • n: specular exponent
    • ks: reflection coeff.
  • Close to Phong shading
rendering time measures
Rendering & Time Measures
  • Use z-buffer algorithm to render the hair & linearly interpolate colors across segments (oversample if hairs are thin)
  • 20,000 hairs with <= 20 segments: 50 sec for modeling, “several” for rendering on a SG Iris Power Series w/ VGX gfx board
  • “The image with a different camera angle was obtained almost in real-time”
split ends closing issues
Split Ends (Closing Issues)
  • If you define (complicated) regional forces, you could create almost any hairstyle, right?
  • It seems hard to add any human touches, e.g. ponytails or dreadlocks.
  • In all honesty, when would anyone really care about the exact physics of hair?
  • It would be nice to have a shot of lighter-colored hair, just to see what it looked like.