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When any figure is moved in MK, you draw a straight pinpoint line from the dot to the max move of the figure. You may put the figure's dot anywhere on that line, as long as its base does not end up on top of figures, or in Blocking terrain.
The movement path of multi-dial figures can cross the base of single-dial figures without penalty, as long as the MDF is in a legal position at the end of the movement.
When moving any standard figure you draw a pinpoint line with a maximum length equal to the figure's Speed value. However, the line must go around blocking terrain features and other figure bases: it cannot move through them unless the figure has flight. This applies to Titans as well. Multi-dial figures can ignore the bases of figures having only one dial: may, in effect, move through them rather than around them.
You cannot move your Shade (or your Living Ballista) 12" in a straight line if the line will pass through my Lancer's base: you have to measure the movement around me. Your Chariot, on the other hand, can measure it's line of movement straight through my figure's base as long as when the movement stops you're not still on top of me.