One.
You can do this by using just one point. A point has three arguments, the X,Y and Z value, now imagine a plane through the (0,0,0) point. The X argument specifies the 'pitch' of the plane, the Y argument the 'roll' and the Z argument translates the plane over the Z-axis.
For example, when you define the Cartesian space as real values from 0-1, the point (0,0,0) defines a plane spanned by the X and Y axis. The point (0.5,0,0) defines the XY plane tilted at 45 deg up. The point (-0.5,0,0) defines the XY plane tilted down at 45deg. The point (-0.5,1,0) defines the plane perpendicular to the previous plane. Now when the plane does not intersect the z-axis at the (0,0,0) point just use the z-argument of the position where it does intersect the Z-axis.
While this function already lets you define most planes there are a few exceptions, these are planes parallel to planes described by 2 of the basis axis which do not cross the z-axis. A way to still describe these planes is to define an exception that whenever a plane is parallel to the X or Y axis, ie (1,0,0) or (0,1,0) the z-argument does not translate the plane over the X-axis but over respectively the Y or X axis.
I hope this makes some sense.
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Nicholas Piël
While i do believe it should be possible with just one point i dont think your solution is the correct one. You won't be able to describe planes that intersect the O-point (0,0,0). Maybe better luck next time;)
Slashdot Mirror
One. You can do this by using just one point. A point has three arguments, the X,Y and Z value, now imagine a plane through the (0,0,0) point. The X argument specifies the 'pitch' of the plane, the Y argument the 'roll' and the Z argument translates the plane over the Z-axis. For example, when you define the Cartesian space as real values from 0-1, the point (0,0,0) defines a plane spanned by the X and Y axis. The point (0.5,0,0) defines the XY plane tilted at 45 deg up. The point (-0.5,0,0) defines the XY plane tilted down at 45deg. The point (-0.5,1,0) defines the plane perpendicular to the previous plane. Now when the plane does not intersect the z-axis at the (0,0,0) point just use the z-argument of the position where it does intersect the Z-axis. While this function already lets you define most planes there are a few exceptions, these are planes parallel to planes described by 2 of the basis axis which do not cross the z-axis. A way to still describe these planes is to define an exception that whenever a plane is parallel to the X or Y axis, ie (1,0,0) or (0,1,0) the z-argument does not translate the plane over the X-axis but over respectively the Y or X axis. I hope this makes some sense. -- Nicholas Piël
While i do believe it should be possible with just one point i dont think your solution is the correct one. You won't be able to describe planes that intersect the O-point (0,0,0). Maybe better luck next time ;)