from __future__ import division, print_function

# Coordinates are given as points in the complex plane
from svgpathtools import Path, Line, QuadraticBezier, CubicBezier, Arc
seg1 = CubicBezier(300 100j, 100 100j, 200 200j, 200 300j)  # A cubic beginning at (300, 100) and ending at (200, 300)
seg2 = Line(200 300j, 250 350j)  # A line beginning at (200, 300) and ending at (250, 350)
path = Path(seg1, seg2)  # A path traversing the cubic and then the line

# We could alternatively created this Path object using a d-string
from svgpathtools import parse_path
path_alt = parse_path('M 300 100 C 100 100 200 200 200 300 L 250 350')

# Let's check that these two methods are equivalent
print(path)
print(path_alt)
print(path == path_alt)

# On a related note, the Path.d() method returns a Path object's d-string
print(path.d())
print(parse_path(path.d()) == path)

# Let's append another to the end of it
path.append(CubicBezier(250 350j, 275 350j, 250 225j, 200 100j))
print(path)

# Let's replace the first segment with a Line object
path[0] = Line(200 100j, 200 300j)
print(path)

# You may have noticed that this path is connected and now is also closed (i.e. path.start == path.end)
print("path is continuous? ", path.iscontinuous())
print("path is closed? ", path.isclosed())

# The curve the path follows is not, however, smooth (differentiable)
from svgpathtools import kinks, smoothed_path
print("path contains non-differentiable points? ", len(kinks(path)) > 0)

# If we want, we can smooth these out (Experimental and only for line/cubic paths)
# Note:  smoothing will always works (except on 180 degree turns), but you may want 
# to play with the maxjointsize and tightness parameters to get pleasing results
# Note also: smoothing will increase the number of segments in a path
spath = smoothed_path(path)
print("spath contains non-differentiable points? ", len(kinks(spath)) > 0)
print(spath)

# Let's take a quick look at the path and its smoothed relative
# The following commands will open two browser windows to display path and spaths
from svgpathtools import disvg
from time import sleep
disvg(path) 
sleep(1)  # needed when not giving the SVGs unique names (or not using timestamp)
disvg(spath)
print("Notice that path contains {} segments and spath contains {} segments."
      "".format(len(path), len(spath)))

# Read SVG into a list of path objects and list of dictionaries of attributes 
from svgpathtools import svg2paths, wsvg
paths, attributes = svg2paths('test.svg')

# Update: You can now also extract the svg-attributes by setting
# return_svg_attributes=True, or with the convenience function svg2paths2
from svgpathtools import svg2paths2
paths, attributes, svg_attributes = svg2paths2('test.svg')

# Let's print out the first path object and the color it was in the SVG
# We'll see it is composed of two CubicBezier objects and, in the SVG file it 
# came from, it was red
redpath = paths[0]
redpath_attribs = attributes[0]
print(redpath)
print(redpath_attribs['stroke'])

# Let's make a new SVG that's identical to the first
wsvg(paths, attributes=attributes, svg_attributes=svg_attributes, filename='output1.svg')

# Example:

# Let's check that the first segment of redpath starts 
# at the same point as redpath
firstseg = redpath[0] 
print(redpath.point(0) == firstseg.point(0) == redpath.start == firstseg.start)

# Let's check that the last segment of redpath ends on the same point as redpath
lastseg = redpath[-1] 
print(redpath.point(1) == lastseg.point(1) == redpath.end == lastseg.end)

# This next boolean should return False as redpath is composed multiple segments
print(redpath.point(0.5) == firstseg.point(0.5))

# If we want to figure out which segment of redpoint the 
# point redpath.point(0.5) lands on, we can use the path.T2t() method
k, t = redpath.T2t(0.5)
print(redpath[k].point(t) == redpath.point(0.5))

# Example:
b = CubicBezier(300 100j, 100 100j, 200 200j, 200 300j)
p = b.poly()

# p(t) == b.point(t)
print(p(0.235) == b.point(0.235))

# What is p(t)?  It's just the cubic b written in standard form.  
bpretty = "{}*(1-t)^3   3*{}*(1-t)^2*t   3*{}*(1-t)*t^2   {}*t^3".format(*b.bpoints())
print("The CubicBezier, b.point(x) = \n\n"   
      bpretty   "\n\n"   
      "can be rewritten in standard form as \n\n"  
      str(p).replace('x','t'))

t = 0.5
### Method 1: the easy way
u1 = b.unit_tangent(t)

### Method 2: another easy way 
# Note: This way will fail if it encounters a removable singularity.
u2 = b.derivative(t)/abs(b.derivative(t))

### Method 2: a third easy way 
# Note: This way will also fail if it encounters a removable singularity.
dp = p.deriv() 
u3 = dp(t)/abs(dp(t))

### Method 4: the removable-singularity-proof numpy.poly1d way  
# Note: This is roughly how Method 1 works
from svgpathtools import real, imag, rational_limit
dx, dy = real(dp), imag(dp)  # dp == dx   1j*dy 
p_mag2 = dx**2   dy**2  # p_mag2(t) = |p(t)|**2
# Note: abs(dp) isn't a polynomial, but abs(dp)**2 is, and,
#  the limit_{t->t0}[f(t) / abs(f(t))] == 
# sqrt(limit_{t->t0}[f(t)**2 / abs(f(t))**2])
from cmath import sqrt
u4 = sqrt(rational_limit(dp**2, p_mag2, t))

print("unit tangent check:", u1 == u2 == u3 == u4)

# Let's do a visual check
mag = b.length()/4  # so it's not hard to see the tangent line
tangent_line = Line(b.point(t), b.point(t)   mag*u1)
disvg([b, tangent_line], 'bg', nodes=[b.point(t)])

# Speaking of tangents, let's add a normal vector to the picture
n = b.normal(t)
normal_line = Line(b.point(t), b.point(t)   mag*n)
disvg([b, tangent_line, normal_line], 'bgp', nodes=[b.point(t)])

# and let's reverse the orientation of b! 
# the tangent and normal lines should be sent to their opposites
br = b.reversed()

# Let's also shift b_r over a bit to the right so we can view it next to b
# The simplest way to do this is br = br.translated(3*mag),  but let's use 
# the .bpoints() instead, which returns a Bezier's control points
br.start, br.control1, br.control2, br.end = [3*mag   bpt for bpt in br.bpoints()]  # 

tangent_line_r = Line(br.point(t), br.point(t)   mag*br.unit_tangent(t))
normal_line_r = Line(br.point(t), br.point(t)   mag*br.normal(t))
wsvg([b, tangent_line, normal_line, br, tangent_line_r, normal_line_r], 
     'bgpkgp', nodes=[b.point(t), br.point(t)], filename='vectorframes.svg', 
     text=["b's tangent", "br's tangent"], text_path=[tangent_line, tangent_line_r])

# Let's take a Line and an Arc and make some pictures
top_half = Arc(start=-1, radius=1 2j, rotation=0, large_arc=1, sweep=1, end=1)
midline = Line(-1.5, 1.5)

# First let's make our ellipse whole
bottom_half = top_half.rotated(180)
decorated_ellipse = Path(top_half, bottom_half)

# Now let's add the decorations
for k in range(12):
    decorated_ellipse.append(midline.rotated(30*k))
    
# Let's move it over so we can see the original Line and Arc object next
# to the final product
decorated_ellipse = decorated_ellipse.translated(4 0j)
wsvg([top_half, midline, decorated_ellipse], filename='decorated_ellipse.svg')

# First we'll load the path data from the file test.svg
paths, attributes = svg2paths('test.svg')

# Let's mark the parametric midpoint of each segment
# I say "parametric" midpoint because Bezier curves aren't 
# parameterized by arclength 
# If they're also the geometric midpoint, let's mark them
# purple and otherwise we'll mark the geometric midpoint green
min_depth = 5
error = 1e-4
dots = []
ncols = []
nradii = []
for path in paths:
    for seg in path:
        parametric_mid = seg.point(0.5)
        seg_length = seg.length()
        if seg.length(0.5)/seg.length() == 1/2:
            dots  = [parametric_mid]
            ncols  = ['purple']
            nradii  = [5]
        else:
            t_mid = seg.ilength(seg_length/2)
            geo_mid = seg.point(t_mid)
            dots  = [parametric_mid, geo_mid]
            ncols  = ['red', 'green']
            nradii  = [5] * 2

# In 'output2.svg' the paths will retain their original attributes
wsvg(paths, nodes=dots, node_colors=ncols, node_radii=nradii, 
     attributes=attributes, filename='output2.svg')

# Let's find all intersections between redpath and the other 
redpath = paths[0]
redpath_attribs = attributes[0]
intersections = []
for path in paths[1:]:
    for (T1, seg1, t1), (T2, seg2, t2) in redpath.intersect(path):
        intersections.append(redpath.point(T1))
        
disvg(paths, filename='output_intersections.svg', attributes=attributes,
      nodes = intersections, node_radii = [5]*len(intersections))

from svgpathtools import parse_path, Line, Path, wsvg
def offset_curve(path, offset_distance, steps=1000):
    """Takes in a Path object, `path`, and a distance,
    `offset_distance`, and outputs an piecewise-linear approximation 
    of the 'parallel' offset curve."""
    nls = []
    for seg in path:
        ct = 1
        for k in range(steps):
            t = k / steps
            offset_vector = offset_distance * seg.normal(t)
            nl = Line(seg.point(t), seg.point(t)   offset_vector)
            nls.append(nl)
    connect_the_dots = [Line(nls[k].end, nls[k 1].end) for k in range(len(nls)-1)]
    if path.isclosed():
        connect_the_dots.append(Line(nls[-1].end, nls[0].end))
    offset_path = Path(*connect_the_dots)
    return offset_path

# Examples:
path1 = parse_path("m 288,600 c -52,-28 -42,-61 0,-97 ")
path2 = parse_path("M 151,395 C 407,485 726.17662,160 634,339").translated(300)
path3 = parse_path("m 117,695 c 237,-7 -103,-146 457,0").translated(500 400j)
paths = [path1, path2, path3]

offset_distances = [10*k for k in range(1,51)]
offset_paths = []
for path in paths:
    for distances in offset_distances:
        offset_paths.append(offset_curve(path, distances))

# Let's take a look
wsvg(paths   offset_paths, 'g'*len(paths)   'r'*len(offset_paths), filename='offset_curves.svg')