Calculating Chain Rank

RANK Value Equation

RANK is the sorting key used to sort multiple chains that have a common node by their angle, starting from 0 at due east and proceeding counterclockwise. A node can be either of the two end-points of a chain.

RANK values have the form ffffff.tttttt, where the ffffff value is used to sort the chain around its from-node and the tttttt component is used to sort the chain around its to-node. The ffffff and tttttt components are calculated using the following formula:

[equation]

is the calculated ranking factor.

is the quadrant number (1 to 4, Quadrant Numbers) that contains the angle [alpha] for the chain. For the ffffff component, [alpha] is defined by the vector F [rarr] D₀, where F is the from-node and D₀ is the first detail point. For chains that have no detail points, D₀ is the to-node. For the tttttt component, [alpha] is defined by the vector T [rarr] D_L, where T is the to-node and D_L is the last detail point. For chains that have no detail points, D_L is the from-node.

is the angle from the chain clockwise to the nearest X or Y axis, and is determined with

[equation]

where

is the clockwise angle from the chain to the positive x-axis (due east).

The tangent term is called the half-angle tangent. Since the angle A/2 can never exceed [pi] /4 (45 degrees), the half-angle tangent has values from 0 to 1. The (Q-1) multiplier adjusts the range of values to 0 to 4. The values 0, 1, 2, 3, and 4 represent angles of 0, 90, 180, 270, and just under 360 degrees, respectively.