## `in_quadtree(point, C, W, CH)`

Traverses a quadtree in logarithmic time to find the smallest cell (and every other cell) containing a given point in 2D space.

Parameters:

Name Type Description Default
`point` `numpy double array`

Query point coordinates

required
`C` `numpy double array`

Matrix of cell centers

required
`W` `numpy double array`

Vector of half cell widths

required
`CH` `numpy int array`

Matrix of child indices (-1 if leaf node)

required

Returns:

Name Type Description
`i` `int`

Index of smallest cell containint P into C,W,CH (-1 means the point is not in the quadtree)

`others` `numpy int array`

others vector of integers to all other (non-leaf) cells containing P

#### Notes

Only works for 2D quadtree. 3D functionality is coming soon.

Examples:

TO-DO

Source code in `src/gpytoolbox/in_quadtree.py`
 ``` 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68``` ``````def in_quadtree(point,C,W,CH): """Find quadtree cell containing point Traverses a quadtree in logarithmic time to find the smallest cell (and every other cell) containing a given point in 2D space. Parameters ---------- point : numpy double array Query point coordinates C : numpy double array Matrix of cell centers W : numpy double array Vector of half cell widths CH : numpy int array Matrix of child indices (-1 if leaf node) Returns ------- i : int Index of smallest cell containint P into C,W,CH (-1 means the point is not in the quadtree) others : numpy int array others vector of integers to all other (non-leaf) cells containing P See Also -------- initialize_quadtree. Notes ----- Only works for 2D quadtree. 3D functionality is coming soon. Examples -------- TO-DO """ others = [] queue = [0] i = -1 # by default it's nowhere dim = C.shape[1] while len(queue)>0: # Pop from queue q = queue.pop(0) # Check if point is inside this cell if is_in_quad(point[None,:],C[q,:],W[q]): # If inside this cell, then add to otthers others.append(q) # Is it child? is_child = (CH[q,1]==-1) if is_child: # If it is, then we're done i = q break else: # If not, add children to queue queue.append(CH[q,0]) queue.append(CH[q,1]) queue.append(CH[q,2]) queue.append(CH[q,3]) if dim==3: queue.append(CH[q,4]) queue.append(CH[q,5]) queue.append(CH[q,6]) queue.append(CH[q,7]) return i, others ``````