1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
|
#include "tobii-settings.hpp"
#include <cmath>
#include <iterator>
#include <utility>
#include <numeric>
/*
def plot(f, max=None, min=None):
if max is None and min is None:
min, max = -1.5, 1.5
elif max is None:
max=-min
elif min is None:
min=-max
assert max > min
c = 1e-4*(max-min)
if c < 1e-12:
c = 1e-6
rng = arange(min, max, c)
plt.plot(rng, map(f, rng))
*/
/*
def richards(b, q, v, c=1):
return lambda x: 1./((c + q * exp(-b * x) ** (1./v)))
*/
void rel_settings::make_spline()
{
const double dz_len_ = dz_len(),
expt_len_ = expt_len(),
expt_norm_ = expt_norm(),
expt_slope_ = expt_slope(),
log_len_ = log_len();
const double expt_deriv_at_end = expt_norm_ * expt_slope_ * std::pow(expt_len_, expt_slope_ - 1); // cnx^(n-1)
const double expt_at_end = expt_norm_ * std::pow(expt_len_, expt_slope_); // cx^n
const double lin_len = 1 - dz_len_ - expt_len_ - log_len_;
// this isn't correct but works.
// we use exponentiation of the linear part to get logarithmic approximation of the linear
// part rather than linear approximation of the linear part
const double lin_at_end = std::pow(M_E, lin_len * expt_deriv_at_end - expt_at_end); // e^(cx + a)
const double lin_deriv_at_end = expt_deriv_at_end * std::exp(-expt_at_end + expt_deriv_at_end * lin_len); // ce^(a + cx)
// this was all derived by the awesome linear approximation
// calculator <http://www.emathhelp.net/calculators/calculus-1/linear-approximation-calculator/>
auto expt_part = [=](double x) { return expt_norm_ * std::pow(x, expt_slope_); };
const double expt_inv_norm = expt_norm_/expt_part(expt_len_);
auto lin_part = [=](double x) { return expt_inv_norm * (expt_at_end + expt_deriv_at_end * (x - expt_len_)); };
const double lin_inv_norm = (1 - expt_norm_ - .25)/lin_part(lin_len);
// TODO needs norm for log/lin parts
auto log_part = [=](double x) { return expt_inv_norm * lin_inv_norm * std::log(lin_at_end + lin_deriv_at_end * (x - lin_len)); };
const double log_inv_norm = .25/log_part(expt_len_);
qDebug() << "lin" << expt_deriv_at_end << lin_inv_norm;
part functors[]
{
{ dz_len_, [](double) { return 0; } },
{ expt_len_, [=](double x) { return expt_inv_norm * expt_part(x); } }, // cx^n
{ lin_len, [=](double x) { return lin_inv_norm * lin_part(x); } }, // cx + a
{ log_len_, [=](double x) { return log_inv_norm * log_part(x); } }, // ln(cx + a)
};
make_spline_(functors, std::distance(std::begin(functors), std::end(functors)));
}
rel_settings::rel_settings() :
opts("tobii-eyex-relative-mode"),
speed(b, "speed", s(3, .1, 10)),
dz_len(b, "deadzone-length", s(.04, 0, .2)),
expt_slope(b, "exponent-slope", s(1.75, 1.5, 3)),
expt_len(b, "exponent-length", s(.2, 0, .5)),
expt_norm(b, "exponent-norm", s(.4, .1, .5)),
log_len(b, "log-len", s(.1, 0, .2)),
acc_mode_spline(100, 100, "")
{
make_spline();
}
// there's an underflow in spline code, can't use 1e0
static constexpr const double spline_max = 1e2;
double rel_settings::gain(double value)
{
return acc_mode_spline.get_value_no_save(value * spline_max) / spline_max;
}
void rel_settings::make_spline_(part* functors, unsigned len)
{
acc_mode_spline.removeAllPoints();
double lastx = 0;
for (unsigned k = 0; k < len; k++)
{
part& fun = functors[k];
static constexpr unsigned nparts = 7;
for (unsigned i = 1; i <= nparts; i++)
{
const double x = i*fun.len/nparts;
const double y = clamp(fun.f(x), 0, 1);
if (i == nparts/2)
qDebug() << k << i << x << y;
acc_mode_spline.addPoint((lastx + x) * spline_max, y * spline_max);
}
lastx += fun.len;
}
}
|
