typerig.core.objects.cubicbezier

typerig.core.objects.cubicbezier (version 0.26.6)

# MODULE: TypeRig / Core / Cubic Bezier (Object)
# -----------------------------------------------------------
# (C) Vassil Kateliev, 2016-2020        (http://www.kateliev.com)
# (C) Karandash Type Foundry            (http://www.karandash.eu)
#------------------------------------------------------------
# www.typerig.com

Modules

• math

Classes

• builtin.object
• • CubicBezier

class CubicBezier(builtin.object)

# - Classes -----------------------------

Methods

init(self, *argv)

repr(self)

asList(self)

# -- Modifiers

doSwap(self)

doTransform(self, transform=None)

get_handle_length(self)

Returns handle length and radii from base points.

lerp_first(self, shift)

lerp_last(self, shift)

solve_curvature(self, time)

Find Curvature of on-curve point at given time

solve_derivative(self, time)

Returns point of on-curve point at given time and vector of 1st and 2nd derivative.

solve_distance_end(self, distance, timeStep=0.01)

Returns time at which the given distance to end of bezier is met. 
Probing is executed withing timeStep in range from 0 to 1. The finer the step the preciser the results.

solve_distance_start(self, distance, timeStep=0.01)

Returns time at which the given distance to beginning of bezier is met. 
Probing is executed withing timeStep in range from 0 to 1. The finer the step the preciser the results.

solve_extremes(self)

Finds curve extremes and returns [(extreme_01_x, extreme_01_y, extreme_01_t)...(extreme_n_x, extreme_n_y, extreme_n_t)]

solve_handle_distance_from_base(self, ratio=(0.5, 0.5))

Finds new handle positions for given ratio from base points.

solve_hobby(self, curvature=(0.9, 0.9))

Calculates and applies John Hobby's mock-curvature-smoothness by given curvature - tuple(float,float) or (float)
Based on Metapolator's Hobby Spline by Juraj Sukop, Lasse Fister, Simon Egli

solve_hobby_curvature(self)

Returns current curvature coefficients (complex(alpha), complex(beta)) for 
both handles according to John Hobby's mock-curvature calculation

solve_parallel(self, vector, fullOutput=False)

Finds the t value along a cubic Bezier where a tangent (1st derivative) is parallel with the direction vector.
vector: a pair of values representing the direction of interest (magnitude is ignored).
returns 0.0 <= t <= 1.0 or None

# Solving the dot product of cubic beziers first derivate to the vector given B'(t) x V. Two vectors are perpendicular if their dot product is zero. 
# So if you could find the (1) perpendicular of V it will be collinear == tangent of the curve so the equation to be solved is:
# B'(t) x V(x,y) = 0; -(a*t^2 + b*t + c)*x + (g*t^2 + h*t + i)*y = 0 solved for t, where a,b,c are coefs for X and g,h,i for Y B'(t) derivate of curve
# 
# Inspired by answer given by 'unutbu' on the stackoverflow question: http://stackoverflow.com/questions/20825173/how-to-find-a-point-if-any-on-quadratic-bezier-with-a-given-tangent-direction
# Recoded and recalculated for qubic beziers. Used 'Rearrange It' app at http://www.wolframalpha.com/widgets/view.jsp?id=4be4308d0f9d17d1da68eea39de9b2ce was invaluable.
#
# DOTO: Fix calculation optimization error - will yield false positive result in cases #1 and #2 if vector is 45 degrees

solve_point(self, time)

Find point on cubic bezier at given time

solve_proportional_handles(self, proportion=0.3)

Equalizes handle length to given float(proportion)

solve_slice(self, time)

Returns two segments representing cubic bezier sliced at given time. 
Output: list [(Start), (Start_BCP_out), (Slice_BCP_in), (Slice), (Slice_BCP_out), (End_BCP_in), (End)] of tuples (x,y)

solve_tunni(self)

Make proportional handles keeping curvature and on-curve point positions 
Based on modified Andres Torresi implementation of Eduardo Tunni's method for control points

Descriptors

dict

dictionary for instance variables (if defined)

weakref

list of weak references to the object (if defined)

height

line

points

tuple

width

x

x_max

y

y_max

CubicBezier

typerig.core.objects.cubicbezier.CubicBezier = class CubicBezier(__builtin__.object)

# - Classes -----------------------------

Methods

__init__(self, *argv)

__repr__(self)

asList(self)

# -- Modifiers

doSwap(self)

doTransform(self, transform=None)

get_handle_length(self)

Returns handle length and radii from base points.

lerp_first(self, shift)

lerp_last(self, shift)

solve_curvature(self, time)

Find Curvature of on-curve point at given time

solve_derivative(self, time)

Returns point of on-curve point at given time and vector of 1st and 2nd derivative.

solve_distance_end(self, distance, timeStep=0.01)

Returns time at which the given distance to end of bezier is met. 
Probing is executed withing timeStep in range from 0 to 1. The finer the step the preciser the results.

solve_distance_start(self, distance, timeStep=0.01)

Returns time at which the given distance to beginning of bezier is met. 
Probing is executed withing timeStep in range from 0 to 1. The finer the step the preciser the results.

solve_extremes(self)

Finds curve extremes and returns [(extreme_01_x, extreme_01_y, extreme_01_t)...(extreme_n_x, extreme_n_y, extreme_n_t)]

solve_handle_distance_from_base(self, ratio=(0.5, 0.5))

Finds new handle positions for given ratio from base points.

solve_hobby(self, curvature=(0.9, 0.9))

Calculates and applies John Hobby's mock-curvature-smoothness by given curvature - tuple(float,float) or (float)
Based on Metapolator's Hobby Spline by Juraj Sukop, Lasse Fister, Simon Egli

solve_hobby_curvature(self)

Returns current curvature coefficients (complex(alpha), complex(beta)) for 
both handles according to John Hobby's mock-curvature calculation

solve_parallel(self, vector, fullOutput=False)

Finds the t value along a cubic Bezier where a tangent (1st derivative) is parallel with the direction vector.
vector: a pair of values representing the direction of interest (magnitude is ignored).
returns 0.0 <= t <= 1.0 or None

# Solving the dot product of cubic beziers first derivate to the vector given B'(t) x V. Two vectors are perpendicular if their dot product is zero. 
# So if you could find the (1) perpendicular of V it will be collinear == tangent of the curve so the equation to be solved is:
# B'(t) x V(x,y) = 0; -(a*t^2 + b*t + c)*x + (g*t^2 + h*t + i)*y = 0 solved for t, where a,b,c are coefs for X and g,h,i for Y B'(t) derivate of curve
# 
# Inspired by answer given by 'unutbu' on the stackoverflow question: http://stackoverflow.com/questions/20825173/how-to-find-a-point-if-any-on-quadratic-bezier-with-a-given-tangent-direction
# Recoded and recalculated for qubic beziers. Used 'Rearrange It' app at http://www.wolframalpha.com/widgets/view.jsp?id=4be4308d0f9d17d1da68eea39de9b2ce was invaluable.
#
# DOTO: Fix calculation optimization error - will yield false positive result in cases #1 and #2 if vector is 45 degrees

solve_point(self, time)

Find point on cubic bezier at given time

solve_proportional_handles(self, proportion=0.3)

Equalizes handle length to given float(proportion)

solve_slice(self, time)

Returns two segments representing cubic bezier sliced at given time. 
Output: list [(Start), (Start_BCP_out), (Slice_BCP_in), (Slice), (Slice_BCP_out), (End_BCP_in), (End)] of tuples (x,y)

solve_tunni(self)

Make proportional handles keeping curvature and on-curve point positions 
Based on modified Andres Torresi implementation of Eduardo Tunni's method for control points

Descriptors

__dict__

dictionary for instance variables (if defined)

__weakref__

list of weak references to the object (if defined)

height

line

points

tuple

width

x

x_max

y

y_max

solve_point

typerig.core.objects.cubicbezier.CubicBezier.solve_point = solve_point(self, time) unbound typerig.core.objects.cubicbezier.CubicBezier method

Find point on cubic bezier at given time

solve_derivative

typerig.core.objects.cubicbezier.CubicBezier.solve_derivative = solve_derivative(self, time) unbound typerig.core.objects.cubicbezier.CubicBezier method

Returns point of on-curve point at given time and vector of 1st and 2nd derivative.

solve_curvature

typerig.core.objects.cubicbezier.CubicBezier.solve_curvature = solve_curvature(self, time) unbound typerig.core.objects.cubicbezier.CubicBezier method

Find Curvature of on-curve point at given time

solve_slice

typerig.core.objects.cubicbezier.CubicBezier.solve_slice = solve_slice(self, time) unbound typerig.core.objects.cubicbezier.CubicBezier method

Returns two segments representing cubic bezier sliced at given time. 
Output: list [(Start), (Start_BCP_out), (Slice_BCP_in), (Slice), (Slice_BCP_out), (End_BCP_in), (End)] of tuples (x,y)

solve_distance_start

typerig.core.objects.cubicbezier.CubicBezier.solve_distance_start = solve_distance_start(self, distance, timeStep=0.01) unbound typerig.core.objects.cubicbezier.CubicBezier method

Returns time at which the given distance to beginning of bezier is met. 
Probing is executed withing timeStep in range from 0 to 1. The finer the step the preciser the results.

solve_distance_end

typerig.core.objects.cubicbezier.CubicBezier.solve_distance_end = solve_distance_end(self, distance, timeStep=0.01) unbound typerig.core.objects.cubicbezier.CubicBezier method

Returns time at which the given distance to end of bezier is met. 
Probing is executed withing timeStep in range from 0 to 1. The finer the step the preciser the results.

solve_extremes

typerig.core.objects.cubicbezier.CubicBezier.solve_extremes = solve_extremes(self) unbound typerig.core.objects.cubicbezier.CubicBezier method

Finds curve extremes and returns [(extreme_01_x, extreme_01_y, extreme_01_t)...(extreme_n_x, extreme_n_y, extreme_n_t)]

solve_parallel

typerig.core.objects.cubicbezier.CubicBezier.solve_parallel = solve_parallel(self, vector, fullOutput=False) unbound typerig.core.objects.cubicbezier.CubicBezier method

Finds the t value along a cubic Bezier where a tangent (1st derivative) is parallel with the direction vector.
vector: a pair of values representing the direction of interest (magnitude is ignored).
returns 0.0 <= t <= 1.0 or None

# Solving the dot product of cubic beziers first derivate to the vector given B'(t) x V. Two vectors are perpendicular if their dot product is zero. 
# So if you could find the (1) perpendicular of V it will be collinear == tangent of the curve so the equation to be solved is:
# B'(t) x V(x,y) = 0; -(a*t^2 + b*t + c)*x + (g*t^2 + h*t + i)*y = 0 solved for t, where a,b,c are coefs for X and g,h,i for Y B'(t) derivate of curve
# 
# Inspired by answer given by 'unutbu' on the stackoverflow question: http://stackoverflow.com/questions/20825173/how-to-find-a-point-if-any-on-quadratic-bezier-with-a-given-tangent-direction
# Recoded and recalculated for qubic beziers. Used 'Rearrange It' app at http://www.wolframalpha.com/widgets/view.jsp?id=4be4308d0f9d17d1da68eea39de9b2ce was invaluable.
#
# DOTO: Fix calculation optimization error - will yield false positive result in cases #1 and #2 if vector is 45 degrees

solve_proportional_handles

typerig.core.objects.cubicbezier.CubicBezier.solve_proportional_handles = solve_proportional_handles(self, proportion=0.3) unbound typerig.core.objects.cubicbezier.CubicBezier method

Equalizes handle length to given float(proportion)

solve_handle_distance_from_base

typerig.core.objects.cubicbezier.CubicBezier.solve_handle_distance_from_base = solve_handle_distance_from_base(self, ratio=(0.5, 0.5)) unbound typerig.core.objects.cubicbezier.CubicBezier method

Finds new handle positions for given ratio from base points.

get_handle_length

typerig.core.objects.cubicbezier.CubicBezier.get_handle_length = get_handle_length(self) unbound typerig.core.objects.cubicbezier.CubicBezier method

Returns handle length and radii from base points.

solve_hobby

typerig.core.objects.cubicbezier.CubicBezier.solve_hobby = solve_hobby(self, curvature=(0.9, 0.9)) unbound typerig.core.objects.cubicbezier.CubicBezier method

Calculates and applies John Hobby's mock-curvature-smoothness by given curvature - tuple(float,float) or (float)
Based on Metapolator's Hobby Spline by Juraj Sukop, Lasse Fister, Simon Egli

solve_hobby_curvature

typerig.core.objects.cubicbezier.CubicBezier.solve_hobby_curvature = solve_hobby_curvature(self) unbound typerig.core.objects.cubicbezier.CubicBezier method

Returns current curvature coefficients (complex(alpha), complex(beta)) for 
both handles according to John Hobby's mock-curvature calculation

solve_tunni

typerig.core.objects.cubicbezier.CubicBezier.solve_tunni = solve_tunni(self) unbound typerig.core.objects.cubicbezier.CubicBezier method

Make proportional handles keeping curvature and on-curve point positions 
Based on modified Andres Torresi implementation of Eduardo Tunni's method for control points