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# Generate a 3200 x 800 geometrical pattern for Eggbot plotting
# See http://www.egg-bot.com/ for info on the Eggbot
#
# Dan Newman, 2 January 2011
# dan dot newman at mtbaldy dot us
# Public domain (http://creativecommons.org/licenses/publicdomain/)
HEIGHT = float( 800.0 )
WIDTH = float( 3200.0 )
scale = WIDTH / ( 16.0 * 3 ) # 16 horizontal repeats
epsilon = float(1.0e-5)
# Relative moves for drawing the vertical elements
DOWN = [[0.0, scale], [scale, 2*scale], [0.0, scale], [-scale, 2*scale]]
UP = [[0.0, -scale], [scale, -2*scale], [0.0, -scale], [-scale, -2*scale]]
# How to switch to going up when you stop going down after DOWN[i]
DU_switch = [scale, -scale, -scale, scale]
# Relative moves for drawing the horizontal elements (L2R = left-to-right)
L2R = [[scale, 0.0], [2*scale, scale], [scale, 0.0], [2*scale, -scale]]
R2L = [[-scale, 0.0], [-2*scale, scale], [-scale, 0.0], [-2*scale, -scale]]
# How to switch to R2L after stopping in L2R at index i
LR_switch = [scale, -scale, -scale, scale]
# Compute the intersection of two lines
# See eggbot_hatch.py for complete details
def intersect( P1, P2, P3, P4 ):
'''
Determine if two line segments defined by the four points P1 & P2 and
P3 & P4 intersect. If they do intersect, then return the fractional
point of intersection "sa" along the first line at which the
intersection occurs.
'''
# Precompute these values -- note that we're basically shifting from
#
# P = P1 + s (P2 - P1)
#
# to
#
# P = P1 + s D
#
# where D is a direction vector. The solution remains the same of
# course. We'll just be computing D once for each line rather than
# computing it a couple of times.
D21x = P2[0] - P1[0]
D21y = P2[1] - P1[1]
D43x = P4[0] - P3[0]
D43y = P4[1] - P3[1]
# Denominator
d = D21x * D43y - D21y * D43x
# Return now if the denominator is zero
if d == 0:
return float( -1 )
# For our purposes, the first line segment given
# by P1 & P2 is the LONG hatch line running through
# the entire drawing. And, P3 & P4 describe the
# usually much shorter line segment from a polygon.
# As such, we compute sb first as it's more likely
# to indicate "no intersection". That is, sa is
# more likely to indicate an intersection with a
# much a long line containing P3 & P4.
nb = ( P1[1] - P3[1] ) * D21x - ( P1[0] - P3[0] ) * D21y
# Could first check if abs(nb) > abs(d) or if
# the signs differ.
sb = float( nb ) / float( d )
if ( sb < 0 ) or ( sb > 1 ):
return float( -1 )
na = ( P1[1] - P3[1] ) * D43x - ( P1[0] - P3[0] ) * D43y
sa = float( na ) / float( d )
if ( sa < 0 ) or ( sa > 1 ):
return float( -1 )
return sa
# Determine whether a line segment needs to be clipped to
# fit within the drawing page
def clip( x1, y1, x2, y2 ):
if ( x1 >= 0.0 ) and ( x1 <= WIDTH ) and ( x2 >= 0.0 ) and ( x2 <= WIDTH ) and \
( y1 >= 0.0 ) and ( y1 <= HEIGHT ) and ( y2 >= 0.0 ) and ( y2 <= HEIGHT ):
return float( -1.0 )
if ( x1 < 0.0 ) or ( x2 < 0.0 ):
s = intersect( [x1, y1], [x2, y2], [0.0, 0.0], [0.0, HEIGHT] )
if ( s > 0.0 ):
return s
if ( x1 > WIDTH ) or ( x2 > WIDTH ):
# We allow going an extra pixel across in case there is drawing error
s = intersect( [x1, y1], [x2, y2], [WIDTH+1.0, 0.0], [WIDTH+1.0, HEIGHT] )
if ( s > 0.0 ):
return s
if ( y1 < 0.0 ) or ( y2 < 0.0 ):
s = intersect( [x1, y1], [x2, y2], [0.0, 0.0], [WIDTH, 0.0] )
if ( s > 0.0 ):
return s
if ( y1 > HEIGHT ) or ( y2 > HEIGHT ):
s = intersect( [x1, y1], [x2, y2], [0.0, HEIGHT], [WIDTH, HEIGHT] )
if ( s > 0.0 ):
return s
return float( -1.0 )
# Plot a collection of line segments
def plot( points, color='black' ):
# First line segment
s = clip( points[0][0], points[0][1], points[1][0], points[1][1] )
if ( s < 0.0 ):
p = 'M %f,%f' % ( points[0][0], points[0][1] )
else:
p = 'M %f,%f' % ( points[0][0] + s * ( points[1][0] - points[0][0] ),
points[0][1] + s * ( points[1][1] - points[0][1] ) )
x0 = points[1][0]
y0 = points[1][1]
p += ' L %f,%f' % ( x0, y0 )
# Intermediate line segments
for i in range(2, len( points ) - 1):
x0 = points[i][0]
y0 = points[i][1]
p += ' L %f,%f' % ( x0, y0 )
# Final line segment
x = points[-1][0]
y = points[-1][1]
s = clip( x0, y0, x, y )
if ( s < 0.0 ):
p += ' L %f,%f' % ( x, y )
else:
p += ' L %f,%f' % ( x0 + s * ( x - x0 ), y0 + s * ( y - y0 ) )
print '
