Posts Tagged ‘CGI’

Hair Maths 1: The curly problem with curly hair
May 6, 2015…………………………………………………………………………
More about Troy’s $million hair here. Hair statistics including how many hairs a human has on their head here.
Mathspig studied hair chemistry at uni. Tricky stuff. Put simply, hair is made of long strands of protein called keratin held together by sulphur (and some hydrogen) bonds. To curl hair, the keratin strands in the outer curve of each hair has to be stretched with curling tongs or hair curlers, heated and dried. The bonds in each hair reform with one side longer than the other … Hence, the hair curls like gift-wrap ribbon. But high humidity allows hair to reabsorb water and straightened hair just goes psycho curly again!
This excellent hair diagram comes from The Chemistry of Shampoo and Conditioner, in an article by EMMA Dux for the Royal Australian Chemical Institute
Some people are born with hair follicles that produce keratin at different rates across the follicle. They have curly hair. Hair perms chemically break and reform the sulphur bonds while the hair is held in small curlers (curly hair) or a very big curlers(relatively straight hair.) thus permanently curling the hair.
Here’s the Maths:
Curly hair looks like a 3D Helix.
More on 3D helix maths here
But, in fact, one strand of curled hair looks more like a spiral staircase.
The outer edge of the staircase is longer than the inner edge.
More helix maths here.
CHALLENGE:
Mathspig doesn’t expect Middle School students to plot a 3D Helix. But if they have started TRIGONOMETRY then they can see that the maths they are studying is used in CGIs for films and computer games in this case to generate realistic curly hair!!!! That’s cool. This maths was needed to model Merida’s curly hair in BRAVE.
SMARTY PANTS CHALLENGE:
Some middle school students could calculate some points on the helix.
Now students must be introduced to radians.
Simple EXPLANATION: Angles eg. 300 are not useful in calculations but fractions are very useful.
Eg. The circumference of a circle:
C = 2πr
Now imagine if you scan with a floodlight set at a radius of 1 km. So:
C = 2π
So the circumference is 2π.
You scan ¼ of a circle, the distance the light moves is ¼(2π)
or ½ π or 1.57 km (see below)
This measurement of an angle is in RADIANS.
00 = 0 circle = 0
450 = 1/8 circle = 2π/ 8 = 2 (3.14) /8 = 0. 79
900 = 1/4 circle = ½ π = ½ (3.14) = 1.57
1350 = 3/8 circle = ¾ π = ¾ (3.14) = 2.36
1800= 1/2 circle = π = 3.14
2250 = 5/8 circle = 5/4 π = 5/4(3.14) = 3.93
2700 = 3/4 circle = 3/2 π = 4.71
3150 = 7/8 circle = 7/4 π = 7/4 (3.14) = 5.50
3600 = 1 circle = 2π = 6.28
…………………………………………………..
You will find Cos tables at NASA Sine tables at Mathhelp
Answer here: Answers- 3D Helix Table
Advanced students may want to look at what the Uber Geek 3D Helix generating program at the free graph website PLOTLY here.

Hair Maths 2: Why CGI needs maths
May 6, 2015The challenge is to make CGI hair look real. This isn’t easy. Some CGI hair doesn’t need maths because it doesn’t move. Some CGI is just ugly. Eg.
More from the worst video game hair cuts ever here and here.
In the world of CGI hair, curly hair is the challenge. It is difficult to model.
According to Pixar animators:
Hair curls due to the way it is grown. Curly hair is almost like a ribbon, while straight hair is more tubular.
(Mike Seymour,Brave New Hair Fxguide)
You will find detailed maths used by Pixar to model Merida’s hair here.
So straight hair swishes and curly hair springs or bobs.
Ariel, the Little Mermaid, was meant to have curly hair, but animators stuck with a ‘flowing block’ of hair. Before Ariel Disney Princess often had up-dos.
Progress was made with Merida’s hair in the Disney/Pixar animation BRAVE. See BRAVE NEW HAIR WIRED and fxguide.
According to Rachel Gross of Wired Magazine in 2009 Chung’s team designed a new simulator named Taz, after the wild Looney Tunes character. It forms individual coils around computer-generated cylinders of varying lengths and diameters. The resulting locks stretch out when Merida runs but snap back into place as soon as she stops. Add a little randomness, some gravity, and more than 1,500 hand-placed corkscrews and flyaway wisps and voilà: hair with depth and texture viewers have never seen before. The result may look wild, but it’s not. “It’s very stylized, very controlled,” Chung says. No hair spray required.
Rachel Newar explained last year in the Scientific American that physicists have modeled the movement of a single curly hair.
But, co-author Pedro Reis, an assistant professor of mechanical engineering and of civil and environmental engineering at MIT noted. “ the geometry of a curly hair is highly nonlinear— a word we often use for something complicated.”
The model could also calculate curvature of steel pipes or other spooled material. “We were engineers trying to solve practical, useful problems from the start,” Reis says. “I’m not a professional hairstylist—I’m bald, actually.”
More @ Mashable Video here.
And, from Stanford, if you’ve ever been curious this is what a curly hair algorithm looks like ie. It is a computer program for curling graphic hair.