From a97e074022bc6c8f38e228f7cf6f3280da94530d Mon Sep 17 00:00:00 2001
From: Kevin O'Connor <kevin@koconnor.net>
Date: Thu, 27 Apr 2017 11:19:30 -0400
Subject: [PATCH] docs: Kinematics document image updates

Signed-off-by: Kevin O'Connor <kevin@koconnor.net>
---
 docs/Kinematics.md              |  41 ++++---
 docs/img/corner-blob.jpg        | Bin 5772 -> 4665 bytes
 docs/img/corner-dimple.jpg      | Bin 5507 -> 4388 bytes
 docs/img/corner-good.jpg        | Bin 5461 -> 4354 bytes
 docs/img/corner.svg             |  42 +++++--
 docs/img/corner.svg.png         | Bin 1176 -> 2157 bytes
 docs/img/lookahead-slow.svg     | 208 ++++++++++++++++++++++++++++++++
 docs/img/lookahead-slow.svg.png | Bin 0 -> 7641 bytes
 docs/img/lookahead.svg          |  36 ++++--
 docs/img/lookahead.svg.png      | Bin 3323 -> 4180 bytes
 docs/img/trapezoids.svg         |  25 ++--
 docs/img/trapezoids.svg.png     | Bin 4748 -> 4613 bytes
 12 files changed, 304 insertions(+), 48 deletions(-)
 create mode 100644 docs/img/lookahead-slow.svg
 create mode 100644 docs/img/lookahead-slow.svg.png

diff --git a/docs/Kinematics.md b/docs/Kinematics.md
index 92de88ad..401554f8 100644
--- a/docs/Kinematics.md
+++ b/docs/Kinematics.md
@@ -73,21 +73,24 @@ flow would result in poor print quality.
 To solve this, the "look-ahead" mechanism queues multiple incoming
 moves and analyzes the angles between moves to determine a reasonable
 speed that can be obtained during the "junction" between two moves. If
-the next move forms an acute angle (the head is going to travel in
-nearly a reverse direction on the next move) then only a small
-junction speed is permitted. If the next move is nearly in the same
-direction then the head need only slow down a little (if at all).
+the next move is nearly in the same direction then the head need only
+slow down a little (if at all).
 
 ![lookahead](img/lookahead.svg.png)
 
+If the next move forms an acute angle (the head is going to travel in
+nearly a reverse direction on the next move) then only a small
+junction speed is permitted.
+
+![lookahead](img/lookahead-slow.svg.png)
+
 The junction speeds are determined using "approximated centripetal
 acceleration". Best
-[described](https://onehossshay.wordpress.com/2011/09/24/improving_grbl_cornering_algorithm/)
-by the author.
+[described by the author](https://onehossshay.wordpress.com/2011/09/24/improving_grbl_cornering_algorithm/).
 
 Klipper implements look-ahead between moves contained in the XY plane
-that have similar extruder flow rates. Other moves are rare and
-implementing look-ahead between them is unnecessary.
+that have similar extruder flow rates. Other moves are relatively rare
+and implementing look-ahead between them is unnecessary.
 
 Key formula for look-ahead:
 ```
@@ -158,20 +161,20 @@ To generate step times on Delta printers it is necessary to correlate
 the movement in cartesian space with the movement on each stepper
 tower.
 
+To simplify the math, for each stepper tower, the code calculates the
+location of a "virtual tower" that is along the line of movement.
+This virtual tower is chosen at the point where the line of movement
+(extended infinitely in both directions) would be closest to the
+actual tower.
+
 ![delta-tower](img/delta-tower.svg.png)
 
-To simplify the math, for each move contained in an XY plane, the code
-calculates the location of a "virtual tower" that is along the line of
-movement.  This virtual tower is chosen at the point where the line of
-movement (extended infinitely in both directions) would be closest to
-the actual tower.
+It is then possible to calculate where the head will be along the line
+of movement after each step is taken on the virtual tower.
 
 ![virtual-tower](img/virtual-tower.svg.png)
 
-It is then possible to calculate where the head will be along the line
-of movement after each step is taken on the virtual tower. The key
-formula is Pythagoras's theorem:
-
+The key formula is Pythagoras's theorem:
 ```
 distance_to_tower^2 = arm_length^2 - tower_height^2
 ```
@@ -196,7 +199,7 @@ must also be used in the calculations.
 
 Should the move contain only Z movement (ie, no XY movement at all)
 then the same math is used - just in this case the tower is parallel
-to the line of movement (its slope is 1.0).
+to the line of movement.
 
 ### Stepper motor acceleration limits ###
 
@@ -248,7 +251,7 @@ pressure. Pressure increases when filament is pushed into the extruder
 (as in [Hooke's law](https://en.wikipedia.org/wiki/Hooke%27s_law)) and
 the pressure necessary to extrude is dominated by the flow rate
 through the nozzle orifice (as in
-[Poiseuille law](https://en.wikipedia.org/wiki/Poiseuille_law)). The
+[Poiseuille's law](https://en.wikipedia.org/wiki/Poiseuille_law)). The
 key idea is that the relationship between filament, pressure, and flow
 rate can be modeled using a linear coefficient:
 ```
diff --git a/docs/img/corner-blob.jpg b/docs/img/corner-blob.jpg
index 6dd529a01bd16541084d93520f515aff727009cf..eaf9024cdbfd064858f02da1b6bf46374d09a138 100644
GIT binary patch
delta 12
TcmeCt-KoO#|HkG}7IPs0B7p?O

delta 1126
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diff --git a/docs/img/corner-dimple.jpg b/docs/img/corner-dimple.jpg
index 14cae0c4598e204736a05c8fdfb6326bbe5aae2b..55402d5ea3cc0bd5c8a5f1c7ff0f47b82834b1be 100644
GIT binary patch
delta 12
TcmZqHUZTYG|HkG-79~LdAs_^q

delta 1160
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diff --git a/docs/img/corner-good.jpg b/docs/img/corner-good.jpg
index 687c73aaf9c4889050b57f60ec73654709c67119..812c82a50d734b6b8052c2f9a686dcc64e49a071 100644
GIT binary patch
delta 11
Scmcbr)uhDq|Hk4_7C`_WTm*^$

delta 1125
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diff --git a/docs/img/corner.svg b/docs/img/corner.svg
index 3383a969..f2e3d0ef 100644
--- a/docs/img/corner.svg
+++ b/docs/img/corner.svg
@@ -102,8 +102,8 @@
      inkscape:pageopacity="0.0"
      inkscape:pageshadow="2"
      inkscape:zoom="2.49"
-     inkscape:cx="27.644"
-     inkscape:cy="0.62950496"
+     inkscape:cx="95.030833"
+     inkscape:cy="-0.17370789"
      inkscape:document-units="px"
      inkscape:current-layer="layer1"
      showgrid="true"
@@ -112,11 +112,11 @@
      fit-margin-right="0"
      fit-margin-bottom="0"
      showborder="false"
-     inkscape:window-width="1920"
-     inkscape:window-height="1032"
-     inkscape:window-x="0"
-     inkscape:window-y="0"
-     inkscape:window-maximized="1">
+     inkscape:window-width="1068"
+     inkscape:window-height="478"
+     inkscape:window-x="378"
+     inkscape:window-y="113"
+     inkscape:window-maximized="0">
     <inkscape:grid
        type="xygrid"
        id="grid6021"
@@ -133,7 +133,7 @@
         <dc:format>image/svg+xml</dc:format>
         <dc:type
            rdf:resource="http://purl.org/dc/dcmitype/StillImage" />
-        <dc:title></dc:title>
+        <dc:title />
       </cc:Work>
     </rdf:RDF>
   </metadata>
@@ -154,5 +154,31 @@
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        inkscape:connector-curvature="0"
        sodipodi:nodetypes="cc" />
+    <text
+       xml:space="preserve"
+       style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:11.25000095px;line-height:125%;font-family:'DejaVu Sans';-inkscape-font-specification:'DejaVu Sans, Normal';text-align:start;letter-spacing:0px;word-spacing:0px;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
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+       sodipodi:linespacing="125%"
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+       inkscape:transform-center-x="1.3563414"
+       inkscape:transform-center-y="-5.7099754"><tspan
+         sodipodi:role="line"
+         id="tspan5552"
+         x="189.09824"
+         y="482.48389">move 1</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:11.25000095px;line-height:125%;font-family:'DejaVu Sans';-inkscape-font-specification:'DejaVu Sans, Normal';text-align:start;letter-spacing:0px;word-spacing:0px;writing-mode:lr-tb;text-anchor:start;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
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+         sodipodi:role="line"
+         id="tspan5554"
+         x="427.95532"
+         y="379.5321">move 2</tspan></text>
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 </svg>
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@@ -55,7 +55,7 @@
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