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# Licensed under the Apache License, Version 2.0 (the "License");
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# http://www.apache.org/licenses/LICENSE-2.0
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"""simple Sympy helper functions
"""
from symengine import sqrt
[docs]def line(x, point_x_1, point_y_1, point_x_2, point_y_2):
"""
line function from point intercepts
Parameters
----------
x : Sympy Symbol/Exp
the `x` in equation `y=a*x+b`
point_x_1 : Sympy Symbol/Exp, float, int
first intercept x position
point_y_1 : Sympy Symbol/Exp, float, int
first intercept y position
point_x_2 : Sympy Symbol/Exp, float, int
second intercept x position
point_y_2 : Sympy Symbol/Exp, float, int
second intercept y position
Returns
-------
y : Sympy Expr
`y=slope*x+intercept`
"""
slope = (point_y_1 - point_y_2) / (point_x_1 - point_x_2)
intercept = point_y_1 - slope * point_x_1
return slope * x + intercept
[docs]def parabola(x, inter_1, inter_2, height):
"""
parabola from point intercepts
Parameters
----------
x : Sympy Symbol/Exp
the `x` in equation `y=a*x*2+b*x+c`
inter_1 : Sympy Symbol/Exp, float, int
first intercept such that `y=0` when `x=inter_1`
inter_2 : Sympy Symbol/Exp, float, int
second intercept such that `y=0` when `x=inter_1`
height : Sympy Symbol/Exp, float, int
max height of parabola
Returns
-------
y : Sympy Expr
`y=factor*(x-inter_1)*(x-+inter_2)`
"""
factor = (4 * height) / (-(inter_1**2) - inter_2**2 + 2 * inter_1 * inter_2)
return factor * (x - inter_1) * (x - inter_2)
[docs]def parabola2D(x, y, inter_1_x, inter_2_x, inter_1_y, inter_2_y, height):
"""
square parabola from point intercepts
Parameters
----------
x : Sympy Symbol/Exp
the `x` in equation `z=parabola(x)*parabola(y)`
y : Sympy Symbol/Exp
the `y` in equation `z=a*x**2+b*y**2+c*xy+d*y+e*x+f`
inter_1_x : Sympy Symbol/Exp, float, int
first intercept such that `z=0` when `x=inter_1_x`
inter_2_x : Sympy Symbol/Exp, float, int
second intercept such that `z=0` when `x=inter_2_x`
inter_1_y : Sympy Symbol/Exp, float, int
first intercept such that `z=0` when `y=inter_1_y`
inter_2_y : Sympy Symbol/Exp, float, int
second intercept such that `z=0` when `y=inter_2_y`
height : Sympy Symbol/Exp, float, int
max height of parabola
Returns
-------
y : Sympy Expr
`y=factor*(x-inter_1)*(x-+inter_2)`
"""
parabola_x = parabola(x, inter_1_x, inter_2_x, sqrt(height))
parabola_y = parabola(y, inter_1_y, inter_2_y, sqrt(height))
return parabola_x * parabola_y