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authorNicolas Schodet2011-10-16 15:07:44 +0200
committerNicolas Schodet2011-10-16 15:07:44 +0200
commit5f202209337a268a4128d691e32b00c23abc06cd (patch)
tree9198552abe8e8646884e06d521f67c111bb31bd8
parent0f1efb0a55b424c558e3298282bac6cf48b07b89 (diff)
host/simu/utils: add intersect util
-rw-r--r--host/simu/utils/intersect.py103
1 files changed, 103 insertions, 0 deletions
diff --git a/host/simu/utils/intersect.py b/host/simu/utils/intersect.py
new file mode 100644
index 00000000..6074dda0
--- /dev/null
+++ b/host/simu/utils/intersect.py
@@ -0,0 +1,103 @@
+# simu - Robot simulation. {{{
+# encoding: utf-8
+#
+# Copyright (C) 2011 Nicolas Schodet
+#
+# APBTeam:
+# Web: http://apbteam.org/
+# Email: team AT apbteam DOT org
+#
+# This program is free software; you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation; either version 2 of the License, or
+# (at your option) any later version.
+#
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program; if not, write to the Free Software
+# Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
+#
+# }}}
+"""Intersection between different kind of primitives."""
+from simu.utils.vector import vector
+
+def segment_segment (a, b, c, d):
+ """Find intersection between [AB] and [CD] line segments. Return i such
+ that A + i * (B - A).unit () gives this intersection. Return None if no
+ intersection found.
+
+ If line segments are parallel or collinear, None is returned.
+ """
+ a, b, c, d = vector (a), vector (b), vector (c), vector (d)
+ # For each point P on the line segment [AB], there is a real u in [0, 1]
+ # for which P = A + u (B - A)
+ #
+ # An intersection point must be on both line segments:
+ #
+ # A + u (B - A) = C + v (D - C)
+ #
+ # xa + u (xb - xa) = xc + v (xd - xc)
+ # ya + u (yb - ya) = yc + v (yd - yc)
+ #
+ # (xc - xa) (yd - yc) - (xd - xc) (yc - ya)
+ # u = -----------------------------------------
+ # (xb - xa) (yd - yc) - (xd - xc) (yb - ya)
+ # (xc - xa) (yb - ya) - (xb - xa) (yc - ya)
+ # v = -----------------------------------------
+ # (xb - xa) (yd - yc) - (xd - xc) (yb - ya)
+ #
+ # u = (vac . vcd.normal()) / (vab . vcd.normal())
+ # v = (vac . vab.normal()) / (vab . vcd.normal())
+ #
+ # If vab . vcd.normal () is 0, AB and CD are parallel.
+ vab = b - a
+ vcd = d - c
+ vac = c - a
+ # Cannot test for 0 because we are using float, cannot test for a very
+ # small number because we do not know what is small enough, therefore,
+ # compare with numerator.
+ den = vab * vcd.normal ()
+ unum = vac * vcd.normal ()
+ if abs (den) <= 1e-6 * abs (unum):
+ return None
+ else:
+ u = unum / den
+ if u >= 0 and u <= 1:
+ v = vac * vab.normal () / den
+ if v >= 0 and v <= 1:
+ return u * vab.norm ()
+ return None
+
+if __name__ == '__main__':
+ import sys
+ import math
+ v00 = vector (0, 0)
+ v02 = vector (0, 2)
+ v20 = vector (2, 0)
+ v22 = vector (2, 2)
+ v44 = vector (4, 4)
+ failed = 0
+ verbose = True
+ def check (test, result):
+ r = eval (test)
+ if r != result:
+ print test, 'is', r, 'but expected', result
+ return 1
+ elif verbose:
+ print test, 'is', r, 'as expected'
+ return 0
+ v2 = math.sqrt (2)
+ failed += check ('segment_segment (v00, v22, v20, v02)', v2)
+ failed += check ('segment_segment (v00, v22, v02, v20)', v2)
+ failed += check ('segment_segment (v22, v00, v20, v02)', v2)
+ failed += check ('segment_segment (v22, v00, v02, v20)', v2)
+ failed += check ('segment_segment (v00, v22, v00, v22)', None)
+ failed += check ('segment_segment (v00, v22, v00, v44)', None)
+ failed += check ('segment_segment (v22, v44, v02, v20)', None)
+ failed += check ('segment_segment (v00, v44, v02, v20)', v2)
+ failed += check ('segment_segment (v44, v00, v02, v20)', 3 * v2)
+ sys.exit (0 if not failed else 1)