"""
N-D Bresenham line algo
"""
import numpy as np
def _bresenhamline_nslope(slope):
"""
Normalize slope for Bresenham's line algorithm.
>>> s = np.array([[-2, -2, -2, 0]])
>>> _bresenhamline_nslope(s)
array([[-1., -1., -1., 0.]])
>>> s = np.array([[0, 0, 0, 0]])
>>> _bresenhamline_nslope(s)
array([[ 0., 0., 0., 0.]])
>>> s = np.array([[0, 0, 9, 0]])
>>> _bresenhamline_nslope(s)
array([[ 0., 0., 1., 0.]])
"""
scale = np.amax(np.abs(slope), axis=1).reshape(-1, 1)
zeroslope = (scale == 0).all(1)
scale[zeroslope] = np.ones(1)
normalizedslope = np.array(slope, dtype=np.double) / scale
normalizedslope[zeroslope] = np.zeros(slope[0].shape)
return normalizedslope
def _bresenhamlines(start, end, max_iter):
"""
Returns npts lines of length max_iter each. (npts x max_iter x dimension)
>>> s = np.array([[3, 1, 9, 0],[0, 0, 3, 0]])
>>> _bresenhamlines(s, np.zeros(s.shape[1]), max_iter=-1)
array([[[ 3, 1, 8, 0],
[ 2, 1, 7, 0],
[ 2, 1, 6, 0],
[ 2, 1, 5, 0],
[ 1, 0, 4, 0],
[ 1, 0, 3, 0],
[ 1, 0, 2, 0],
[ 0, 0, 1, 0],
[ 0, 0, 0, 0]],
<BLANKLINE>
[[ 0, 0, 2, 0],
[ 0, 0, 1, 0],
[ 0, 0, 0, 0],
[ 0, 0, -1, 0],
[ 0, 0, -2, 0],
[ 0, 0, -3, 0],
[ 0, 0, -4, 0],
[ 0, 0, -5, 0],
[ 0, 0, -6, 0]]])
"""
if max_iter == -1:
max_iter = np.amax(np.amax(np.abs(end - start), axis=1))
npts, dim = start.shape
nslope = _bresenhamline_nslope(end - start)
# steps to iterate on
stepseq = np.arange(1, max_iter + 1)
stepmat = np.tile(stepseq, (dim, 1)).T
# some hacks for broadcasting properly
bline = start[:, np.newaxis, :] + nslope[:, np.newaxis, :] * stepmat
# Approximate to nearest int
return np.array(np.rint(bline), dtype=start.dtype)
def bresenhamline(start, end, max_iter=5):
"""
Returns a list of points from (start, end] by ray tracing a line b/w the
points.
Parameters:
start: An array of start points (number of points x dimension)
end: An end points (1 x dimension)
or An array of end point corresponding to each start point
(number of points x dimension)
max_iter: Max points to traverse. if -1, maximum number of required
points are traversed
Returns:
linevox (n x dimension) A cumulative array of all points traversed by
all the lines so far.
>>> s = np.array([[3, 1, 9, 0],[0, 0, 3, 0]])
>>> bresenhamline(s, np.zeros(s.shape[1]), max_iter=-1)
array([[ 3, 1, 8, 0],
[ 2, 1, 7, 0],
[ 2, 1, 6, 0],
[ 2, 1, 5, 0],
[ 1, 0, 4, 0],
[ 1, 0, 3, 0],
[ 1, 0, 2, 0],
[ 0, 0, 1, 0],
[ 0, 0, 0, 0],
[ 0, 0, 2, 0],
[ 0, 0, 1, 0],
[ 0, 0, 0, 0],
[ 0, 0, -1, 0],
[ 0, 0, -2, 0],
[ 0, 0, -3, 0],
[ 0, 0, -4, 0],
[ 0, 0, -5, 0],
[ 0, 0, -6, 0]])
"""
# Return the points as a single array
return _bresenhamlines(start, end, max_iter).reshape(-1, start.shape[-1])
if __name__ == "__main__":
import doctest
doctest.testmod()
Diff to Previous Revision
--- revision 1 2012-04-25 21:44:27
+++ revision 2 2012-05-16 16:15:04
@@ -2,20 +2,20 @@
N-D Bresenham line algo
"""
import numpy as np
-def bresenhamline_nslope(slope):
+def _bresenhamline_nslope(slope):
"""
Normalize slope for Bresenham's line algorithm.
>>> s = np.array([[-2, -2, -2, 0]])
- >>> bresenhamline_nslope(s)
+ >>> _bresenhamline_nslope(s)
array([[-1., -1., -1., 0.]])
>>> s = np.array([[0, 0, 0, 0]])
- >>> bresenhamline_nslope(s)
+ >>> _bresenhamline_nslope(s)
array([[ 0., 0., 0., 0.]])
>>> s = np.array([[0, 0, 9, 0]])
- >>> bresenhamline_nslope(s)
+ >>> _bresenhamline_nslope(s)
array([[ 0., 0., 1., 0.]])
"""
scale = np.amax(np.abs(slope), axis=1).reshape(-1, 1)
@@ -25,52 +25,46 @@
normalizedslope[zeroslope] = np.zeros(slope[0].shape)
return normalizedslope
-def bresenhamline_step(start, normalizedslope, err):
+def _bresenhamlines(start, end, max_iter):
"""
- Performs a single incremental step according to Bresenham's algorithm.
+ Returns npts lines of length max_iter each. (npts x max_iter x dimension)
- >>> s = np.array([[4, 4, 4, 0]])
- >>> ns = bresenhamline_nslope(np.array([[-2, -2, -2, 0]]))
- >>> e = np.zeros((1, 4))
- >>> bresenhamline_step(s, ns, e)
- (array([[ 3., 3., 3., 0.]]), array([[ 0., 0., 0., 0.]]))
+ >>> s = np.array([[3, 1, 9, 0],[0, 0, 3, 0]])
+ >>> _bresenhamlines(s, np.zeros(s.shape[1]), max_iter=-1)
+ array([[[ 3, 1, 8, 0],
+ [ 2, 1, 7, 0],
+ [ 2, 1, 6, 0],
+ [ 2, 1, 5, 0],
+ [ 1, 0, 4, 0],
+ [ 1, 0, 3, 0],
+ [ 1, 0, 2, 0],
+ [ 0, 0, 1, 0],
+ [ 0, 0, 0, 0]],
+ <BLANKLINE>
+ [[ 0, 0, 2, 0],
+ [ 0, 0, 1, 0],
+ [ 0, 0, 0, 0],
+ [ 0, 0, -1, 0],
+ [ 0, 0, -2, 0],
+ [ 0, 0, -3, 0],
+ [ 0, 0, -4, 0],
+ [ 0, 0, -5, 0],
+ [ 0, 0, -6, 0]]])
+ """
+ if max_iter == -1:
+ max_iter = np.amax(np.amax(np.abs(end - start), axis=1))
+ npts, dim = start.shape
+ nslope = _bresenhamline_nslope(end - start)
- >>> s = np.array([[0, 0, 9, 0]])
- >>> ns = bresenhamline_nslope(-1 * s)
- >>> e = np.zeros((1, 4))
- """
- nextpoint = start + normalizedslope + err
- nextvox = np.rint(nextpoint)
- err = nextpoint - nextvox
- return nextvox, err
+ # steps to iterate on
+ stepseq = np.arange(1, max_iter + 1)
+ stepmat = np.tile(stepseq, (dim, 1)).T
-def bresenhamline_gen(start, end):
- """
- Returns a generator of points from (start, end] by ray tracing a line b/w
- the points.
- Parameters:
- start: An array of start points (number of points x dimension)
- end: An end points (1 x dimension)
- or An array of end point corresponding to each start point
- (number of points x dimension)
+ # some hacks for broadcasting properly
+ bline = start[:, np.newaxis, :] + nslope[:, np.newaxis, :] * stepmat
- Returns:
- A generator that returns a point being traversed at each step
- corresponding to each start point.
-
- >>> [p for p in bresenhamline_gen(np.array([[3, 1, 3, 0]]), np.zeros(4))]
- [array([[2, 1, 2, 0]]), array([[1, 0, 1, 0]]), array([[0, 0, 0, 0]])]
- """
- dim = start.shape[1]
- err = np.zeros(start.shape)
- slope = np.array(end - start, dtype=np.float32)
- nslope = bresenhamline_nslope(slope)
- cur_vox = start
- while (np.sum(nslope != 0)):
- cur_vox, err = bresenhamline_step(cur_vox, nslope, err)
- # reached end ?
- nslope[(np.abs(end - cur_vox) < 1).all(1)] = np.zeros(dim)
- yield np.array(cur_vox, dtype=start.dtype)
+ # Approximate to nearest int
+ return np.array(np.rint(bline), dtype=start.dtype)
def bresenhamline(start, end, max_iter=5):
"""
@@ -81,40 +75,37 @@
end: An end points (1 x dimension)
or An array of end point corresponding to each start point
(number of points x dimension)
- max_iter: Max points to traverse
+ max_iter: Max points to traverse. if -1, maximum number of required
+ points are traversed
Returns:
linevox (n x dimension) A cumulative array of all points traversed by
all the lines so far.
- >>> s = np.array([[0, 0, 3, 0]])
- >>> bresenhamline(s, np.zeros(s.shape[1]), max_iter=9)
- array([[0, 0, 2, 0],
- [0, 0, 1, 0],
- [0, 0, 0, 0]])
+ >>> s = np.array([[3, 1, 9, 0],[0, 0, 3, 0]])
+ >>> bresenhamline(s, np.zeros(s.shape[1]), max_iter=-1)
+ array([[ 3, 1, 8, 0],
+ [ 2, 1, 7, 0],
+ [ 2, 1, 6, 0],
+ [ 2, 1, 5, 0],
+ [ 1, 0, 4, 0],
+ [ 1, 0, 3, 0],
+ [ 1, 0, 2, 0],
+ [ 0, 0, 1, 0],
+ [ 0, 0, 0, 0],
+ [ 0, 0, 2, 0],
+ [ 0, 0, 1, 0],
+ [ 0, 0, 0, 0],
+ [ 0, 0, -1, 0],
+ [ 0, 0, -2, 0],
+ [ 0, 0, -3, 0],
+ [ 0, 0, -4, 0],
+ [ 0, 0, -5, 0],
+ [ 0, 0, -6, 0]])
+ """
+ # Return the points as a single array
+ return _bresenhamlines(start, end, max_iter).reshape(-1, start.shape[-1])
- >>> s = np.array([[3, 1, 9, 0]])
- >>> bresenhamline(s, np.zeros(s.shape[1]), max_iter=9)
- array([[3, 1, 8, 0],
- [2, 1, 7, 0],
- [2, 1, 6, 0],
- [2, 1, 5, 0],
- [1, 0, 4, 0],
- [1, 0, 3, 0],
- [1, 0, 2, 0],
- [0, 0, 1, 0],
- [0, 0, 0, 0]])
- """
- dim = start.shape[1]
- linevox = np.zeros((0, dim), dtype=start.dtype)
- linegen = bresenhamline_gen(start, end)
- try:
- for i in range(max_iter):
- cur_vox = linegen.next()
- linevox = np.vstack((linevox, cur_vox))
- except StopIteration:
- pass
- return np.array(linevox, dtype=start.dtype)
if __name__ == "__main__":
import doctest
