def get_world_segments(root_a, root_b, root_c, initial_t, final_t,
intersection_radius):
"""
The world consists of
three axis lines,
six circles marking the intersections,
and a single parametric curve.
@return: a collection of (p0, p1, style) triples
"""
seg_length_min = 0.1
segments = []
# add the axis line segments
d = 5
f_x = pcurve.LineSegment(np.array([-d, 0, 0]), np.array([d, 0, 0]))
f_y = pcurve.LineSegment(np.array([0, -d, 0]), np.array([0, d, 0]))
f_z = pcurve.LineSegment(np.array([0, 0, -d]), np.array([0, 0, d]))
x_axis_segs = pcurve.get_piecewise_curve(f_x, 0, 1, 10, seg_length_min)
y_axis_segs = pcurve.get_piecewise_curve(f_y, 0, 1, 10, seg_length_min)
z_axis_segs = pcurve.get_piecewise_curve(f_z, 0, 1, 10, seg_length_min)
segments.extend((p0, p1, STYLE_X) for p0, p1 in x_axis_segs)
segments.extend((p0, p1, STYLE_Y) for p0, p1 in y_axis_segs)
segments.extend((p0, p1, STYLE_Z) for p0, p1 in z_axis_segs)
# add the parametric curve
roots = (root_a, root_b, root_c)
polys = interlace.roots_to_differential_polys(roots)
f_poly = interlace.Multiplex((sympyutils.WrappedUniPoly(p) for p in polys))
poly_segs = pcurve.get_piecewise_curve(f_poly, initial_t, final_t, 10,
seg_length_min)
segments.extend((p0, p1, STYLE_CURVE) for p0, p1 in poly_segs)
# add the intersection circles
x_roots_symbolic = sympy.roots(polys[0])
y_roots_symbolic = sympy.roots(polys[1])
z_roots_symbolic = sympy.roots(polys[2])
x_roots = [float(r) for r in x_roots_symbolic]
y_roots = [float(r) for r in y_roots_symbolic]
z_roots = [float(r) for r in z_roots_symbolic]
for r in x_roots:
f = pcurve.OrthoCircle(f_poly(r), intersection_radius, 0)
segs = pcurve.get_piecewise_curve(f, 0, 1, 10, seg_length_min)
segments.extend((p0, p1, STYLE_X) for p0, p1 in segs)
for r in y_roots:
f = pcurve.OrthoCircle(f_poly(r), intersection_radius, 1)
segs = pcurve.get_piecewise_curve(f, 0, 1, 10, seg_length_min)
segments.extend((p0, p1, STYLE_Y) for p0, p1 in segs)
for r in z_roots:
f = pcurve.OrthoCircle(f_poly(r), intersection_radius, 2)
segs = pcurve.get_piecewise_curve(f, 0, 1, 10, seg_length_min)
segments.extend((p0, p1, STYLE_Z) for p0, p1 in segs)
# return the segments
return segments
def get_world_segments(root_a, root_b, root_c, initial_t, final_t, intersection_radius):
"""
The world consists of
three axis lines,
six circles marking the intersections,
and a single parametric curve.
@return: a collection of (p0, p1, style) triples
"""
seg_length_min = 0.1
segments = []
# add the axis line segments
d = 5
f_x = pcurve.LineSegment(np.array([-d, 0, 0]), np.array([d, 0, 0]))
f_y = pcurve.LineSegment(np.array([0, -d, 0]), np.array([0, d, 0]))
f_z = pcurve.LineSegment(np.array([0, 0, -d]), np.array([0, 0, d]))
x_axis_segs = pcurve.get_piecewise_curve(f_x, 0, 1, 10, seg_length_min)
y_axis_segs = pcurve.get_piecewise_curve(f_y, 0, 1, 10, seg_length_min)
z_axis_segs = pcurve.get_piecewise_curve(f_z, 0, 1, 10, seg_length_min)
segments.extend((p0, p1, STYLE_X) for p0, p1 in x_axis_segs)
segments.extend((p0, p1, STYLE_Y) for p0, p1 in y_axis_segs)
segments.extend((p0, p1, STYLE_Z) for p0, p1 in z_axis_segs)
# add the parametric curve
roots = (root_a, root_b, root_c)
polys = interlace.roots_to_differential_polys(roots)
f_poly = interlace.Multiplex((sympyutils.WrappedUniPoly(p) for p in polys))
poly_segs = pcurve.get_piecewise_curve(f_poly, initial_t, final_t, 10, seg_length_min)
segments.extend((p0, p1, STYLE_CURVE) for p0, p1 in poly_segs)
# add the intersection circles
x_roots_symbolic = sympy.roots(polys[0])
y_roots_symbolic = sympy.roots(polys[1])
z_roots_symbolic = sympy.roots(polys[2])
x_roots = [float(r) for r in x_roots_symbolic]
y_roots = [float(r) for r in y_roots_symbolic]
z_roots = [float(r) for r in z_roots_symbolic]
for r in x_roots:
f = pcurve.OrthoCircle(f_poly(r), intersection_radius, 0)
segs = pcurve.get_piecewise_curve(f, 0, 1, 10, seg_length_min)
segments.extend((p0, p1, STYLE_X) for p0, p1 in segs)
for r in y_roots:
f = pcurve.OrthoCircle(f_poly(r), intersection_radius, 1)
segs = pcurve.get_piecewise_curve(f, 0, 1, 10, seg_length_min)
segments.extend((p0, p1, STYLE_Y) for p0, p1 in segs)
for r in z_roots:
f = pcurve.OrthoCircle(f_poly(r), intersection_radius, 2)
segs = pcurve.get_piecewise_curve(f, 0, 1, 10, seg_length_min)
segments.extend((p0, p1, STYLE_Z) for p0, p1 in segs)
# return the segments
return segments
def get_tikz_lines(fs):
"""
@param fs: user input
@return: a sequence of tikz lines
"""
roots = (fs.root_a, fs.root_b, fs.root_c)
nsegs = 128
npoints = nsegs + 1
incr = (fs.final_t - fs.initial_t) / nsegs
polys = interlace.roots_to_differential_polys(roots)
t_values = [fs.initial_t + incr*i for i in range(npoints)]
# get the tikz lines
lines = []
lines.extend(get_function_tikz_lines(
(lambda t: 0), (t_values[0], t_values[-1]), 'black'))
colors = ('w-blue', 'w-red', 'w-olive')
for p, color in zip(polys, colors):
lines.extend(get_function_tikz_lines(
p.eval, t_values, color))
return lines
def get_tikz_lines(fs):
"""
@param fs: user input
@return: a sequence of tikz lines
"""
roots = (fs.root_a, fs.root_b, fs.root_c)
nsegs = 128
npoints = nsegs + 1
incr = (fs.final_t - fs.initial_t) / nsegs
polys = interlace.roots_to_differential_polys(roots)
t_values = [fs.initial_t + incr * i for i in range(npoints)]
# get the tikz lines
lines = []
lines.extend(
get_function_tikz_lines((lambda t: 0), (t_values[0], t_values[-1]),
'black'))
colors = ('w-blue', 'w-red', 'w-olive')
for p, color in zip(polys, colors):
lines.extend(get_function_tikz_lines(p.eval, t_values, color))
return lines
def get_tikz_lines(fs):
"""
@param fs: user input
@return: a sequence of tikz lines
"""
# construct a 'matrix' of three vertically stacked panes
colors = ("black", "w-blue", "w-red", "w-olive")
p0 = sympy.Poly(1, sympy.abc.x)
roots = (fs.root_a, fs.root_b, fs.root_c)
polys = [p0] + interlace.roots_to_differential_polys(roots)
# get the tikz lines
lines = []
lines.append("\\matrix {")
lines.extend(get_pane_tikz_lines(polys[0:2], colors[0:2], fs.initial_t, fs.final_t))
lines.append("\\\\")
lines.extend(get_pane_tikz_lines(polys[1:3], colors[1:3], fs.initial_t, fs.final_t))
lines.append("\\\\")
lines.extend(get_pane_tikz_lines(polys[2:4], colors[2:4], fs.initial_t, fs.final_t))
lines.append("\\\\")
lines.append("};")
return lines
def get_tikz_lines(fs):
"""
@param fs: user input
@return: a sequence of tikz lines
"""
# construct a 'matrix' of three vertically stacked panes
colors = ('black', 'w-blue', 'w-red', 'w-olive')
p0 = sympy.Poly(1, sympy.abc.x)
roots = (fs.root_a, fs.root_b, fs.root_c)
polys = [p0] + interlace.roots_to_differential_polys(roots)
# get the tikz lines
lines = []
lines.append('\\matrix {')
lines.extend(get_pane_tikz_lines(
polys[0:2], colors[0:2], fs.initial_t, fs.final_t))
lines.append('\\\\')
lines.extend(get_pane_tikz_lines(
polys[1:3], colors[1:3], fs.initial_t, fs.final_t))
lines.append('\\\\')
lines.extend(get_pane_tikz_lines(
polys[2:4], colors[2:4], fs.initial_t, fs.final_t))
lines.append('\\\\')
lines.append('};')
return lines