Photorealistic Math

by Wayne Radinsky, Nov. 14, 2006

This doc gives some data points. Original XBox was 150 million polygons/second.

Game Consoles: A Specs Comparison of GameCube, PlayStation 2, XBox and others

This article gives 500 million polygons for XBox 360 and 125 million for the original XBox.

Q&A: The Xbox 360
The Xbox 360 can draw up to 500 million polygons per second to depict game scenes. By contrast the original Xbox's upper limit was 125 million.

Some more stats: PlayStation 2: Around 20 million polygons per second, Dreamcast: Around 3 million polygons per second, Nintendo 64: Around 150,000 polygons per second, PlayStation: Around 360,000 polygons per second (lacks comparable effects)

Polygon Power

This page says visual reality is 80 million polygons per picture (Catmull et al., 1984). If we wish photorealistic VEs at 10 frames/s, this translates into 800 million polygons/s. There is no current graphics hardware that provides this.

Computer Hardware and Software for the Generation of Virtual Environments

So reality == 80 million polygons/frame x frame rate. 10 frames/s is slow. Movies go at 24 frames per second (== 1.92 billion polygons/second), and television goes at 60 frames per second (== 4.8 billion polygons/second).

This page describes human vision system but does not describe how many photoreceptors are in the eye. Section on modelling is interesting too, shows different shading algorithms.

Basic Understanding of Virtual Reality Fundamentals

This page says there's approximately 120 million photoreceptors, 5-8 million are cones; the rest (vast majority) are rods.

Psych 129 - Sensory processes - Light and the eye

This page says there's about 130 million photoreceptors absorb light, yet roughly 1.2 million axons of ganglion cells transmit information from the retina to the brain. So there is immediately a dramatic compression of information going from the eye to the brain.

Visual system - Wikipedia

What's missing in all this is where does the "80 million polygons/frame" come from. It turns out that that is not, and cannot be, an exact figure. The reason is because the number of polygons needed varies depending on the distance to the object being viewed, its motion, and where it is in the field of view. This powerpoint presentation (55 slides) describes some of these issues:

Dynamic Level of Detail Tutorial

I'm going to proceed from here using the 80 million polygons == reality assumption.

Some "back-of-the-envelope" math:

Let's look at the XBox and XBox 360 as two data points.

XBox - launched November 15, 2001, 150 million polygons/second. (I'm going to use the figures given at launch for both boxes, assuming these represent the hardware specs and the number of polygons you get "in practice" is a little lower -- hopefully lower in the same proportions for both boxes.)

XBox 360 - November 22, 2005, 500 million polygons per second.

So, using only these 2 data points to keep the math simple:

• 4 years, 3.33 factor of increase,
• Annual increase == 35.1%
• Doubling time == 2.30 years

Time it will take to reach 4.8 billion polygons/second at 60 frames per second:

• Factor of 9.6 increase
• Should take 7.514 years (From XBox 360 launch date)
• That's May 29th, 2013 (the math here is probably a little more precise than is justified).
• A more accurate statement would be, photorealistic VR should arrive "sometime in 2013".

So now let's look at the "Worst Case Scenario" ...

If you assume 1 polygon for each photoreceptor in the eye, that gives you 130 million polygons/frame x 60 frames/second = 7.8 billion polygons/second as an absolute upper limit.

Doing the exact same calculations with 7.8 billion instead of 4.8 billion we get:

• Factor of 15.6 increase
• Should take 9.127 years (from XBox 360 launch date)
• That's January 8th, 2015 (the math here is probably a little more precise than is justified).
• So, photorealistic VR must arrive by at least "sometime in early 2015"

That's based on the XBox specs -- so we are talking about XBox 2015 here. XBox 2015 will be fully-photorealistic VR.

Taking both dates into account, I'm saying "Fully photorealistic VR will arrive between 2013 and 2015" should be a correct and accurate prediction.

Of course, there is a deep assumption here which is that the software people will figure out how to use all these polygons to make images that look like photographs and not like cartoons.

One time I saw a football game on TV in a store. But when I walked up to the TV and saw the football game up close, I realized it was actually a video game. From a great enough distance, it could fool me. And if you look at the computer animated movies, they are getting more realistic-looking all the time.

The fact that computers are aproaching photorealism, yet failing to achieve it, has led to the concept of "Uncanny Valley". This was talked about a lot after the release of the movie "The Polar Express", because the makers of the film tried very hard to make photorealistic characters, but because they didn't quite get there, a lot of people thought the caracters were "creepy" and thought the filmmakers should have made the film more cartoony. In order to get the right emotional response from the movie characters, they need to be either totally photorealistic or cartoony. The valley in between -- that's Uncanny Valley.

Actually the term "Uncanny Valley" predates modern video games and computer-animated movies. Wikipedia has a good article on the history

Uncanny Valley

As a postcript... I should mention I posted this analysis some months ago on the Bay Area Futurists list, and it was harshly criticized by some people on the grounds that:

1. I failed to take into account a double-exponential. (Ray Kurzweil believes Moore's Law is a double exponential rather than a single exponential. He also believes the doubling time is 12 months, which would cause photorealistic video games to arrive much sooner than 2015.)

2. The figure I used for Moore's Law, a 2.3 year doubling time, was too precise -- using 2 significant digits of precision was unjustified.

3. Now, I don't think the actual doubling time is too far from 2.3 years, because in 2000 I calculated the doubling time using Pentium performance numbers from an Intel press release where they talked about the last 10 years of the Pentium. But I will agree that more data points would be useful. I have a hard time believing Kurzweil's 12-month doubling time estimate (Kurzweil claims to have used a massive amount of data to calculate it) not just because my calculations are different, but just because at a subjective level it seems wrong -- computers *seem* to double in processing power every 2 years or so, not ever 1 year or so. Just my $0.02 though.