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Hair and Fur Modeling


 
 

Hair and Fur Modeling 

Kelly Ward

Comp 259

Spring 2002


 
 

Overview 

  • Hair and fur animation used in movies, games, virtual reality, etc.
  • Problem due to complexity 
    • Human head has over 100,000 strands of hair
    • Computation time for simulation and rendering is costly
 
 

Overview 

  • Fur Modeling
    • Shorter Hair
    • Animals
 

Final Fantasy 

102 Dalmatians 

  • Hair Modeling
    • Longer Hair
    • People
 
 

Fur 

  • “Real-Time Fur over Arbitrary Surfaces”
    • Jerome Lengyel, Emil Praun, Adam Finkelstein, Hughes Hoppe
    • Proc. of ACM Simp. on Interactive 3D Graphics, 2001
  • Volume textures are rendered as series of semi-transparent concentric shells 
 
 

Fur 

  • Create shell texture:
    • Simulate virtual hair with a particle system
    • Sample it into volume texture
 
 

Fur 

  • Fur near silhouettes, render textured fins
 
 

Fur 

  • Render a series of textured, concentric shells, offset from the surface
 
 

Fur


 
 

Hair Modeling 

  • Different modeling techniques based on desired outcome
    • Speed vs. Appearance
    • Short vs. Long
    • Wavy vs. Straight
 
 

Individual Strands 

  • “A Simple Method for Extracting the Natural Beauty of Hair”
    • K. Anjyo, Y. Usami, and T. Kurihara
    • Computer Graphics, 1992
  • “Hair Animation with Collision Detection 
    • T. Kurihara, K. Anjyo, D. Thalmann
    • Models and Techniques in Computer Animation, 1993
 
 

Individual Hair Strands 

  • Each strand represented as a series of connected line segments
 
 

Strand of Hair 

  • Shape represented by angles specified between two segments
  • Polar coordinates
    • Zenith θi
    • Azimuth Φi
  • Specify resting position for hair as θ0 and Φ0
 
 

Polar Coordinate System


 
 

Polar Coordinate System 

Section 0 

Node 0 

Section 1 

Node 1 




Φ1 

θ1 

N1 

N2 



0 θ 180° 



0 Ф 360° 

Nodes, or control points, control the shape of the skeleton 

d


 
 

Mθ = Mθspring + Mθexternal

MΦ = MΦspring + MΦexternal 

Physics of Motion 

  • Apply forces to control points
  • Use torque for resulting motion of control points
    • Mθspring, MΦspring between two segments
    • Mθexternal, MΦexternal from external forces
      • Gravity, Wind
 
 

Physics of Motion 

Where kθ and kΦ are spring constants and θ0 and Φ0 are initial angles 

Where

  • u is (1/2)d,
  • d is the length of a segment of hair
  • v is the half length of the segment that is the projection of si onto the Φ plane.
 
 

Collision 

  • Hair-Hair collision ignored
  • Collision Detection with Head and Body 
    • Divide human body into several parts and create a cylindrical representation
      • Collision detection reduced to checking for control points inside or outside of cylinders
 
 

Collision 

  • Collision Reaction
    • Use lookup table and bi-linear interpolation to find normal vectors for collision response direction
    • Reaction constraint method by Platt and Barr 1988 is used:
 

N = normal vector at point T

V = velocity of point P

c = damping coefficient

k = strength of the constraint

Finput = applied force to node point P


 
 

Limitations of Method 

  • Simulating each strand very costly
  • Collision detection is just rough estimation
    • Can fail to detect collisions
      • Table Resolution
      • Some objects cannot be represented well as cylinder, particularly top of head
    • Cannot be applied to hair-hair collisions
 
 

Setup and Styling Hair


 
 

Results


 
 

Group Strands 

  • Strands close to each other behave similarly
  • Use some strands as a guide, interpolate position and motion of strands near it 
  • Save computation time 
 
 

Layered Wisp Model 

  • “A Layered Wisp Model for Simulating Interactions inside Long Hair”
    • E. Plante, M. Cani, P. Poulin
    • Proc. of Eurographics Workshop on Animation and Simulation, 2001
  • Strands are grouped together into a deformable wisp 
 
 

Layered Wisp Model 

  • Three Layers to Wisp
    • Skeleton Curve
      • Defines global motion and deformations
    • Deformable Envelope
      • Coats skeleton, defines deformations of wisp sections
    • Hair Strands
      • Individual strands of hair for rendering
 
 

Wisp Skeleton 

  • Defines global movements and deformations of wisp
  • Chain of point-masses linked by linear damping
  • Create motion by applying forces to point-masses
  • Similar to strand of previous works
 
 

Wisp Envelope 

  • Surrounds the skeleton and defines deformations of the wisp sections
  • Responsible for motion that occurs when the group of hair, or wisp, is stretched or compressed 
 
 

Wisp Envelope 

  • Broken up into cross-sections that are associated with each point-mass of skeleton
 
  • Shape of cross-section dependent on number of envelope point-masses used
  • Envelope point-masses linked to skeleton point-masses through damped springs 
 
 

Hair Strands 

  • Individual strands of hair are placed within the wisp for rendering
  • Strands placed randomly within cross-section of wisp, skeleton is origin 
  • Catmull-Rom piecewise cubic curves are used to define strands 
 
 

Collisions 

  • Interactions between wisps
    • Create bounding boxes around wisp segments
    • Test bounding boxes against each other to detect collision
      • Checks for penetration of envelope or skeleton point mass into another bounding volume
    • Wisp envelopes can be compressed depending on orientation of colliding wisps
      • If same orientation, allow collision
 
 

Collisions 

  • Check orientations of wisps
  • Determine if collision is allowed
    • If not, determine if a point-mass is inside the volume of another wisp section
 
  • Volume defined by two cross-sections
 
 

Collisions 

  • Interactions between wisp and person
    • Sliding Contact
      • Check point-mass close to body (within threshold)
      • Eliminate velocity of point-mass
    • Penetration Reaction 
      • If point-mass (either envelope or skeleton) collides with the body, move point-mass outside of body then use “sliding contact” method
 
 

Results 

  • http://w3imagis.imag.fr/Publications/2001/PCP01/long.mpg
 
 

2D Strips 

  • “A Simple Physics Model to Animate Human Hair Modeled in 2D Strips in Real Time”
    • C. K. Koh, Z. Huang
    • Proc. of Eurographics Workshop on Animation and Simulation, 2001
  • Group hairs into 2D strips represented as NURBS surfaces 
 
 

Physics of Motion 

  • Dynamic equations are defined and solved for the control points of the surface
  • Physics model used is same as previous examples
 
 

Setup of Hair 

  • Hair strands are represented in layers of strips overlaying each other to cover the head
  • Surfaces are texture mapped with hair images
  • Alpha map is used to define transparency
 
 

Setup of Hair


 
 

Collision Detection & Avoidance 

  • Hair strips and external objects (head)
    • Ellipsoids used to represent head
    • Similar to previous techniques
  • Hair strips and other hair strips 
    • Use avoidance
    • Springs between strips
      • Spring force used for either repulsion or attraction.
 
 

Fi = Σ(-ks * xs) 

Where ks is the spring constant and xs is the displacement from initial rest length, i is control point index, s is spring index


 
 

Results


 
 

NURBS 

  • NonUniform Rational B-Spline
  • Powerful tool in representing free-form shapes and common analytic shapes 
  • Drawback  
    • User has to manually adjust multiple control points & associated weights in order to design shapes
 
 

NURBS 

  • Curve
    • Combination of a set of piecewise rational functions with n+1 control points pi associated with weights wi
      • Bi,k(u) are B-spline basis functions 
         
         
         
      • Assuming basis functions of degree k-1, NURBS curve has n+k+1 knots
 
 

Dynamic NURBS 

  • Dynamic NonUniform Rational B-Spline
  • Physics-based models  
    • Brings time, mass, deformation energy into standard NURBS
  • Create curves by applying simulated forces and local and global shape constraints 
 
 

D-NURBS 

  • Curve
    • Function of spatial parameter u and time t:
      • Control points pi(t) and weights wi(t) are functions of time & are the generalized coordinates of D-NURBS 
         
         
      • Curve c(u,t) can be expressed as c(u,p) to emphasize dependence on vector p (which is a function of time)
 
 

Dynamic NURBS 

  • Incorporates dynamic behavior with geometric modeling for shape representation
  • Replaces connected line segments to give hair smoother, more realistic appearance 
 
 

Apply Forces


 
 

Simplified Representations 

  • Uses Levels of Detail (LODs) to speed up computation and rendering
  • Three Representations: 
    • Patch: D-NURBS surface
    • Cluster: Cylinders created with texture-mapped D-NURBS surfaces
    • Individual Strands: D-NURBS curves
 
 

Simplified Representations 

  • All three representations follow the same basic skeleton model for dynamic behavior
  • Change LOD based on number of criteria 
    • Distance to Camera
    • Occlusion
    • Placement on Head
 
 

Simplified Representations


 
 

Simplified Representations


 
 

Simplified Representations


 
 

References 

  • K. Anjyo, Y. Usami, and T. Kurihara.  A simple method for extracting the natural beauty of hair.  Computer Graphics, 26(2):111-120, 1992.
  • T. Kurihara, K. Anjyo, and D. Thalmann.  Hair animation with collision detection.  In Models and Techniques in Computer Animation, pages 128-38.  Springer-Verlag, 1993.
  • C. K. Koh and Z. Huang.  A simple physics model to animate human hair modeled in 2d strips in real time.  Proc. of Eurographics Workshop on Animation and Simulation, 2001.
  • E. Plante, M. Cani, and P. Poulin.  A layered wisp model for simulating interactions inside long hair.  Proc. of Eurographics Workshop on Animation and Simulation, 2001.
  • H. Qin and D. Terzopoulos.  D-NURBS: A physics-based framework for geometric design.  IEEE Transactions on Visualization and Computer Graphics, 2(1):85-96, March 1996.  ISSN 1077-2626.
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