Module specrel.spacetime.gradient
Objects that form color gradients across regions of spacetime, representing continuous change of some sort.
Source code
"""Objects that form color gradients across regions of spacetime, representing
continuous change of some sort.
"""
from matplotlib.colors import to_rgba
import specrel.geom as geom
def _calc_colorgrad(x, point1, point2, color1, color2):
"""Calculate a linear color gradient value between two points at some
proportion x, where 0 is the start point/color, and 1 is the end
point/color.
"""
color1 = to_rgba(color1)
color2 = to_rgba(color2)
xpoint = tuple([p1 + x*(p2 - p1) for p1, p2 in zip(point1, point2)])
xcolor = tuple([c1 + x*(c2 - c1) for c1, c2 in zip(color1, color2)])
return xpoint, xcolor
def _valid_color(col):
"""Checks whether an rgba value is a valid color or not."""
for c in col:
if c < 0 or c > 1:
return False
return True
def _colorgrad_extremes(point1, point2, color1, color2, divisions):
"""Extrapolates a linear color gradient between two points to the extreme
endpoints of colorspace, at some interval resolution.
"""
# Extend the range backwards
i1 = 0
while _valid_color(_calc_colorgrad(
-(i1+1)/divisions, point1, point2, color1, color2)[1]):
i1 += 1
# Extend the range forwards
i2 = 0
while _valid_color(_calc_colorgrad(
1 + (i2+1)/divisions, point1, point2, color1, color2)[1]):
i2 += 1
# Get the final extremes of the range
ext_point1, ext_color1 = _calc_colorgrad(-i1/divisions,
point1, point2, color1, color2)
ext_point2, ext_color2 = _calc_colorgrad(1 + i2/divisions,
point1, point2, color1, color2)
return ext_point1, ext_point2, ext_color1, ext_color2, divisions + i1 + i2
def gradient_line(point1, point2, color1, color2, divisions=100,
extrapolate_color=True, draw_options=geom.geomrc['draw_options']):
"""A line with a color gradient. The gradient transition will happen over
a finite range in spacetime, and be monochromatic at either end.
Args:
point1 (specrel.geom.STVector or iterable): Starting point of the
gradient.
point2 (specrel.geom.STVector or iterable): Ending point of the
gradient.
color1 (color): A Matplotlib color for the gradient starting color.
color2 (color): A Matplotlib color for the gradient ending color.
divisions (int, optional): The number of line segment divisions in the
gradient. More divisions means a smoother gradient.
extrapolate_color (bool, optional): Flag for whether or not to
extrapolate the color gradient across the line past the specified
endpoints so that the color change spans as far as possible across
the line.
draw_options (dict, optional): See `specrel.geom.LorentzTransformable`.
Returns:
specrel.geom.Collection:
Collection containing the color gradient increments, in the order:
1. `specrel.geom.Ray` before `point1` with `color1`.
2. Line segments changing color from `point1` to `point2`.
3. `specrel.geom.Ray` after `point2` with `color2`.
"""
# Copy draw_options and remove color if it's there
draw_options = dict(draw_options)
draw_options.pop('color', None)
# If extrapolating color, calculate the color gradient extremes
if extrapolate_color:
point1, point2, color1, color2, divisions = _colorgrad_extremes(
point1, point2, color1, color2, divisions)
# Color gradient calculator for the given points and colors
def this_colorgrad(x):
return _calc_colorgrad(x, point1, point2, color1, color2)
# Line direction vector
direc = geom.STVector(point2) - geom.STVector(point1)
grad = geom.Collection()
# Monochromatic ray at the tail end of the gradient line
grad.append(geom.Ray(-direc, point1,
draw_options={'color': color1, **draw_options}))
# The line segments comprising the color gradient
for i in range(divisions):
start_point, _ = this_colorgrad(i/divisions)
end_point, _ = this_colorgrad((i+1)/divisions)
_, grad_color = this_colorgrad((i+1/2)/divisions)
grad.append(geom.line_segment(start_point, end_point,
draw_options={'color': grad_color, **draw_options}))
# Monochromatic ray at the head end of the gradient line
grad.append(geom.Ray(direc, point2,
draw_options={'color': color2, **draw_options}))
return grad
def longitudinal_gradient_ribbon(line1_endpoints, line2_endpoints, color1,
color2, divisions=100, extrapolate_color=True,
draw_options=geom.geomrc['draw_options']):
"""A `specrel.geom.Ribbon`-esque object with a longitudinal color gradient
(across the infinite direction).
Args:
line1_endpoints (list): list of two `specrel.geom.STVector`-convertible
points defining the start and end positions of the gradient along
the first edge of the ribbon.
line2_endpoints (list): Same as `line1_endpoints`, but for the second
edge of the ribbon.
color1 (color): A Matplotlib color for the gradient starting color.
color2 (color): A Matplotlib color for the gradient ending color.
divisions (int, optional): The number of line segment divisions in the
gradient. More divisions means a smoother gradient.
extrapolate_color (bool, optional): Flag for whether or not to
extrapolate the color gradient across the ribbon past the specified
endpoints so that the color change spans as far as possible across
the ribbon.
draw_options (TYPE, optional): See `specrel.geom.LorentzTransformable`.
Returns:
specrel.geom.Collection:
Collection containing the color gradient increments, in the order:
1. `specrel.geom.HalfRibbon` with `color1` before both line starting
points.
2. Polygons changing color from starts of the lines to the ends.
3. `specrel.geom.HalfRibbon` with `color2` after both line ending
points.
"""
# Copy draw_options and remove color, facecolor, and edgecolor if they're
# there
draw_options = dict(draw_options)
draw_options.pop('color', None)
draw_options.pop('facecolor', None)
draw_options.pop('edgecolor', None)
# If extrapolating color, calculate the color gradient extremes
if extrapolate_color:
point1, point2, color1, color2, divisions = _colorgrad_extremes(
*line1_endpoints, color1, color2, divisions)
line1_endpoints = (point1, point2)
point1, point2, _, _, _ = _colorgrad_extremes(
*line2_endpoints, color1, color2, divisions)
line2_endpoints = (point1, point2)
# Color gradient calculators for each line with the given colors
def line1_colorgrad(x):
return _calc_colorgrad(x, *line1_endpoints, color1, color2)
def line2_colorgrad(x):
return _calc_colorgrad(x, *line2_endpoints, color1, color2)
# Direction vectors of each line
direc1 = geom.STVector(line1_endpoints[1]) - geom.STVector(line1_endpoints[0])
direc2 = geom.STVector(line2_endpoints[1]) - geom.STVector(line2_endpoints[0])
grad = geom.Collection()
# Form the monochromatic half ribbon at the tail end of the gradient
# Overlap with the first polygon by half a division to mitigate any
# boundary gaps
start_point1, _ = line1_colorgrad(1/(2*divisions))
start_point2, _ = line2_colorgrad(1/(2*divisions))
grad.append(geom.HalfRibbon(
geom.Ray(-direc1, start_point1),
geom.Ray(-direc2, start_point2),
# Explicitly turn off edge coloring
draw_options={'facecolor': color1, 'edgecolor': 'None', **draw_options}))
# Interior polygons comprising the color gradient
for i in range(divisions):
start_point1, _ = line1_colorgrad(i/divisions)
# Overlap bands by half a division
end_point1, _ = line1_colorgrad((i+1+1/2)/divisions)
start_point2, _ = line2_colorgrad(i/divisions)
end_point2, _ = line2_colorgrad((i+1+1/2)/divisions)
_, grad_color = line1_colorgrad((i+1/2)/divisions)
grad.append(geom.polygon(
[start_point1, end_point1, end_point2, start_point2],
draw_options={'facecolor': grad_color, **draw_options}))
# Monochromatic half ribon at the head end of the gradient
grad.append(geom.HalfRibbon(
geom.Ray(direc1, line1_endpoints[1]),
geom.Ray(direc2, line2_endpoints[1]),
draw_options={'facecolor': color2, 'edgecolor': 'None', **draw_options}))
return grad
def lateral_gradient_ribbon(direction, point1, point2, color1, color2,
divisions=100, draw_options=geom.geomrc['draw_options']):
"""A `specrel.geom.Ribbon`-esque object with a lateral color gradient
(across the finite direction).
Args:
direction (specrel.geom.STVector or iterable): Direction vector for the
gradient.
point1 (specrel.geom.STVector or iterable): A point that the first edge
of the ribbon passes through.
point2 (specrel.geom.STVector or iterable): A point that the second edge
of the ribbon passes through.
color1 (color): A Matplotlib color for the gradient starting color.
color2 (color): A Matplotlib color for the gradient ending color.
divisions (int, optional): The number of line segment divisions in the
gradient. More divisions means a smoother gradient.
draw_options (TYPE, optional): See `specrel.geom.LorentzTransformable`.
Returns:
specrel.geom.Collection:
Collection containing the `specrel.geom.Ribbon` objects of slowly
changing color from `point1` to `point2`.
"""
# Copy draw_options and remove color, facecolor, and edgecolor if they're
# there
draw_options = dict(draw_options)
draw_options.pop('color', None)
draw_options.pop('facecolor', None)
draw_options.pop('edgecolor', None)
# Color gradient calculator for the given points and colors
def this_colorgrad(x):
return _calc_colorgrad(x, point1, point2, color1, color2)
grad = geom.Collection()
# Ribbons comprising the color gradient, as we move from point1 to point2
for i in range(divisions):
start_point, _ = this_colorgrad(i/divisions)
# Overlap bands by half a division, except the last one
end_point, _ = this_colorgrad(min((i+1+1/2)/divisions, 1))
_, grad_color = this_colorgrad((i+1/2)/divisions)
# Explicitly turn off edge coloring
grad.append(geom.Ribbon(
geom.Line(direction, start_point),
geom.Line(direction, end_point),
draw_options={'facecolor': grad_color, 'edgecolor': 'None',
**draw_options}
))
return gradFunctions
def gradient_line(point1, point2, color1, color2, divisions=100, extrapolate_color=True, draw_options={})-
A line with a color gradient. The gradient transition will happen over a finite range in spacetime, and be monochromatic at either end.
Args
point1:STVectororiterable- Starting point of the gradient.
point2:STVectororiterable- Ending point of the gradient.
color1:color- A Matplotlib color for the gradient starting color.
color2:color- A Matplotlib color for the gradient ending color.
divisions:int, optional- The number of line segment divisions in the gradient. More divisions means a smoother gradient.
extrapolate_color:bool, optional- Flag for whether or not to extrapolate the color gradient across the line past the specified endpoints so that the color change spans as far as possible across the line.
draw_options:dict, optional- See
LorentzTransformable.
Returns
Source code
def gradient_line(point1, point2, color1, color2, divisions=100, extrapolate_color=True, draw_options=geom.geomrc['draw_options']): """A line with a color gradient. The gradient transition will happen over a finite range in spacetime, and be monochromatic at either end. Args: point1 (specrel.geom.STVector or iterable): Starting point of the gradient. point2 (specrel.geom.STVector or iterable): Ending point of the gradient. color1 (color): A Matplotlib color for the gradient starting color. color2 (color): A Matplotlib color for the gradient ending color. divisions (int, optional): The number of line segment divisions in the gradient. More divisions means a smoother gradient. extrapolate_color (bool, optional): Flag for whether or not to extrapolate the color gradient across the line past the specified endpoints so that the color change spans as far as possible across the line. draw_options (dict, optional): See `specrel.geom.LorentzTransformable`. Returns: specrel.geom.Collection: Collection containing the color gradient increments, in the order: 1. `specrel.geom.Ray` before `point1` with `color1`. 2. Line segments changing color from `point1` to `point2`. 3. `specrel.geom.Ray` after `point2` with `color2`. """ # Copy draw_options and remove color if it's there draw_options = dict(draw_options) draw_options.pop('color', None) # If extrapolating color, calculate the color gradient extremes if extrapolate_color: point1, point2, color1, color2, divisions = _colorgrad_extremes( point1, point2, color1, color2, divisions) # Color gradient calculator for the given points and colors def this_colorgrad(x): return _calc_colorgrad(x, point1, point2, color1, color2) # Line direction vector direc = geom.STVector(point2) - geom.STVector(point1) grad = geom.Collection() # Monochromatic ray at the tail end of the gradient line grad.append(geom.Ray(-direc, point1, draw_options={'color': color1, **draw_options})) # The line segments comprising the color gradient for i in range(divisions): start_point, _ = this_colorgrad(i/divisions) end_point, _ = this_colorgrad((i+1)/divisions) _, grad_color = this_colorgrad((i+1/2)/divisions) grad.append(geom.line_segment(start_point, end_point, draw_options={'color': grad_color, **draw_options})) # Monochromatic ray at the head end of the gradient line grad.append(geom.Ray(direc, point2, draw_options={'color': color2, **draw_options})) return grad def lateral_gradient_ribbon(direction, point1, point2, color1, color2, divisions=100, draw_options={})-
A
Ribbon-esque object with a lateral color gradient (across the finite direction).Args
direction:STVectororiterable- Direction vector for the gradient.
point1:STVectororiterable- A point that the first edge of the ribbon passes through.
point2:STVectororiterable- A point that the second edge of the ribbon passes through.
color1:color- A Matplotlib color for the gradient starting color.
color2:color- A Matplotlib color for the gradient ending color.
divisions:int, optional- The number of line segment divisions in the gradient. More divisions means a smoother gradient.
draw_options:TYPE, optional- See
LorentzTransformable.
Returns
Collection:- Collection containing the
Ribbonobjects of slowly changing color frompoint1topoint2.
Source code
def lateral_gradient_ribbon(direction, point1, point2, color1, color2, divisions=100, draw_options=geom.geomrc['draw_options']): """A `specrel.geom.Ribbon`-esque object with a lateral color gradient (across the finite direction). Args: direction (specrel.geom.STVector or iterable): Direction vector for the gradient. point1 (specrel.geom.STVector or iterable): A point that the first edge of the ribbon passes through. point2 (specrel.geom.STVector or iterable): A point that the second edge of the ribbon passes through. color1 (color): A Matplotlib color for the gradient starting color. color2 (color): A Matplotlib color for the gradient ending color. divisions (int, optional): The number of line segment divisions in the gradient. More divisions means a smoother gradient. draw_options (TYPE, optional): See `specrel.geom.LorentzTransformable`. Returns: specrel.geom.Collection: Collection containing the `specrel.geom.Ribbon` objects of slowly changing color from `point1` to `point2`. """ # Copy draw_options and remove color, facecolor, and edgecolor if they're # there draw_options = dict(draw_options) draw_options.pop('color', None) draw_options.pop('facecolor', None) draw_options.pop('edgecolor', None) # Color gradient calculator for the given points and colors def this_colorgrad(x): return _calc_colorgrad(x, point1, point2, color1, color2) grad = geom.Collection() # Ribbons comprising the color gradient, as we move from point1 to point2 for i in range(divisions): start_point, _ = this_colorgrad(i/divisions) # Overlap bands by half a division, except the last one end_point, _ = this_colorgrad(min((i+1+1/2)/divisions, 1)) _, grad_color = this_colorgrad((i+1/2)/divisions) # Explicitly turn off edge coloring grad.append(geom.Ribbon( geom.Line(direction, start_point), geom.Line(direction, end_point), draw_options={'facecolor': grad_color, 'edgecolor': 'None', **draw_options} )) return grad def longitudinal_gradient_ribbon(line1_endpoints, line2_endpoints, color1, color2, divisions=100, extrapolate_color=True, draw_options={})-
A
Ribbon-esque object with a longitudinal color gradient (across the infinite direction).Args
line1_endpoints:list- list of two
STVector-convertible points defining the start and end positions of the gradient along the first edge of the ribbon. line2_endpoints:list- Same as
line1_endpoints, but for the second edge of the ribbon. color1:color- A Matplotlib color for the gradient starting color.
color2:color- A Matplotlib color for the gradient ending color.
divisions:int, optional- The number of line segment divisions in the gradient. More divisions means a smoother gradient.
extrapolate_color:bool, optional- Flag for whether or not to extrapolate the color gradient across the ribbon past the specified endpoints so that the color change spans as far as possible across the ribbon.
draw_options:TYPE, optional- See
LorentzTransformable.
Returns
Collection:-
Collection containing the color gradient increments, in the order:
HalfRibbonwithcolor1before both line starting points.- Polygons changing color from starts of the lines to the ends.
HalfRibbonwithcolor2after both line ending points.
Source code
def longitudinal_gradient_ribbon(line1_endpoints, line2_endpoints, color1, color2, divisions=100, extrapolate_color=True, draw_options=geom.geomrc['draw_options']): """A `specrel.geom.Ribbon`-esque object with a longitudinal color gradient (across the infinite direction). Args: line1_endpoints (list): list of two `specrel.geom.STVector`-convertible points defining the start and end positions of the gradient along the first edge of the ribbon. line2_endpoints (list): Same as `line1_endpoints`, but for the second edge of the ribbon. color1 (color): A Matplotlib color for the gradient starting color. color2 (color): A Matplotlib color for the gradient ending color. divisions (int, optional): The number of line segment divisions in the gradient. More divisions means a smoother gradient. extrapolate_color (bool, optional): Flag for whether or not to extrapolate the color gradient across the ribbon past the specified endpoints so that the color change spans as far as possible across the ribbon. draw_options (TYPE, optional): See `specrel.geom.LorentzTransformable`. Returns: specrel.geom.Collection: Collection containing the color gradient increments, in the order: 1. `specrel.geom.HalfRibbon` with `color1` before both line starting points. 2. Polygons changing color from starts of the lines to the ends. 3. `specrel.geom.HalfRibbon` with `color2` after both line ending points. """ # Copy draw_options and remove color, facecolor, and edgecolor if they're # there draw_options = dict(draw_options) draw_options.pop('color', None) draw_options.pop('facecolor', None) draw_options.pop('edgecolor', None) # If extrapolating color, calculate the color gradient extremes if extrapolate_color: point1, point2, color1, color2, divisions = _colorgrad_extremes( *line1_endpoints, color1, color2, divisions) line1_endpoints = (point1, point2) point1, point2, _, _, _ = _colorgrad_extremes( *line2_endpoints, color1, color2, divisions) line2_endpoints = (point1, point2) # Color gradient calculators for each line with the given colors def line1_colorgrad(x): return _calc_colorgrad(x, *line1_endpoints, color1, color2) def line2_colorgrad(x): return _calc_colorgrad(x, *line2_endpoints, color1, color2) # Direction vectors of each line direc1 = geom.STVector(line1_endpoints[1]) - geom.STVector(line1_endpoints[0]) direc2 = geom.STVector(line2_endpoints[1]) - geom.STVector(line2_endpoints[0]) grad = geom.Collection() # Form the monochromatic half ribbon at the tail end of the gradient # Overlap with the first polygon by half a division to mitigate any # boundary gaps start_point1, _ = line1_colorgrad(1/(2*divisions)) start_point2, _ = line2_colorgrad(1/(2*divisions)) grad.append(geom.HalfRibbon( geom.Ray(-direc1, start_point1), geom.Ray(-direc2, start_point2), # Explicitly turn off edge coloring draw_options={'facecolor': color1, 'edgecolor': 'None', **draw_options})) # Interior polygons comprising the color gradient for i in range(divisions): start_point1, _ = line1_colorgrad(i/divisions) # Overlap bands by half a division end_point1, _ = line1_colorgrad((i+1+1/2)/divisions) start_point2, _ = line2_colorgrad(i/divisions) end_point2, _ = line2_colorgrad((i+1+1/2)/divisions) _, grad_color = line1_colorgrad((i+1/2)/divisions) grad.append(geom.polygon( [start_point1, end_point1, end_point2, start_point2], draw_options={'facecolor': grad_color, **draw_options})) # Monochromatic half ribon at the head end of the gradient grad.append(geom.HalfRibbon( geom.Ray(direc1, line1_endpoints[1]), geom.Ray(direc2, line2_endpoints[1]), draw_options={'facecolor': color2, 'edgecolor': 'None', **draw_options})) return grad