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blender/release/scripts/bpymodules/BPyMathutils.py
Campbell Barton f1eed11ad7 Missing constant added.
2006-07-13 13:41:26 +00:00

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# $Id$
#
# --------------------------------------------------------------------------
# helper functions to be used by other scripts
# --------------------------------------------------------------------------
# ***** BEGIN GPL LICENSE BLOCK *****
#
# 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.
#
# ***** END GPL LICENCE BLOCK *****
# --------------------------------------------------------------------------
import Blender
from Blender.Mathutils import *
# ------ Mersenne Twister - start
# Copyright (C) 1997 Makoto Matsumoto and Takuji Nishimura.
# Any feedback is very welcome. For any question, comments,
# see http://www.math.keio.ac.jp/matumoto/emt.html or email
# matumoto@math.keio.ac.jp
# The link above is dead, this is the new one:
# http://www.math.sci.hiroshima-u.ac.jp/m-mat/MT/emt.html
# And here the license info, from Mr. Matsumoto's site:
# Until 2001/4/6, MT had been distributed under GNU Public License,
# but after 2001/4/6, we decided to let MT be used for any purpose, including
# commercial use. 2002-versions mt19937ar.c, mt19937ar-cok.c are considered
# to be usable freely.
#
# So from the year above (1997), this code is under GPL.
# Period parameters
N = 624
M = 397
MATRIX_A = 0x9908b0dfL # constant vector a
UPPER_MASK = 0x80000000L # most significant w-r bits
LOWER_MASK = 0x7fffffffL # least significant r bits
# Tempering parameters
TEMPERING_MASK_B = 0x9d2c5680L
TEMPERING_MASK_C = 0xefc60000L
def TEMPERING_SHIFT_U(y):
return (y >> 11)
def TEMPERING_SHIFT_S(y):
return (y << 7)
def TEMPERING_SHIFT_T(y):
return (y << 15)
def TEMPERING_SHIFT_L(y):
return (y >> 18)
mt = [] # the array for the state vector
mti = N+1 # mti==N+1 means mt[N] is not initialized
# initializing the array with a NONZERO seed
def sgenrand(seed):
# setting initial seeds to mt[N] using
# the generator Line 25 of Table 1 in
# [KNUTH 1981, The Art of Computer Programming
# Vol. 2 (2nd Ed.), pp102]
global mt, mti
mt = []
mt.append(seed & 0xffffffffL)
for i in xrange(1, N + 1):
mt.append((69069 * mt[i-1]) & 0xffffffffL)
mti = i
# end sgenrand
def genrand():
global mt, mti
mag01 = [0x0L, MATRIX_A]
# mag01[x] = x * MATRIX_A for x=0,1
y = 0
if mti >= N: # generate N words at one time
if mti == N+1: # if sgenrand() has not been called,
sgenrand(4357) # a default initial seed is used
for kk in xrange((N-M) + 1):
y = (mt[kk]&UPPER_MASK)|(mt[kk+1]&LOWER_MASK)
mt[kk] = mt[kk+M] ^ (y >> 1) ^ mag01[y & 0x1]
for kk in xrange(kk, N):
y = (mt[kk]&UPPER_MASK)|(mt[kk+1]&LOWER_MASK)
mt[kk] = mt[kk+(M-N)] ^ (y >> 1) ^ mag01[y & 0x1]
y = (mt[N-1]&UPPER_MASK)|(mt[0]&LOWER_MASK)
mt[N-1] = mt[M-1] ^ (y >> 1) ^ mag01[y & 0x1]
mti = 0
y = mt[mti]
mti += 1
y ^= TEMPERING_SHIFT_U(y)
y ^= TEMPERING_SHIFT_S(y) & TEMPERING_MASK_B
y ^= TEMPERING_SHIFT_T(y) & TEMPERING_MASK_C
y ^= TEMPERING_SHIFT_L(y)
return ( float(y) / 0xffffffffL ) # reals
#------ Mersenne Twister -- end
""" 2d convexhull
Based from Dinu C. Gherman's work,
modified for Blender/Mathutils by Campell Barton
"""
######################################################################
# Public interface
######################################################################
from Blender.Mathutils import DotVecs
def convexHull(point_list_2d):
"""Calculate the convex hull of a set of vectors
The vectors can be 3 or 4d but only the Xand Y are used.
returns a list of convex hull indicies to the given point list
"""
######################################################################
# Helpers
######################################################################
def _myDet(p, q, r):
"""Calc. determinant of a special matrix with three 2D points.
The sign, "-" or "+", determines the side, right or left,
respectivly, on which the point r lies, when measured against
a directed vector from p to q.
"""
return (q.x*r.y + p.x*q.y + r.x*p.y) - (q.x*p.y + r.x*q.y + p.x*r.y)
def _isRightTurn((p, q, r)):
"Do the vectors pq:qr form a right turn, or not?"
#assert p[0] != q[0] and q[0] != r[0] and p[0] != r[0]
if _myDet(p[0], q[0], r[0]) < 0:
return 1
else:
return 0
# Get a local list copy of the points and sort them lexically.
points = [(p, i) for i, p in enumerate(point_list_2d)]
points.sort(lambda a,b: cmp((a[0].x, a[0].y), (b[0].x, b[0].y)))
# Build upper half of the hull.
upper = [points[0], points[1]] # cant remove these.
for i in xrange(len(points)-2):
upper.append(points[i+2])
while len(upper) > 2 and not _isRightTurn(upper[-3:]):
del upper[-2]
# Build lower half of the hull.
points.reverse()
lower = [points.pop(0), points.pop(1)]
for p in points:
lower.append(p)
while len(lower) > 2 and not _isRightTurn(lower[-3:]):
del lower[-2]
# Concatenate both halfs and return.
return [p[1] for ls in (upper, lower) for p in ls]
SMALL_NUM = 0.000001
def lineIntersect2D(v1a, v1b, v2a, v2b):
'''
Do 2 lines intersect, if so where.
If there is an error, the retured X value will be None
the y will be an error code- usefull when debugging.
the first line is (v1a, v1b)
the second is (v2a, v2b)
by Campbell Barton
This function accounts for all known cases of 2 lines ;)
'''
x1,y1= v1a.x, v1a.y
x2,y2= v1b.x, v1b.y
_x1,_y1= v2a.x, v2a.y
_x2,_y2= v2b.x, v2b.y
# Bounding box intersection first.
if min(x1, x2) > max(_x1, _x2) or \
max(x1, x2) < min(_x1, _x2) or \
min(y1, y2) > max(_y1, _y2) or \
max(y1, y2) < min(_y1, _y2):
return None, 100 # Basic Bounds intersection TEST returns false.
# are either of the segments points? Check Seg1
if abs(x1 - x2) + abs(y1 - y2) <= SMALL_NUM:
return None, 101
# are either of the segments points? Check Seg2
if abs(_x1 - _x2) + abs(_y1 - _y2) <= SMALL_NUM:
return None, 102
# Make sure the HOZ/Vert Line Comes first.
if abs(_x1 - _x2) < SMALL_NUM or abs(_y1 - _y2) < SMALL_NUM:
x1, x2, y1, y2, _x1, _x2, _y1, _y2 = _x1, _x2, _y1, _y2, x1, x2, y1, y2
if abs(x2-x1) < SMALL_NUM: # VERTICLE LINE
if abs(_x2-_x1) < SMALL_NUM: # VERTICLE LINE SEG2
return None, 111 # 2 verticle lines dont intersect.
elif abs(_y2-_y1) < SMALL_NUM:
return x1, _y1 # X of vert, Y of hoz. no calculation.
yi = ((_y1 / abs(_x1 - _x2)) * abs(_x2 - x1)) + ((_y2 / abs(_x1 - _x2)) * abs(_x1 - x1))
if yi > max(y1, y2): # New point above seg1's vert line
return None, 112
elif yi < min(y1, y2): # New point below seg1's vert line
return None, 113
return x1, yi # Intersecting.
if abs(y2-y1) < SMALL_NUM: # HOZ LINE
if abs(_y2-_y1) < SMALL_NUM: # HOZ LINE SEG2
return None, 121 # 2 hoz lines dont intersect.
# Can skip vert line check for seg 2 since its covered above.
xi = ((_x1 / abs(_y1 - _y2)) * abs(_y2 - y1)) + ((_x2 / abs(_y1 - _y2)) * abs(_y1 - y1))
if xi > max(x1, x2): # New point right of seg1's hoz line
return None, 112
elif xi < min(x1, x2): # New point left of seg1's hoz line
return None, 113
return xi, y1 # Intersecting.
# Accounted for hoz/vert lines. Go on with both anglular.
b1 = (y2-y1)/(x2-x1)
b2 = (_y2-_y1)/(_x2-_x1)
a1 = y1-b1*x1
a2 = _y1-b2*_x1
if b1 - b2 == 0.0:
return None, 200
xi = - (a1-a2)/(b1-b2)
yi = a1+b1*xi
if (x1-xi)*(xi-x2) >= 0 and (_x1-xi)*(xi-_x2) >= 0 and (y1-yi)*(yi-y2) >= 0 and (_y1-yi)*(yi-_y2)>=0:
return xi, yi
else:
return None, 300
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