Module: Geospatial::Hilbert

Defined in:
lib/geospatial/hilbert.rb,
lib/geospatial/hilbert/curve.rb

Defined Under Namespace

Classes: Curve

Class Method Summary collapse

Class Method Details

.map(hilbert_axes, bits) ⇒ Object

Given the coordinates of a point in N-Dimensional space, find the distance to that point along the Hilbert curve. That distance will be transposed; broken into pieces and distributed into an array.

The number of dimensions is the length of the hilbert_index array.

Parameters:

  • hilbert_index —

    Point in N-space.

  • bits —

    Depth of the Hilbert curve. If bits is one, this is the top-level Hilbert curve.

Returns:

  • The Hilbert distance (or index) as a transposed Hilbert index.



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# File 'lib/geospatial/hilbert.rb', line 83

def self.map(hilbert_axes, bits)
	x = hilbert_axes.dup
	n = x.length # n: Number of dimensions
	m = 1 << (bits - 1)
	
	# Inverse undo
	q = m
	while q > 1
		p = q - 1
		i = 0
		
		while i < n
			if (x[i] & q) != 0
					x[0] ^= p # invert
			else
				t = (x[0] ^ x[i]) & p;
				x[0] ^= t;
				x[i] ^= t;
			end
			
			i += 1
		end
		
		q >>= 1
	end # exchange
	
	# Gray encode
	1.upto(n-1) {|i| x[i] ^= x[i-1]}
	
	t = 0
	q = m
	while q > 1
		if x[n-1] & q != 0
			t ^= q - 1
		end
		
		q >>= 1
	end
	
	0.upto(n-1) {|i| x[i] ^= t}
	
	return x
end

.unmap(transposed_index, bits) ⇒ Object

Convert the Hilbert index into an N-dimensional point expressed as a vector of uints.

Parameters:

  • transposed_index —

    The Hilbert index stored in transposed form.

  • bits —

    Number of bits per coordinate.

Returns:

  • Coordinate vector.



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# File 'lib/geospatial/hilbert.rb', line 41

def self.unmap(transposed_index, bits)
	x = transposed_index.dup #var X = (uint[])transposedIndex.Clone();
	n = x.length # n: Number of dimensions
	m = 1 << bits
	
	# Gray decode by H ^ (H/2)
	t = x[n-1] >> 1 # t = X[n - 1] >> 1;
	
	(n-1).downto(1) {|i| x[i] ^= x[i-1]}
	x[0] ^= t
	
	# Undo excess work
	q = 2
	while q != m
		p = q - 1
		
		i = n - 1
		while i >= 0
			if x[i] & q != 0
				x[0] ^= p # invert
			else
				t = (x[0] ^ x[i]) & p;
				x[0] ^= t;
				x[i] ^= t;
			end
			
			i -= 1
		end

		q <<= 1
	end
	
	return x
end