From 763ca4fd15f4ae4bd272709bf5e187475ca4e4a3 Mon Sep 17 00:00:00 2001
From: Atsushi Sakai <asakai.amsl+github@gmail.com>
Date: Sun, 5 Jan 2020 22:37:08 +0900
Subject: [PATCH] update jupyter docs

---
 .../quintic_polynomials_planner.ipynb                | 12 +++++++++---
 .../quintic_polynomials_planner.py                   |  1 +
 2 files changed, 10 insertions(+), 3 deletions(-)

diff --git a/PathPlanning/QuinticPolynomialsPlanner/quintic_polynomials_planner.ipynb b/PathPlanning/QuinticPolynomialsPlanner/quintic_polynomials_planner.ipynb
index 7b83a87b..804b7fba 100644
--- a/PathPlanning/QuinticPolynomialsPlanner/quintic_polynomials_planner.ipynb
+++ b/PathPlanning/QuinticPolynomialsPlanner/quintic_polynomials_planner.ipynb
@@ -24,13 +24,19 @@
     "\n",
     "$x(0) = a_0 = x_s$\n",
     "\n",
-    "x_s is a start x position.\n",
+    "$x_s$ is a start x position.\n",
     "\n",
+    "Then, differentiating this equation with t, \n",
     "\n",
+    "$x'(t) = a_1+2a_2t+3a_3t^2+4a_4t^3$\n",
     "\n",
-    "$e^{i\\pi} + 1 = 0$\n",
+    "So, when time is 0,\n",
     "\n",
-    "\n"
+    "$x'(0) = a_1 = v_s$\n",
+    "\n",
+    "$v_s$ is a initial speed for x axis.\n",
+    "\n",
+    "=== TBD ==== \n"
    ],
    "metadata": {
     "collapsed": false
diff --git a/PathPlanning/QuinticPolynomialsPlanner/quintic_polynomials_planner.py b/PathPlanning/QuinticPolynomialsPlanner/quintic_polynomials_planner.py
index 8600f1d7..5538731d 100644
--- a/PathPlanning/QuinticPolynomialsPlanner/quintic_polynomials_planner.py
+++ b/PathPlanning/QuinticPolynomialsPlanner/quintic_polynomials_planner.py
@@ -26,6 +26,7 @@ class QuinticPolynomial:
 
     def __init__(self, xs, vxs, axs, xe, vxe, axe, time):
         # calc coefficient of quintic polynomial
+        # See jupyter notebook document for derivation of this equation.
         self.a0 = xs
         self.a1 = vxs
         self.a2 = axs / 2.0