“D System – Système” and “D Scale” for rating and grading backcountry ski and snowboard mountain descents
(edited by Louis Dawson and Andrew McLean)
(latest revision of this page: May, 2014) (Please leave your D System comments HERE.)
The “D System” described here is a linear method of rating, grading, or describing how difficult a slope is to ski or snowboard DOWNHILL, how dangerous the route is, and how long it takes to climb.
In other words, the D System COMPARES the difficulty and danger of routes to one another.
The term “D” is shorthand for words such as descendere, detail, détail, descent, détaillé, detalle, difficulty, descente, downhill, down, drop, difference, degree, etcetera. The word “detail” is the same in French, German and English, and is “detalle” in Spanish, so perhaps the D System could be called the DETAIL System if one wishes to be international, as said en français.
Before reading further, please be aware that the D System has three parts or scales:
- D Scale (détaillé, difficulty)
- R Scale (rischio, risk)
- Grade Scale (length of route, longueur d’itinéraire, as a roman numeral)
The D Scale is the most important part of the D rating and grading System (and may be used without the other scales). Routes are rated on the D Scale according to the difficulty of skiing or snowboarding — such difficulty varies mostly because of terrain features and slope angle, but many other factors play a part as well. Thus, most importantly, routes are rated by public consensus of how routes compare to each other as to technical difficulty (as in rock climbing ratings).
D0 – Flat ground or slightly rolling terrain.
D1– Easy low angled terrain such as beginner run at ski resort.
D2 – Angle around 25 degrees with simple topography.
D3 – Perhaps slightly steeper than D2, or may include more challenging terrain features.
D4 – Similar to an easier "Expert" run at a resort. Slope angles usually around 30 degrees.
D5 – Similar to an "Expert" run at a resort, steeper (35 degree range) or more terrain obstacles than previous rating.
D6 – Similar angles to previous, harder because it might have longer steep sections or complicating terrain features such as longer crux sections, dogleg turns, rollovers, trees, ridges, etc.
D7 – Change in angle category would usually occur here, to slopes probably around 40 degrees. Few terrain obstacles (e.g., steep sections not that long, no cliffs you have to work around, no runnels, easy tree skiing).
D8 – While similar in angle to a D7, terrain, angle or long crux sections make this harder than a D7.
D9 – Slopes probably around 45 degrees. Crux sections are short.
D10 – Slopes probably around 45 degrees, with a few complicating terrain features. This is the spot on the scale where true extreme skiing begins.
D11 – Slopes probably around 45 degrees, moderate amount of complicating terrain features.
D12 – Steeper, and/or complicating terrain features.
D13 – Steepest section probably around 50 degrees, moderate or no terrain obstacles.
D14 – Terrain more difficult, steep sections longer. Steepest section probably around 50 degrees.
D15 – Steepest section of route probably steeper than 50 degrees, harder than previous rating because of terrain, length of cruxes, or steeper angles.
D16 – Angles about the same as previous rating, steep sections may be longer or route has more terrain features.
D17 – Excessive terrain problems and/or steeper terrain (probably over or around 55 degrees) make this harder than previous level on D Scale.
D18 – Larger sections of the route may be steeper than 55 degrees, few or no terrain obstacles.
D19 – Similar angles to previous, extenuating circumstances and plentiful terrain obstacles make the route harder.
D20 – A number of sections probably just under 60 degrees, short sections may be 60 degrees. Little to no terrain obstacles.
D21 – Terrain obstacles common, and/or long sections of the route probably around 60 degrees steep.
D22 – Large sections of route are probably around 60 degrees, skiable snow is connected by technical maneuvers. Numerous terrain obstacles.
Difficulty “D” Rating Scale Explanation
In the D System, routes receive a “D Rating” on the “D Scale” (shown above) according to their toughest terrain and steepest angle. If a route has 3,000 vertical feet of low angle skiing, but starts with a 50 degree headwall above a bergschrund, it would be rated for the headwall and for negotiating the ‘schrund (though a route with a similar but longer crux section might rate one or two steps higher on the scale.)
Routes generally increase in difficulty on the D Scale as slope angle increases, but slope angle is only part of the picture. In other words, a route that’s a few degrees lower angled than another could actually rate higher on the scale if it had terrain features that made it tougher to descend. Thus, In the case of routes with similar slope pitches, terrain features and obstacles would ratchet a route higher or lower on the D Scale, but length of steep crux sections would play a part as well. Terrain features of concern include but are not limited to: tree skiing (open or tight), narrows, melt or avalanche runnels (if usually present), drops, cliff jumps, traverses to link sections of a route, narrows, mandatory rappels, etcetera.
Since this is a linear system of describing difficulty, some routes fall close to each other on the scale and their rating may be debatable. To help refine ratings, factors such as the total length of the route, length of the steep sections and amount of tough terrain may be considered as well. Again, as this is a linear system, public consensus will provide the final rating of routes. In other words, rating routes for the D Scale part of the D System should first be based on terrain features and slope angles, but should allow other factors to place the route in the continuum of the rating scale. In the end, just as in rock climbing difficulty ratings (5.x), eventually there will be little need to describe criteria for each rating, as numerous routes will serve as examples.
The D System is inclusive — it is designed to work with the diverse culture and languages of worldwide ski and snowboard alpinism. Hence it uses letters and numbers instead of any specific language (the letters “D” and “R” translate to numerous related words in many languages, see intro above). The D System is intended to work for routes anywhere in the world. More, all rating scales (grade, D and R) in the D System are open ended, thus allowing for development of the sport without re-rating routes to fit in a closed end scale, or contriving ways of extending a scale.
What Doesn’t Count on the D Scale
— The D Scale is NOT a rating scale for route length or approach length (see “Grade” below), though a route with a longer crux would generally rate higher than with a shorter but equally difficult crux.
— The D Scale is NOT a danger rating system (danger is rated with the R Scale explained below), but it still may communicate hazards intrinsic to the slope angle and terrain features. More, in the case of steeper routes, if two routes had everything else equal, but one involved extreme hazard such as skiing a few feet above certain-death cliffs or the possibility of a long sliding fall with no safe runout, such a route could be ratcheted up one D Scale grade higher since skiing such terrain is more difficult because it requires no-fall technique with limited maneuvering space. Conversely, objective hazards such as an icefall above the route have no influence on the D Scale rating of a route (but rather are rated with the R Scale covered below).
— The D Scale is NOT a slope angle rating system. While routes on the D Scale usually fit in angle categories such as “the 45 degree range,” a route could be slightly less steep than another yet still rate higher because of difficult terrain. In other words, there is some overlap in slope angle when routes are rated. Nonetheless, slope angle IS important, and overlap should only occur within smaller angle ranges. For example, a 30 degree route with tight trees (probably rated D5) could never rate higher on the scale than a 45 degree route with no terrain obstacles (probably a D9). If guidebook writers, alpinists or barstool conversationalists are concerned with exact slope angles, they can always append an exact slope angle to a rating, or include it in a route description. Another reason not to make a god out of slope angle is that it may never have been accurately measured, especially in the case of difficult routes that have only been done a few times.
Historical note about slope angles: In the formative days of extreme skiing it was all about slope angle, as most descents were done on open slopes or wider couloirs where angle was the determining factor of difficulty. Thus, it was easy to rate route difficulty based on slope angle alone, as is done with the S System (see end of this page). Today’s extreme skiing explores terrain where features other than slope angle frequently play a part in how hard a route is. Hence, a modern rating system must combine all factors to rate difficulty on a linear scale. Nonetheless, ski alpinists still tend to emphasize slope angle when communicating about routes, so it’s important to keep that in mind.
Route Length “Grade”
In the D System, routes optionally receive a Roman Numeral “Grade” rating for how long they take an average party to complete in average conditions — this is virtually the same as that commonly used in North American mountaineering ascent ratings. Again, know that while routes are rated on the D Scale mostly according to the difficulty of the hardest section of the route, a much longer route will tend to get a harder D Scale rating as well as a higher Grade rating.
Grade I routes are usually done in a few hours.
Grade II routes take about a half day for an average party.
Grade III means the trip requires a normal day.
Grade IV routes are the longest normally done without an overnight.
Grade V means the route requires a mega day or overnight.
Grade VI trips usually require a night out or a huge push.
Grade VII is reserved for routes such as those on Denali or Mount Everest.
See examples below for routes with length grade ratings. More than in climbing, the question of how much the approach is part of a ski route’s length grade will no doubt come up while rating ski routes. We’ll leave that detail up to locals and guidebook writers.
Risk “R” Scale
D System routes may also receive an optional risk rating that considers things such as potential for icefall, rockfall, crevasse danger, consequences of a fall on the route, avalanche terrain traps, rocky areas that tend to be hidden by thin snow, and so forth — but is not a rating for avalanche danger (snow instability). The “R” scale (standing for words such as rischio, risque, and riesgo) goes from 1 to 5.
R1 – Average backcountry ski routes, meaning the route has little to no objective hazard (other than possible avalanche danger that varies with the snowpack).
R2 – Slightly more inherent danger.
R3 – Route probably has sliding fall potential if snow is firm, moderate amount of obstacles or features that could cause injury, or moderate exposure to rockfall, tributary avalanches and other dangers.
R4 – Route has plentiful hazards such as fall potential, rockfall, crevasses, etcetera. etc.
R5 – Reserved for the most hazardous routes.
In the case of average backcountry routes the R Scale rating is optional, and in many cases might not be used.The “R” Scale is more subjective than any other part of the D System. As with all other parts of the D System, the R Scale is intended to compare routes to one another rather than giving a final word on how dangerous a route actually is (this could only be done in a narrative style guidebook description or trip report, if even then). And to repeat: the R scale is not an avalanche risk rating, though it does consider the probability of “tributary” avalanches that threaten the route from above, such as in the case of Himalayan climbing.
—- Municipal Golf Course Nordic Trails, Aspen, Colorado (I, D0)
[No R Scale rating for risk is necessary for this sort of terrain, using the”grade I” is also somewhat ridiculous, just as it would be when writing about or speaking of a short easy rock climb. In future writing, the risk rating may be revised due to cougars that young single men may meet on these trails.]
—- South Trees Aspen Forest, Huntsman Ridge, McClure Pass, Colorado
—- Big Emma, Snowbird Resort, Utah
—- Cabin Run, Loveland Pass, Colorado
—- Southeast Face, James Peak, Front Range, Colorado
—- Northern Slopes, Williams Peak, Glenwood Springs, Colorado (II D3 R1)
[In most cases the grade and R rating would be dropped from rating this short easy route]
—- Lakeview Avalanche Path, Buffalo Mountain, Gore Range, Colorado (II D4 R1)
—- South Slopes, Cardiff Pass, Alta, Utah (I D4 R1)
[As nearly every route in the Utah Wasatch is grade II, one would tend to drop the grade part of the rating, just as in rock climbing, you don’t refer to smaller climbs by including their grade along with the 5.x part of the rating.]
—- Ruby Gulch (SW Face) Grays Peak, Colorado
—- East Bowl, Marble Peak, Elk Mountains, Colorado
—- Standard Route, Ski Hayden, Elk Mountains, Colorado
—- Standard Route, Athabasca Glacier & Snow Dome, Rocky Mountains, Canada (V D5 R3)
[Snow Dome is an excellent example of a long and slightly more dangerous route that has nothing but moderate terrain. The hazard arises because of glacier travel and a section on the Athabasca where an icefall threatens skiers from above.]
—- East Slopes summit ski descent, Mount Elbert, Colorado
—- South Face, (Pinko or Redneck Gullies) Mount Democrat, Colorado
—- Avalanche Gulch, Mount Shasta, California
[Avalanche Gulch might rate higher if skied from exact summit.]
—- Emmons Glacier and summit ski descent, Mount Rainier, Washington (V D6 R3)
[Emmons gets more difficult as the crevasses open up, so D6 reflects “average” condition of route when most people would attempt to ski it in springtime]
—- Southwest Chute, Mount Adams, Cascades, Washington
—- Argenta Slide Path, Big Cottonwood Canyon, Utah
—- Suicide Chute, Little Cottonwood Canyon, Utah
—- Tuning Fork, Torreys Peak, Colorado, (via easiest entrance)
—- Be One, Highland Bowl, Highlands Ski Resort, Colorado
—- The Ribbon (splits NW face), Grays Peak, Colorado (III D7 R2)
—- Main Baldy Chute, Alta Resort, Utah
—- Y-Couloir, Little Cottonwood Canyon, Utah
—- Polar Star Couloir, Baffin Island
—- Red Slate Couloir, Red Slate Mountain, California
—- Silver Couloir (North Couloir), Buffalo Mountain, Gore Range, Colorado (II D8 R2)
—- Dana Couloir, Mount Dana, Sierra, California ( III D8 R2)
—- The Big Draw, San Gorgonio, Southern California
—- NE Face, Matier Peak, Southern Coast Mountains, Southwest British Columbia (III D8 R3)
—- South Face of Mt. Superior, Little Cottonwood Canyon, Utah (IV D9 R2)
—- North Face, Mount Democrat, Colorado
—- Little Chute, Alta Resort, Utah
—- Crystal Chute, Mount Sopris, Colorado (IV D9 R3)
—- Mount Tom, Elderberry Canyon (including upper steeper terrain), Sierra, California (IV D9 R3)
[Elderberry is another example of a route that’s mostly moderate terrain, but is rated for the crux. If Elderberry is skied without the upper headwall, it could be rated in the D6 range, and such could be mentioned in a guidebook.]
—- Bloody Mountain, Bloody Couloir, Sierra, California (III D9 R3)
—- Zeke’s Chute, Mount Baldy (San Antonio), Southern California
—- North Couloir, Mount Jepson, Southern California
—- Northeast Face via Brohm Ridge, Mount Garibaldi, Southern Coast Mountains, Southwest British Columbia
—- NW Face, Matier Peak, Southern Coast Mountains, Southwest British Columbia (IV D9 R3)
—- Hogback Couloir (Pearly Gates) summit ski descent, Mount Hood, Oregon
—- The Fuhrer Finger, Mt. Rainier, Washington (V D10 R3)
—- Deming Drop, Deming Peak (just W of Buffalo Mtn.), Gore Range, Colorado (III D10 R3)
—- Cristo Couloir, Quandary Peak, Colorado (III D10 R2)
—- Tuckerman Ravine (including headwall), Mount Washington, New Hampshire (III D10 R2)
—- Ellery Chute, Mount Dana, Sierra, California
—- Aussie Couloir, Joffre Peak, Southern Coast Mountains, Southwest British Columbia (IV D10 R3)
[This appears to be an almost perfect example of D10, the length grade is for the total trip, car-to-car.]
—- North Face of Mt. Buckner, North Cascades, Washington
—- Leuthold Couloir, Mount Hood, Oregon (III D11 R3)
—- Grunge Couloir, Provo, Utah
—- Mt. Mohl, Antarctica
—- Snake Couloir, Mount Sneffels, Colorado (rappel to enter)
—- Dostie’s Dare, Mount Baldy (San Antonio), Southern California
—- Messner Couloir, Denali, AK (V1 D12 R4)
—- NW Couloir, Pfiefferhorn, Little Cottonwood Canyon, Utah (rappel)
—- Orient Express, Denali, Alaska
—- North Face Cable Route, Longs Peak, Colorado
—- North Couloir (looker’s left on north face), Mt. Buckner, North Cascades, Washington
—- Northwest Face, Fissile Peak, Southern Coast Mountains, Southwest British Columbia (III D12 R3)
—- Dead Dog Couloir, Torreys Peak, Colorado
—- Edmunds Headwall/Mowich Face, Mt. Rainier, Washington
—- North Face, Mount Shuksan, Washington
—- Birthday Chutes (South Face), Mount Sneffels, Colorado (II D13 R4)
[Birthday Chutes are a very quick climb from a high trailhead, but the route is steep and a fall would put you over or in to numerous rock outcrops and cliff bands, hence the R4 rating]
—- North Face Northwest Ridge, Mount Adams, Cascades, Washington
—- Girly Man Chute, Mount Baldy (San Antonio), Southern California (I D13 R3) (a very short route with a very short crux brings this down one notch in the ratings, but it has a 50 degree crux so it hovers around D13)
—- Park Headwall, Mount Baker, Washington
—- CJ Couloir, Johannesburg Mtn., North Cascades, Washington (III D14 R4)
—- Skillet Glacier, Mount Moran, Tetons, Wyoming (VI D14 R3)
—- Castle Peak, East Face, Elk Mountains, Colorado
—- Mendel Couloir, Mount Mendel, California
—- Cooper Spur, Mount Hood, Oregon (III D15 R3)
[Cooper Spur is a good example of D Scale and R Scale ratings, as most of the route is moderate terrain, but it starts with technical skiing in the 55 degree range, at least one person has fallen and been killed while trying to snowboard the route, and at least 14 people have died on the route over past years .]
—- Stammberger Route, North Face, North Maroon Peak, Colorado (IV D15 R3)
[Stammberger Route has has several crux sections that are usually around 50 degrees, and terrain that’s more complex than most routes, so it rates higher on the scale.]
—- Ford/Stettner, Grand Teton, Wyoming (IV D16 R4)
—- East Face, Teewinot, Tetons, Wyoming
—- South Face, Castle Peak, Colorado (IV D17 R4)
[According to Peter Sowar, who did the first and second descents of Castle south face: “It definitely goes to 57 degrees , if not a touch more. As you enter the walled couloir the angle steepens to 50 and gradually gets steeper until you reach the left turn. The last 50 feet of this is at least 57. Then you make the traverse across rock and begin the southeast facing banana. This is between 50 and 55 for 400 feet, never dropping below 50 until near the top, where it may ease off to 45. So you are over 50 degrees for 800 feet with a max of 57 – 58. After you make the turn into the banana you are exposed to a nasty slide and will be launched over a big cliff to near certain death if you
fall or get pulled by a slough or slide. “]
—- North Face, Mount Robson, Canada (VI D18 R4)
—- Skyladder, Mount Andromeda, Canadian Rocky Mountains (V D18 R4)
—- Mount Fury, NE Face, North Cascades (V D18 R4)
—- Great White Icicle – Little Cottonwood, UT (rappel)
—- Glacier Route (from summit), Middle Teton, Tetons, Wyoming (V D19 R4)
—- Notch Couloir, Longs Peak, CO (IV D19 R4)
—- Landry Route, East Face, Pyramid Peak, Colorado (IV D20 R4)
—- North Face, Le Triolet, France
—- Southeast Couloir, South Teton, Tetons, Wyoming (V D21 R4)
—- Le Nant Blanc, North Face Aiguille Verte, Alps, France (V D21 R5)
[After his descent of this Jean Marc Boivin route (the second), Marco Siffredi said, ” The route started off…45°…until I reached a very exposed, 50° to 55° traverse underneath a ridge that lead to a little 50° to 55° gully. The gully carried out onto a 50° to 55° ramp, which ended at a 60-meter rappel past a vertical rock band. Just past the rock band is where I came to the steepest part of the route: 500 meters of 55° to 60° with a section of 65°. After that I came to another rock band where I had a little jump before making the final turns back to the rimaye…” from a Mountainzone.com article.]
—- South Col route, summit ski descent, Mount Everest (VII D21 R5)
—- Davenport-Beidleman, Capitol Peak, Colorado (V D21 R5)
[This route is rated high because of terrain features (rock steps and a transition over a rib) and technical moves on skis. It may rate a few grades lower with more snow cover than during the first descent. It gets an R5 because nearly anywhere on the route a fall would result in death.
—- Hossack/MacGowan, Grand Teton, Wyoming
—- Hornbein Couloir summit ski descent, Mount Everest
—- Mahogany Ridge, Crested Butte, Colorado (VII D23 R5)
Snow Conditions and Glisse Equipment
The D System ski and snowboard descent ratings assume the snow is in average condition for the given route, e.g., ice or breakable crust might make the route at least one grade harder than the indicated rating; perfect soft corn snow or perfect powder might make it one grade easier. All ratings assume the competent use of your chosen glisse method: telemark or latched heel skis, or snowboard. Remember this scale is based on terrain angle and features as well as perceived difficulty, thus allowing it to cross between different glisse methods. With this in mind, be advised that a D9 is still a D9 be your skis sharp or dull, the snow mank or ice — or you glisse one plank or two. (Nonetheless, just as in rock climbing one could say something like, “yeah, the couloir is rated D11, but it skied D14 because the whole thing was filled with blue ice.”)
The D System ski and snowboard rating method is based on the S System, which was first proposed for North American use by California guide Bela Vadaz, it was expanded by Louis Dawson in 1998 to include a +/- split for each level, and the expanded S System was first published in the Chuting Gallery by Andrew McLean. Andrew and others suggested that using plus and minus symbols was too confusing, and the system needed more divisions around the steeper angles, hence the D Scale using an open ended series of numbers. On first glance the D Scale may appear to have a confusing number of divisions. In reality, the most common backcountry ski terrain falls between D3 and D12 and thus only about 10 divisions are necessary to describe the vast majority of backcountry ski and snowboard routes around the world.
Other rating systems
Several other ski rating systems are in use. The Swiss Alpine Club system has 15 or 19 levels (depends on use of + or – qualifiers) designated by letters and numbers such as TD+, this is then combined with an S rating (see below) for slope angle. This results in a tedious and somewhat redundant rating that’s no more intuitive than anything else. More, the letter combinations are based on one language, French, and if you don’t speak French they look like gobbledygook. The Swiss system may be combined with the S System (otherwise known as the the Traynard) and thus ends up using two ratings where one could suffice. It has no specific danger scale or length scale.
Example: Mount Extremo, North Face TD+ S7.
The S System (incorporated into the Swiss system above, and also known as the Traynard) was the first ski and snowboard rating system to gain attention. It is based primarily on on slope angle and has seven levels. Over the past decade the S System was promulgated for use in North America, but never gained traction. With only seven levels it is severely limited in comparing one route to another (especially considering that harder routes are done every season, thus creating the need for more levels.) More, the difficulty of modern ski routes is defined by much more than slope angle, so rating them on angle alone is a dated method of limited use. More, the S System has no length or risk scale.
Louis Dawson modified the S System some time ago with plus and minus designators, to yield 21 levels. This was used in several North American guidebooks but never gained favor, and was confusing since it still used the “S” designator and was based on slope angles. The new D System grew out of the ashes of the modified S System.
Example: Mount Freeride, North Face, S8+
The Toponeige Ski Route Rating Grading System is complex and non intuitive, but is nonetheless popular in some circles. It includes a danger scale called “Expo” with four levels, again somewhat limited (Andrew and I feel that five danger grades are necessary to provide any real idea of how safe a route is). Possibly the worst problem with the Toponeige System is it attempts to categorize ski descents in five categories. While that sounds good on the surface, as the sport changes because of gear and technique such categories become meaningless and will force the re-rating of routes when they shift from one category to another.
Along with problematic categories, the Toponeige scale is only open ended by adding numbers to the top category 5, thus ending up with 5.1, 5.2, 5.3, 5.4, 5.5 and so forth. This is not a truly open ended scale as this top category doesn’t line up with the other categories, which only allow 4 subdivisions.
Potential confusion also arises because the Toponeige top level is similar to the YDS system of rock climbing rating, i.e, grade 5.4, 5.5 etc. Not only that, but it uses a ski ascent difficulty scale with the same designators as the Swiss Alpine Club grades for ski alpinism, yet according to Cairn Publishing even though these designators are the same “they do not describe the same thing.” We made this mistake with the modified S System (see above) and don’t care to see it repeated.
As a North American and a rock climber, I’m uncomfortable saying I skied a 5.6 route when I’m trying to communicate how hard the skiing was (that is unless I’m describing the ski descent of a rock climb, as in “I skied the North Face of Longs Peak, it’s a 5.4 rock route in the summer.” More, it is plain unwise to to use the same level designators as another ski rating system, but give them a different meaning. That’s why the D System uses the typical grades of one through seven (I to VII) for route length, and uses the same definition of those as one would for climbing.
(To prevent confusion, realize the D System of rating and grading backcountry skiing routes does not rate the difficulty of the ascent. We feel this is unnecessary in the case of ski descents and ski tours as the climb is frequently by a different route than the descent, the difficulty of the ski climb or approach can easily be inferred from route descriptions and common knowledge, and if the ascent route is a climb it can be rated with any of the numerous existing rating systems for alpine climbing.)
It’s said that the Toponeige System is better than the D System because it has fewer rating levels; that the D System’s 21 existing levels are too many and overly complex. To put that argument to bed take a hard look at the Toponeige and realize that if you used it to rate today’s top level descents you could probably find a few 5.7 routes — meaning the Toponeige would have 18 levels and such routes would go to about 22 on the D scale. The difference between 22 levels of the D System and 18 of the Toponeige is insignificant in terms of complexity, and a spurious argument as to why one system would be better or worse than the other.
Example of Toponeige: Mount Neige Extrême, North Face, Ski 5.7 TD- Expo 4.
With D System that would be something like V D18 R5
Special thanks to Neal Beidleman, Craig Dostie, Matt Gunn, Jason Hummel, Joel Levenberg, Ted Mahon, Sky Sjue, Pete Sowar, Stan Wagon, Stephen Ziff and many others for their help with feedback and examples.