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