# Andrew Lines

Caltech alumni,
Fulcrum Microsystems founder,
Intel
Principal Engineer via acquisition. Likely to be found in
Portland, Oregon.

My Mom has a nice web page
too.

# Patents

Paste this into the Query box
at USPTO
Search and it will find (almost?) all of my issued patents. More
in the pipe of course.
IN/Lines-Andrew AND (AN/Microsoft OR AN/"California Institute of Technology" OR AN/Fulcrum OR AN/Intel)

# Asynchronous VLSI

My specialty is designing chips without clocks. I began in 1993 as
a Caltech undergrad, continued in the PhD program until 1999, then
founded Fulcrum Microsystems with Uri Cummings in 2000. After 12
years and 4 products, we were bought by Intel in 2011, where I remain.

Here are some chips from the Caltech days:

### Caltech MiniMIPS (1998)

# Mandelbrot Sets

I wrote my first Mandelbrot Set rendering program in high school.
It was very clever and computationally efficient. Recently I wrote
another version which is just brute force. But computers have come a
long ways since my 386/387. Here are a few really, really big plots:

### Zoom 1

### Zoom 2

### Zoom 4

### Zoom 5

### Zoom 6

More recently I added support for Julia sets and a full-color scheme:

### Julia 2

### Julia 3

# Minimal Surfaces

One day I got bored and rewrote a high school science project of
mine. It approximately solves for minimal area surfaces on parametric
boundary curves. This is the same shape you get with soap films on
a wire frame. Here are some nifty pictures:

### Catenoid

### Moebius strip

### Linked rings

### Wavy ring

### Very wavy ring

# CS 174 Project

Caltech's CS 174 involves writing a rendering and image processing
program. Some interesting pictures are linked below:

### Ray-traced spheres

### Ray-traced spheres

### Ray-traced spheres

### Ray-traced spheres

### Ray-traced spheres

### Ray-traced sphere and cube

### Ray-traced spheres (coolest)

# Beam Tracer

This was once planned to be part of Fulcrum's core technology, but
we quickly abandoned graphics to do networking. Someday I'd like to
finish this rendering algorithm. Fractals make great test cases since
you can easily scale up the polygon count. They also look cool. Also
I converted the polygons of a Quake2 level (Sewer64).

### Koch Snowflake

### Fractal Mountains

### Quake2 Sewer64 Level

# 3D Mouse Rotation Patent

This is patent for a software algorithm I invented while working
as an intern at Microsoft in the summer of 1991. It allows you to
grab the corner of a 3D graph and rotate it by dragging it with the
mouse. The particular improvement here is that the graph only rotates
about the X and Y axes (not Z), and the point you grab stays under the
mouse pointer (if possible). The movement is also easily reversible.
You used to be able to demo my coding of this algorithm in any copy of
Microsoft Excel, Graph, and Word since around 1992. However, they
removed my feature around 2010 about when the patent expried. There
was some wailing and gnashing of teeth on the webs.