from sympy import *

x, p, d, C, S = symbols('x p d C S')

x1 = - (p * C)
y1 = p * S

x2 = (1 - p + d) * C 
y2 = (1 - p + d) * S

x3 = -(p + d) * C
y3 = (p + d) * S

x4 = (1 -p) * C
y4 = (1 -p) * S

f1 = ((y2 - y1) / (x2 - x1)) * (x - x1) + y1
f2 = ((y4 - y3) / (x4 - x3)) * (x - x3) + y3

f1_eq_f2 = Eq(f1, f2)

pp = solve(f1_eq_f2, p)[0]
print(latex(simplify(pp)))

curve = simplify(f1.subs(p, pp))
print(latex(curve))