Reach and Spellcasting

[moon glum]

If a creature has reach and they cast a spell with, say, an area of effect that is a line or a cone, can the point of origin of the spell be any square within the creature's reach, or must it originate from a space that they occupy? For example, if an ogre mage with a 10' reach uses a cone of cold, can they choose as a point of origin for the cone of cold any point within 10' of the 10'x10' square that they occupy?

Similarly, can monsters with reach choose as a point of origin any point within the reach of the appropriate member? For example, can a dragon whose bite has a 15' reach choose as a point of origin for their breath weapon any point within the reach of their bite?

[Gisher]

CRB wrote:

Cone, Cylinder, Line, or Sphere: Most spells that affect an area have a particular shape.

A cone-shaped spell shoots away from you in a quarter-circle in the direction you designate. It starts from any corner of your square and widens out as it goes. Most cones are either bursts or emanations (see above), and thus won't go around corners.

...

A line-shaped spell shoots away from you in a line in the direction you designate. It starts from any corner of your square and extends to the limit of its range or until it strikes a barrier that blocks line of effect. A line-shaped spell affects all creatures in squares through which the line passes.

Both Cones and Lines start at your choice of any corner of your square. If you take up multiple squares the point of origin can be any corner of any square that you occupy. It is occupied squares that matter, not threatened squares.