Simple Linear Algebra

Somewhere on the path between computer science and art inevitably lies the town of linear algebra: Vectors, rotations, matrices and so on. Field comes with a number of well-populated classes to make manipulating these things slightly less tedious. Here's a quick and incomplete set of examples to give you a flavor of Vector2, which is used to represent a point or a direction in 2d space:

v1 = Vector2() # a vector at 0,0
v2 = Vector2(1, -2.5) # a vector at 1, -2.5

#they act a lot like Python tuples
print v2[0], v2.x # prints 1, 1
print v2[1], v2.y # prints -2.5, -2.5

#which mean you can pass them to PLine methods using * notation
PLine().moveTo( *v2 ) # is the same as .moveTo(1, -2.5)

v3 = v1+v2 # vectors can be added
v4 = v2*2.0 # vectors can be scaled
v5 = v2*v1 # vectors can be element-wise multipled
v1 += Vector2(5,5) #vectors can be mutated in place

Vector2 also has all manner of useful methods:

v1.normalize() # makes the length 1
v1.rotateBy(1) # angle in radians
dot = v1.dot(v2) # dot product
angle = v1.angle(v2) # the angle between v1 and v2
v6 = v1.orthogonal() # a vector2 that's at right angles to this one
v1.projectOut(v2) # remove part of the vector that's pointing in the direction v2

v1.interpolate(v2, 0.25) # move 25% of the way towards v2

By convention, any method that doesn't have anything better to return, returns the Vector2 that it operated on. This means that you can chain things together:

print v1.normalize().scale(5).projectOut(v2)+v3

Likewise, Vector3, Vector4, Color4, VectorN (an 'any dimension' Vector). See also Quaternion.

"See also?" Yes, Field contains its best source of documentation about this kind of thing: autocompletion is always the most authoritative way of getting info on these kinds of classes. Since it reads the source files that are ultimately compiled into your Vector2, it's never out of date and always complete. Also, don't miss right-click "open in Eclipse" and "search openendedgroup.com/field" options in the text editor.

Finally, Vector2,3,4,N can be "sliced" as in Python lists:

v = Vector4(1,2,3,4)
print v[:] # prints [1,2,3,4]

v[:] = (4,3,2,1) # sets this vector to a new value
print v # prints [4,3,2,1]

print v[0:2] # prints [4,3]

This is sometimes very useful for setting the values inside a VectorX very tersely.