A Simple Method for Extracting the Natural Beauty of Hair

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# A Simple Method for Extracting the Natural Beauty of Hair - PowerPoint PPT Presentation

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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Presentation Transcript

### 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:
• 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

(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
• 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
• 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
• 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
• 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
• 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
• 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
• (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
• 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
• 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
• 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
• 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!
• 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) 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
• 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
• 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
• 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.