def get_tikzpicture_body_beta(fs):
"""
This alternative visualization literally warps the x axis.
The other one makes a smoother picture by
computing a different function for y that is equivalent to this warping.
"""
ncurves = fs.ncurves
morph = fs.morph
# define the number of segments
nsegs = 128
npoints = nsegs + 1
t_initial = -1.0
t_final = 1.0
incr = (t_final - t_initial) / float(nsegs)
# define the sequence of t values
t_seq = [t_initial + t*incr for t in range(npoints)]
t_seq_inv_warped = [
inv_warp(t)*morph + t*(1-morph) for t in t_seq]
# define the sequences of y values
y_seqs = []
for i in range(ncurves):
mypoly = sympy.chebyshevt_poly(i+1, sympy.abc.x, polys=True)
y_seqs.append([mypoly.eval(t) for t in t_seq])
width = 8
height = 4
text = interlace.tikz_superposition(
t_seq_inv_warped, y_seqs, width, height)
return text
def __init__(self):
# predefine the shape
self.initial_t = -1.0
self.final_t = 1.0
self.polys = [sympy.chebyshevt_poly(
i+1, sympy.abc.t, polys=True) for i in range(3)]
self.shape = interlace.CubicPolyShape(
self.polys, self.initial_t, self.final_t)
def __init__(self):
# predefine the shape
self.initial_t = -1.0
self.final_t = 1.0
self.polys = [
sympy.chebyshevt_poly(i + 1, sympy.abc.t, polys=True)
for i in range(3)
]
self.shape = interlace.CubicPolyShape(self.polys, self.initial_t,
self.final_t)
def get_tikzpicture_body_gamma(fs):
"""
This was the latest pre-bezier version.
"""
ncurves = fs.ncurves
morph = fs.morph
# define the number of segments
nsegs = 128
npoints = nsegs + 1
t_initial = -1.0
t_final = 1.0
incr = (t_final - t_initial) / float(nsegs)
# define the sequence of t values
t_seq = [t_initial + t*incr for t in range(npoints)]
# define the sequences of y values
y_seqs = []
for i in range(ncurves):
mypoly = sympy.chebyshevt_poly(i+1, sympy.abc.x, polys=True)
y_seq = [mypoly.eval(warp(t)*morph + t*(1-morph)) for t in t_seq]
y_seqs.append(y_seq)
width = 8
height = 4
return interlace.tikz_superposition(t_seq, y_seqs, width, height)
def get_tikzpicture_body(ncurves, nsegs, morph):
"""
Try to use sympy for computation and bezier for drawing.
"""
# define the sympy expression for the warp
sympy_t = sympy.abc.t
sympy_t_warped = sympy.sin((sympy.pi / 2) * sympy_t)
sympy_t_morphed = morph*sympy_t_warped + (1-morph)*sympy_t
# define the shapes
shapes = []
x_axis = interlace.PiecewiseLinearPathShape([(-1, 0), (1, 0)])
shapes.append(x_axis)
for i in range(ncurves):
x_expr = sympy_t
y_expr = sympy.chebyshevt_poly(i+1, sympy_t_morphed)
#cheby_expr = sympy.chebyshevt_poly(i+1, sympy_t)
#y_expr = cheby_expr.subs(sympy_t, sympy_t_morphed)
shape = interlace.DifferentiableShape(
(x_expr, y_expr), -1.0, 1.0, nsegs)
shapes.append(shape)
width = 6
height = 6
return interlace.tikz_shape_superposition(shapes, width, height)
