A hexagonal grid combat map is commonly used in GURPS. The conventions for using it are described in Chapter 12, Book 2 of the Basic Rules.
Under these rules a figure must always face one side of a “hex”. If a figure wishes to move in a direction other than the principle six this involves a non-linear path. In the real world people do make course changes of 45 or 90 degrees!
Many table-top games do not use squares or hexes. Movement distance is measured and figures are moved, independent of markings on the surface. An example of this is classic Car Wars. The grid on the map was just an aid and vehicles and figures could cross it at any vector.
Such a system can easily be adapted to GURPS. One inch/25mm per yard is a convenient scale and very suitable for readily available 25-32mm figures, which often have bases of an inch or smaller. Where Chapter 12 says “hex” or “movement point” “inch” can usually be substituted.
To keep things consistent with official rules, turns are in increments of up to 60 degrees, each 60 degree change of facing or part thereof costing one movement point or reducing total move by one inch. A 90 degree turn is therefore -2 inches of movement. Inch/ movement point costs for other actions and conditions are given on p.B387.
It may be useful to remember that one hour on a clock-face is 30 degrees and 60 degrees two hours.
When using these movement rules on a hex-map the GM may require any movement to finish within a hex. If a figure finishes more than halfway across a hex they occupy that hex. If they were halfway across or less the figure moves back to the hex they were leaving. If a figure is across multiple hexes use majority, least advantage, dice roll or narrative imperative as a guide. As I discuss in one of my books, rules should facilitate a story rather than hinder.
Scatter
The scatter rules on p.B414 use a d6 to move an object in one of six possible directions. If you require a more random system try this method, adapted from “The Rules With No Name”.
Near the point from which the object will scatter, cast two d6 of different colours. Visualize a line between the centres of the two dice. This is the angle at which the object will scatter. Treat the higher scoring dice as the “pointer head” to give the direction of scatter. If you roll a double treat the darker/ redder dice as the pointer.
