tracker/tobii: flush, but still broken

Needs the spline class to allow initializing itself from a function. Even if the
passed control points are correct, it still looks like shit. Presently they
aren't correct though. Need to work on linear approximation.

4 files changed, 106 insertions, 170 deletions

diff --git a/tracker-tobii-eyex/tobii-eyex-dialog.cpp b/tracker-tobii-eyex/tobii-eyex-dialog.cpp
index 0388ddfb..8997c6c2 100644
--- a/tracker-tobii-eyex/tobii-eyex-dialog.cpp
+++ b/tracker-tobii-eyex/tobii-eyex-dialog.cpp
@@ -20,9 +20,7 @@ tobii_eyex_dialog::tobii_eyex_dialog()
     tie_setting(rs.expt_len, ui.exponent_len);
     tie_setting(rs.expt_norm, ui.exponent_norm);
 
-    tie_setting(rs.log_slope, ui.log_base);
     tie_setting(rs.log_len, ui.log_len);
-    tie_setting(rs.log_norm, ui.log_norm);
 
     connect(rs.b.get(), &bundle_::changed, this, [this]() { rs.make_spline(); }, Qt::QueuedConnection);
 
diff --git a/tracker-tobii-eyex/tobii-eyex-dialog.ui b/tracker-tobii-eyex/tobii-eyex-dialog.ui
index 1e622f93..b6138514 100644
--- a/tracker-tobii-eyex/tobii-eyex-dialog.ui
+++ b/tracker-tobii-eyex/tobii-eyex-dialog.ui
@@ -192,19 +192,22 @@
               </property>
              </widget>
             </item>
-            <item row="0" column="1">
-             <widget class="QLabel" name="speed_label">
-              <property name="minimumSize">
-               <size>
-                <width>24</width>
-                <height>0</height>
-               </size>
+            <item row="1" column="2">
+             <widget class="QSlider" name="deadzone">
+              <property name="sizePolicy">
+               <sizepolicy hsizetype="Expanding" vsizetype="Maximum">
+                <horstretch>0</horstretch>
+                <verstretch>0</verstretch>
+               </sizepolicy>
               </property>
-              <property name="text">
-               <string>0</string>
+              <property name="orientation">
+               <enum>Qt::Horizontal</enum>
               </property>
-              <property name="alignment">
-               <set>Qt::AlignRight|Qt::AlignTrailing|Qt::AlignVCenter</set>
+              <property name="tickPosition">
+               <enum>QSlider::TicksAbove</enum>
+              </property>
+              <property name="tickInterval">
+               <number>25</number>
               </property>
              </widget>
             </item>
@@ -224,25 +227,6 @@
               </property>
              </widget>
             </item>
-            <item row="1" column="2">
-             <widget class="QSlider" name="deadzone">
-              <property name="sizePolicy">
-               <sizepolicy hsizetype="Expanding" vsizetype="Maximum">
-                <horstretch>0</horstretch>
-                <verstretch>0</verstretch>
-               </sizepolicy>
-              </property>
-              <property name="orientation">
-               <enum>Qt::Horizontal</enum>
-              </property>
-              <property name="tickPosition">
-               <enum>QSlider::TicksAbove</enum>
-              </property>
-              <property name="tickInterval">
-               <number>25</number>
-              </property>
-             </widget>
-            </item>
             <item row="2" column="2">
              <widget class="QSlider" name="exponent">
               <property name="sizePolicy">
@@ -262,8 +246,8 @@
               </property>
              </widget>
             </item>
-            <item row="1" column="1">
-             <widget class="QLabel" name="deadzone_label">
+            <item row="0" column="1">
+             <widget class="QLabel" name="speed_label">
               <property name="minimumSize">
                <size>
                 <width>24</width>
@@ -291,6 +275,22 @@
               </property>
              </widget>
             </item>
+            <item row="1" column="1">
+             <widget class="QLabel" name="deadzone_label">
+              <property name="minimumSize">
+               <size>
+                <width>24</width>
+                <height>0</height>
+               </size>
+              </property>
+              <property name="text">
+               <string>0</string>
+              </property>
+              <property name="alignment">
+               <set>Qt::AlignRight|Qt::AlignTrailing|Qt::AlignVCenter</set>
+              </property>
+             </widget>
+            </item>
             <item row="5" column="0">
              <widget class="QLabel" name="label_8">
               <property name="sizePolicy">
@@ -333,19 +333,6 @@
               </property>
              </widget>
             </item>
-            <item row="3" column="0">
-             <widget class="QLabel" name="label_5">
-              <property name="sizePolicy">
-               <sizepolicy hsizetype="Maximum" vsizetype="Preferred">
-                <horstretch>0</horstretch>
-                <verstretch>0</verstretch>
-               </sizepolicy>
-              </property>
-              <property name="text">
-               <string>Exponent segment length</string>
-              </property>
-             </widget>
-            </item>
             <item row="5" column="2">
              <widget class="QSlider" name="log_len">
               <property name="sizePolicy">
@@ -365,8 +352,8 @@
               </property>
              </widget>
             </item>
-            <item row="6" column="0">
-             <widget class="QLabel" name="label_9">
+            <item row="3" column="0">
+             <widget class="QLabel" name="label_5">
               <property name="sizePolicy">
                <sizepolicy hsizetype="Maximum" vsizetype="Preferred">
                 <horstretch>0</horstretch>
@@ -374,42 +361,7 @@
                </sizepolicy>
               </property>
               <property name="text">
-               <string>Log slope</string>
-              </property>
-             </widget>
-            </item>
-            <item row="6" column="1">
-             <widget class="QLabel" name="log_base_label">
-              <property name="minimumSize">
-               <size>
-                <width>24</width>
-                <height>0</height>
-               </size>
-              </property>
-              <property name="text">
-               <string>0</string>
-              </property>
-              <property name="alignment">
-               <set>Qt::AlignRight|Qt::AlignTrailing|Qt::AlignVCenter</set>
-              </property>
-             </widget>
-            </item>
-            <item row="6" column="2">
-             <widget class="QSlider" name="log_base">
-              <property name="sizePolicy">
-               <sizepolicy hsizetype="Expanding" vsizetype="Maximum">
-                <horstretch>0</horstretch>
-                <verstretch>0</verstretch>
-               </sizepolicy>
-              </property>
-              <property name="orientation">
-               <enum>Qt::Horizontal</enum>
-              </property>
-              <property name="tickPosition">
-               <enum>QSlider::TicksAbove</enum>
-              </property>
-              <property name="tickInterval">
-               <number>25</number>
+               <string>Exponent segment length</string>
               </property>
              </widget>
             </item>
@@ -448,19 +400,6 @@
               </property>
              </widget>
             </item>
-            <item row="4" column="0">
-             <widget class="QLabel" name="label_6">
-              <property name="sizePolicy">
-               <sizepolicy hsizetype="Maximum" vsizetype="Preferred">
-                <horstretch>0</horstretch>
-                <verstretch>0</verstretch>
-               </sizepolicy>
-              </property>
-              <property name="text">
-               <string>Exponent norm</string>
-              </property>
-             </widget>
-            </item>
             <item row="4" column="2">
              <widget class="QSlider" name="exponent_norm">
               <property name="sizePolicy">
@@ -480,6 +419,19 @@
               </property>
              </widget>
             </item>
+            <item row="4" column="0">
+             <widget class="QLabel" name="label_6">
+              <property name="sizePolicy">
+               <sizepolicy hsizetype="Maximum" vsizetype="Preferred">
+                <horstretch>0</horstretch>
+                <verstretch>0</verstretch>
+               </sizepolicy>
+              </property>
+              <property name="text">
+               <string>Exponent norm</string>
+              </property>
+             </widget>
+            </item>
             <item row="3" column="2">
              <widget class="QSlider" name="exponent_len">
               <property name="sizePolicy">
@@ -515,53 +467,18 @@
               </property>
              </widget>
             </item>
-            <item row="7" column="1">
-             <widget class="QLabel" name="log_norm_label">
-              <property name="minimumSize">
+            <item row="6" column="1">
+             <spacer name="verticalSpacer">
+              <property name="orientation">
+               <enum>Qt::Vertical</enum>
+              </property>
+              <property name="sizeHint" stdset="0">
                <size>
-                <width>24</width>
+                <width>20</width>
                 <height>0</height>
                </size>
               </property>
-              <property name="text">
-               <string>0</string>
-              </property>
-              <property name="alignment">
-               <set>Qt::AlignRight|Qt::AlignTrailing|Qt::AlignVCenter</set>
-              </property>
-             </widget>
-            </item>
-            <item row="7" column="2">
-             <widget class="QSlider" name="log_norm">
-              <property name="sizePolicy">
-               <sizepolicy hsizetype="Expanding" vsizetype="Maximum">
-                <horstretch>0</horstretch>
-                <verstretch>0</verstretch>
-               </sizepolicy>
-              </property>
-              <property name="orientation">
-               <enum>Qt::Horizontal</enum>
-              </property>
-              <property name="tickPosition">
-               <enum>QSlider::TicksAbove</enum>
-              </property>
-              <property name="tickInterval">
-               <number>25</number>
-              </property>
-             </widget>
-            </item>
-            <item row="7" column="0">
-             <widget class="QLabel" name="label_12">
-              <property name="sizePolicy">
-               <sizepolicy hsizetype="Maximum" vsizetype="Preferred">
-                <horstretch>0</horstretch>
-                <verstretch>0</verstretch>
-               </sizepolicy>
-              </property>
-              <property name="text">
-               <string>Log norm</string>
-              </property>
-             </widget>
+             </spacer>
             </item>
            </layout>
           </widget>
diff --git a/tracker-tobii-eyex/tobii-settings.cpp b/tracker-tobii-eyex/tobii-settings.cpp
index fb5bb8f6..0dcb377f 100644
--- a/tracker-tobii-eyex/tobii-settings.cpp
+++ b/tracker-tobii-eyex/tobii-settings.cpp
@@ -28,14 +28,45 @@
 
 void rel_settings::make_spline()
 {
-    const double log_c = 1./std::log(log_slope());
+    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[]
     {
-        { 1, dz_len(), 0, [](double) { return 0; } },
-        { 5, expt_len(), expt_norm(), [=](double x) { return std::pow(x, expt_slope()); } },
-        { 7, 1 - dz_len() - expt_len() - log_len(), std::max(0., 1 - expt_norm() - log_norm()), [](double x) { return x; } },
-        { 7, log_len(), log_norm(), [=](double x) { return std::log(1+x)*log_c; } },
+        { 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)));
@@ -45,12 +76,10 @@ 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, 1.25, 3)),
-    expt_len(b, "exponent-length", s(.25, 0, .5)),
-    expt_norm(b, "exponent-norm", s(.3, .1, .5)),
-    log_slope(b, "log-slope", s(2.75, 1.25, 10)),
+    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)),
-    log_norm(b, "log-norm", s(.1, .05, .3)),
     acc_mode_spline(100, 100, "")
 {
     make_spline();
@@ -68,30 +97,23 @@ void rel_settings::make_spline_(part* functors, unsigned len)
 {
     acc_mode_spline.removeAllPoints();
 
-    double lastx = 0, lasty = 0;
-
-    using std::accumulate;
-
-    const double inv_norm_y = 1./accumulate(functors, functors + len, 1e-4, [](double acc, const part& functor) { return acc + functor.norm; });
-    const double inv_norm_x = 1./accumulate(functors, functors + len, 1e-4, [](double acc, const part& functor) { return acc + functor.len; });
+    double lastx = 0;
 
     for (unsigned k = 0; k < len; k++)
     {
         part& fun = functors[k];
 
-        const double xscale = fun.len * spline_max * inv_norm_x;
-        const double maxx = fun.f(1);
-        const double yscale = fun.norm * spline_max * inv_norm_y * (maxx < 1e-3 ? 0 : 1./maxx);
+        static constexpr unsigned nparts = 7;
 
-        for (unsigned i = 0; i <= fun.nparts; i++)
+        for (unsigned i = 1; i <= nparts; i++)
         {
-            const double x = lastx + (fun.nparts == 0 ? 1 : i) / (1.+fun.nparts) * xscale;
-            const double y = lasty + clamp(fun.f(x) * yscale, 0, spline_max);
-            qDebug() << k << i << x << y;
-            acc_mode_spline.addPoint(x, y);
+            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 += xscale;
-        lasty += yscale;
+        lastx += fun.len;
     }
 }
diff --git a/tracker-tobii-eyex/tobii-settings.hpp b/tracker-tobii-eyex/tobii-settings.hpp
index 4346a156..5c09b201 100644
--- a/tracker-tobii-eyex/tobii-settings.hpp
+++ b/tracker-tobii-eyex/tobii-settings.hpp
@@ -24,8 +24,7 @@ class rel_settings final : public QObject, public opts
 
     struct part
     {
-        int nparts;
-        double len, norm;
+        double len;
         functor f;
     };
 
@@ -33,7 +32,7 @@ class rel_settings final : public QObject, public opts
 
 public:
     using s = slider_value;
-    value<slider_value> speed, dz_len, expt_slope, expt_len, expt_norm, log_slope, log_len, log_norm;
+    value<slider_value> speed, dz_len, expt_slope, expt_len, expt_norm, log_len;
     spline acc_mode_spline;
     rel_settings();
     double gain(double value);