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My rendering results using different shading models for different hair colors. (Right) Model of Kajiya and Kay. (Center) Model of Marschner et al.
(left) Generalized model of Zinke with multiple scattering. Hair models are courtesy of Walt Disney Animation Studios.

*Always click on the images to see the full resolution images!

Abstract

Photorealistic rendering of human hair has been a challenge in computer graphics for many years. These challenges include: coming up with a practical yet accurate light scattering model for individual hair fibers, handling the complex geometry of large number of hair fibers, properly simulating the global illumination and complex interaction of light and shadows between the hair strands, and overcoming aliasing problems due to the fine geometry of the hairs. In this paper, we present an overview of the physical and optical properties of human hair fibers, investigate the most prominent hair shading models, and at the end we critically analyze each shading model. We also briefly go over the approaches for simulating multiple scattering of light in hair rendering. We have implemented all of the shading models which have been discussed in the paper and we will discuss their strengths and weaknesses in detail. Furthermore, we discuss missing behaviors in current shading models compared to the experimental measurements and propose possible avenues of future research.

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[Kajiya and Kay 1989] Rendering fur with three dimensional textures.

My rendered results:

Click to enlarge

Kajiya and Kay's rendering results:

 
Rendered teddy bear using the three dimensional textures and
Kajiya and Kay's shading model. From [Kajiya and Kay 1989].

 

[Goldman 1997] Fake fur rendering.

My rendered results:

Click to enlarge

Goldman's rendering results:

 
A frame from the film 101 Dalmatians. (c) Disney 1996.
Only the two adult Dalmatians are photographs and all of the puppies in the
scene are rendered using Goldman's shading model. From [Goldman 1997]

 

[Kim 2002] Modeling, rendering and animating human hair

My rendered results:

Click to enlarge

Kim's rendering results:

 
Kim's rendering result. (left) Rendered image using Kim's shading model.
(right) Comparison with a photograph. From [Kim 2002].

[Marschner et al. 2003] Light scattering from human hair fibers

My rendered results:

Click to enlarge

Marschner et al.'s rendering results:

Comparison between (left) Kajiya and Kay's model, (center) model of Marschner et al.,
and (right) a photograph. From [Marschner et al. 2003].

 
A hair model under different illumination angles rendered by
the model of Marschner et al. From [Marschner et al. 2003].

 

[Zinke et al. 2004] Photorealistic rendering of blond hair

My rendered results:

Click to enlarge

Zinke's rendering results:

 
Zinke's shading model with multiple scattering [Zinke2004]

Comparison

Azimuthal Scattering Functions: 

Evolution of Azimuthal scattering functions:
(a) shows the azimuthal independent model of Kajiya and Kay, (b) shows the effect
of Goldman's refinements to the Kajiya and Kay's model. (c) shows the combined phase function of Kim model with the upper lobe being the
reflected component and the lower sharper lobe being the transmitted component, and (d) plots the physically based model of Marschner et
al. The gray plot which resembles a flipped heart is the R component, thre colored lower lobes present the TT component, and three colored
upper lobes which look like hearts represent the TRT component (glints), Zinke has used the azimuthal scattering function of Marschner et al.

Longitudinal Scattering Functions:

Evolution of longitudinal functions:
(a) Before the model of Marschner et al. (Kajiya and Kay, Goldman and Kim)
(b) After the model of Marschner et al. (Marschner et al. and Zinke)

Dark Hair

	Kajiya and Kay 1989	Goldman 1997	Kim 2002	Marschner 2003
R & TT
R & (TRT)
Our comparison between different shading models for rendering dark hair. Top row demonstrates the forward scattering effect and bottom row shows the  result of primary ( and secondary) highlight(s). A dark brown color has used as a diffuse component for the model of Kajiya and Kay, Goldman, and Kim. For the model of Marschner et al. no diffuse color has been used and all the coloration is due to absorption.

	Direct Illumination	Indirect Illumination	5th depth	10th depth
M a r s c h n e r
Z i n k e
Our comparison between the model of Marschner et al. and Zinke's generalized model. The effect of Zinke's generalizations becomes more visible  by increasing the recursion depth for simulating the multiple scattering effect.