font-Roboto/third_party/spiro/curves/cornu.py

from math import *

# implementation adapted from cephes

def polevl(x, coef):
    ans = coef[-1]
    for i in range(len(coef) - 2, -1, -1):
        ans = ans * x + coef[i]
    return ans

sn = [
-2.99181919401019853726E3,
 7.08840045257738576863E5,
-6.29741486205862506537E7,
 2.54890880573376359104E9,
-4.42979518059697779103E10,
 3.18016297876567817986E11
]
sn.reverse()
sd = [
 1.00000000000000000000E0,
 2.81376268889994315696E2,
 4.55847810806532581675E4,
 5.17343888770096400730E6,
 4.19320245898111231129E8,
 2.24411795645340920940E10,
 6.07366389490084639049E11
]
sd.reverse()
cn = [
-4.98843114573573548651E-8,
 9.50428062829859605134E-6,
-6.45191435683965050962E-4,
 1.88843319396703850064E-2,
-2.05525900955013891793E-1,
 9.99999999999999998822E-1
]
cn.reverse()
cd = [
 3.99982968972495980367E-12,
 9.15439215774657478799E-10,
 1.25001862479598821474E-7,
 1.22262789024179030997E-5,
 8.68029542941784300606E-4,
 4.12142090722199792936E-2,
 1.00000000000000000118E0
]
cd.reverse()

fn = [
  4.21543555043677546506E-1,
  1.43407919780758885261E-1,
  1.15220955073585758835E-2,
  3.45017939782574027900E-4,
  4.63613749287867322088E-6,
  3.05568983790257605827E-8,
  1.02304514164907233465E-10,
  1.72010743268161828879E-13,
  1.34283276233062758925E-16,
  3.76329711269987889006E-20
]
fn.reverse()
fd = [
  1.00000000000000000000E0,
  7.51586398353378947175E-1,
  1.16888925859191382142E-1,
  6.44051526508858611005E-3,
  1.55934409164153020873E-4,
  1.84627567348930545870E-6,
  1.12699224763999035261E-8,
  3.60140029589371370404E-11,
  5.88754533621578410010E-14,
  4.52001434074129701496E-17,
  1.25443237090011264384E-20
]
fd.reverse()
gn = [
  5.04442073643383265887E-1,
  1.97102833525523411709E-1,
  1.87648584092575249293E-2,
  6.84079380915393090172E-4,
  1.15138826111884280931E-5,
  9.82852443688422223854E-8,
  4.45344415861750144738E-10,
  1.08268041139020870318E-12,
  1.37555460633261799868E-15,
  8.36354435630677421531E-19,
  1.86958710162783235106E-22
]
gn.reverse()
gd = [
  1.00000000000000000000E0,
  1.47495759925128324529E0,
  3.37748989120019970451E-1,
  2.53603741420338795122E-2,
  8.14679107184306179049E-4,
  1.27545075667729118702E-5,
  1.04314589657571990585E-7,
  4.60680728146520428211E-10,
  1.10273215066240270757E-12,
  1.38796531259578871258E-15,
  8.39158816283118707363E-19,
  1.86958710162783236342E-22
]
gd.reverse()


def fresnel(xxa):
    x = abs(xxa)
    x2 = x * x
    if x2 < 2.5625:
        t = x2 * x2
        ss = x * x2 * polevl(t, sn) / polevl(t, sd)
        cc = x * polevl(t, cn) / polevl(t, cd)
    elif x > 36974.0:
        ss = 0.5
        cc = 0.5
    else:
        t = pi * x2
        u = 1.0 / (t * t)
        t = 1.0 / t
        f = 1.0 - u * polevl(u, fn) / polevl(u, fd)
        g = t * polevl(u, gn) / polevl(u, gd)
        t = pi * .5 * x2
        c = cos(t)
        s = sin(t)
        t = pi * x
        cc = 0.5 + (f * s - g * c) / t
        ss = 0.5 - (f * c + g * s) / t
    if xxa < 0:
        cc = -cc
        ss = -ss
    return ss, cc

def eval_cornu(t):
    spio2 = sqrt(pi * .5)
    s, c = fresnel(t / spio2)
    s *= spio2
    c *= spio2
    return s, c