When cutting for plain sawn (aka flat sawn) which is the most common method today, a board is cut from the log, and then turned 90º before taking the next cut. This process is continued until the entire log is cut. The graining in plain sawn wood are at 0-30 degree angles, which create large open patterns on the face of the boards (referred to as the cathedral effect).
The sawing techniques for quarter sawn and rift sawn are very wasteful and inefficient. Most of the log is left unusable and the boards that are produced are generally very narrow. Because of these downfalls, rift sawn and quarter sawn are often cut together as rift and quarter sawn. In this sawing technique the log is still quartered, but then each quarter is cut along alternating sides producing about half rift sawn and half quarter sawn. This is very popular today because it produces the wide widths that the modern customer is looking for, while producing a very stable plank and keeping waste to a minimum.
Live sawn is the oldest method of cutting, but the newest to America. The most common method in Europe, is gaining popularity in the states. Instead of being cut to produce plain sawn, quarter sawn, or rift sawn wood, the log is cut straight through with each cut parallel to the last. This produces a mix of plain, quarter, and rift sawn woods (about of third of each) and eliminates virtually all waste. This method also yields wider boards making it very popular.