more changes and I think a better approach to long descriptions

Author: acharraggi

docs/source/game_specific_resources/field_coordinate_system/field-coordinate-system.rst

@@ -1,21 +1,26 @@
-Field Coordinate System Definition
-==================================
+*FIRST* Tech Challenge Field Coordinate System Definition
+=========================================================
+
+.. meta::
+   :description: This document defines the Field Coordinate System which can be used to specify position on the playing field.
+
+
+Summary: The *FIRST* Tech Challenge Field Coordinate System is a Cartesian Coordinate System of three dimensions.
+The X and Y axes will refer to a position on the Field and the Z axis a height above the Field.
+
+.. contents:: In This Article:
+   :local:
+   :depth: 1
+   :backlinks: none
 
 Scope
 -----
-
 
 This document defines the Field Coordinate System 
 for a *FIRST* Tech Challenge playing Field. This definition can be
 used for consistent field-centric navigation, target localization and path
 planning.
 
-The Field Coordinate System is a 
-`three-dimensional Cartesian coordinate system 
-<https://en.wikipedia.org/wiki/Cartesian_coordinate_system#Three_dimensions>`__ 
-which means that the three axes are at right angles to each other. 
-The X and Y axes will refer to a position on the Field and Z axis a height above the Field. 
-
 Reference Frame
 ---------------
 
@@ -24,11 +29,21 @@ to the red Alliance Area, known here after as the Red Wall.  The definition is
 from the perspective of a person, standing outside the Field, in the center of
 Red Wall, looking towards the center of the Field.
 
-.. note::
+.. note:: 
    If the red Alliance Area is ever adjacent to two perimeter walls,
    the Red Wall will be the one with *most* contact with the Alliance Area. If
    the red Alliance Area is ever adjacent to two perimeter walls *equally*, then
    the most clockwise of the two walls will be considered to be the Red Wall.
+   
+Coordinate System
+-----------------
+
+The Field Coordinate System is a Cartesian Coordinate System of three dimensions.
+X and Y will refer to a position on the field.
+Z will refer to a height above the field.
+You may use any length measure as long as the same measure is used for all three axes.
+The coordinates are ordered (X, Y, Z).
+Example: coordinate position (10, -10, 0) has X = 10, Y = -10 and Z = 0.
 
 Origin
 ^^^^^^
@@ -65,58 +80,54 @@ Rotation About Axes
 When considering rotations about an axis, consider yourself looking down the
 axis from the positive end towards the origin. Positive
 rotations are then counterclockwise and negative rotations clockwise.
-This rotation convention comes from the 
-`right hand rule <https://en.wikipedia.org/wiki/Right-hand_rule>`__ of classic geometry.
-
-.. figure:: images/image1.jpg
-   :width: 35%
-   :align: center
-   :class: no-scaled-link
-   :alt: illustration 
 
-   showing the counterclockwise rotations about each axis.
+.. figure:: images/image1.jpg
+   :alt:   
 
-A rotation example: consider looking down the positive Z axis towards the origin. 
-This would be like standing in the middle of the Field
-looking down at the intersection of the tiles in the very center of the Field.
-A positive rotation about the Z axis is then counterclockwise.
-Example: a robot spinning clockwise on the Field is making a negative rotation about the Z axis. 
+   Rotations about each axis.
+
+   Imagine looking down the positive Z axis towards the origin.
+   This would be like standing in the middle of the Field
+   looking down at the intersection of the tiles in the very center of the Field.
+   A positive rotation about the Z axis is then counterclockwise.
+
+Example: a robot spinning clockwise on the Field is making a negative rotation about the Z axis.
 
 Field Configuration Examples
 ----------------------------
 
 Below are two examples illustrating the Field Coordinate System for different
 *FIRST* Tech Challenge Field configurations.
 
-In a diamond Field configuration the two Alliance walls are adjacent. 
-The Field is rotated 45 degrees such that both Alliance Areas face the audience.
-From the audience perspective the Field forms a diamond shape.
-The Red Wall will be on the right as seen from the audience,
-and the blue wall will be on the left.
-The Y axis points across the Field as seen from the Red Wall. 
-The X axis points to the blue wall.
+Diamond Field
+^^^^^^^^^^^^^
 
 .. figure:: images/image2.jpg
-   :width: 75%
-   :align: center
-   :class: no-scaled-link
-   :alt: a diamond Field
+   :alt: 
 
-   from the *FIRST* RES-Q game 
-
-In a square Field configuration the two Alliances face each other across the Field.
-The Field is oriented such that the Red Wall is on the right as seen from the audience,
-and the blue wall will be on the left.
-The Y axis points across the Field from the Red Wall to the blue wall.
-The X axis points away from the audience to the rear of the Field.
+   The *FIRST* RES-Q game Field with X, Y and Z axes shown.
+   
+   In a diamond Field configuration the two Alliance walls are adjacent.
+   The Field is rotated 45 degrees such that both Alliances face the audience.
+   From the audience perspective the Field forms a diamond shape.
+   The Red Wall will be on the right as seen from the audience,
+   and the blue wall will be on the left.
+   The Y axis points across the Field as seen from the Red Wall.
+   The X axis points to the blue wall.
+   
+Square Field
+^^^^^^^^^^^^
 
 .. figure:: images/image3.jpg
-   :width: 75%
-   :align: center
-   :class: no-scaled-link
-   :alt: a square Field
+   :alt: 
 
-   from the Cascade Effect game
+   The Cascade Effect game Field with X, Y and Z axes shown.
+
+   In a square Field configuration the two Alliances face each other across the Field.
+   The Field is oriented such that the Red Wall is on the right as seen
+   from the audience, and the blue wall will be on the left.
+   The Y axis points across the Field from the Red Wall to the blue wall.
+   The X axis points away from the audience to the rear of the Field.
 
 .. note::
    In both Field configurations the red Alliance is facing out along the positive Y axis,
@@ -126,10 +137,24 @@ The X axis points away from the audience to the rear of the Field.
    towards the blue Alliance. In the square Field configuration
    the Y axis is pointing towards the blue Alliance.
 
+Coordinate Position Example
+---------------------------
+
+Let's consider a robot on the Cascade Effect Field at coordinates 
+(60, -60, 10) in inches. So X = 60, y = -60, and Z = 10. 
+Measured in inches, the walls would be about 72 inches from the origin.
+Cascade Effect was a Sqaure Field configuration, so
+the X axis value of positive 60 would be located close to the rear field wall, away from the audience.
+The Y axis value of negative 60 would be located close to the Red Wall, away from the origin.
+Together the X and Y values (60, -60) indicate a position in the corner of the Field.
+That corner is adjacent to the Red Wall and furthest from the audience. 
+The Z axis value of 10 places the robot on top of the red
+ramp that is in that corner in the Cascade Effect game. 
+
 Measured Values
 ---------------
 
-The following values have been measured from a 2016 competition Field. They are
+The following metric values have been measured from a 2016 competition Field. They are
 representative only, and should not be assumed to be exact, or guaranteed.
 
 -  Distance between opposite inside faces of panels: 3580 mm,
@@ -141,7 +166,31 @@ representative only, and should not be assumed to be exact, or guaranteed.
 
 So, for a diamond Field configuration, the corner of the Field closest to the
 audience, at a height equal to the top of the perimeter wall, would have a
-coordinate position of: (-1790, 1790, 300).
+coordinate position of: (-1790, 1790, 300) in millimeters.
+
+Additional Information
+----------------------
+
+See this Wikipedia article on `Cartesian coordinate system
+<https://en.wikipedia.org/wiki/Cartesian_coordinate_system#Three_dimensions>`__
+in three dimensions.
+The Field Coordinate System rotation convention comes from the 
+`right hand rule <https://en.wikipedia.org/wiki/Right-hand_rule>`__ 
+of classic geometry.
+
+Robots with a webcam can use :ref:`AprilTags <apriltag/vision_portal/apriltag_intro/apriltag-intro:apriltag introduction>`
+to determine where an :ref:`AprilTag is located 
+<apriltag/understanding_apriltag_detection_values/understanding-apriltag-detection-values:introduction>` 
+with respect to the robot.
+Since AprilTags are in known locations on the field, you can also determine the
+:ref:`location of the robot <apriltag/vision_portal/apriltag_localization/apriltag-localization:apriltag localization>`
+on the field.
+
+Robots can use an inertial measurement unit (IMU) to measure rotations about axes
+with respect to the robot. See :ref:`IMU axes definition. <programming_resources/imu/imu:axes definition>`
+The yaw value from the IMU, also known the heading, measures rotation about the Z axis
+which points up from the robot. 
+You can use the IMU to determine which direction a robot is facing.
 
 Glossary
 --------
@@ -154,12 +203,21 @@ Glossary
       and an Alliance in the blue Alliance Area is known as the blue Alliance.
 
    Alliance Area
-      A 120 inch (~304.8 cm) wide by 42 inch (~106.7 cm) deep by infinitely tall volume formed
-      by placing Alliance colored tape onto the flooring surface outside of the Field.
-      The Alliance Area includes the taped lines.
+      A 120 inch wide by 42 inch deep (304.8 cm by 106.7 cm) by infinitely tall volume 
+      formed by placing Alliance colored tape onto the flooring surface outside of the Field.
       The red Alliance Area will have red tape, the blue Alliance Area will have blue tape.
+      The Alliance Area includes the taped lines.
+      
+   Cartesian Coordinate System
+      A Cartesian coordinate system for three-dimensional space consists of an ordered triplet of lines 
+      (the axes) that go through a common point (the origin). The axes are pair-wise perpendicular 
+      (at right-angles to each other). A single unit of measure applies to all three axes.
+      A point P in space can then be referenced by three numbers which correspond to the three axes.
+      The Cartesian coordinates of P are those three numbers, in the chosen order.
 
    Field
-      An approximately 12 foot (3.66m) by 12 foot (3.66m) Area bounded by the
+      A square area with walls approximately 12 feet (3.66 meters) long bounded by the
       outside edge of the extrusion that frames the walls of the Field perimeter.
-      The flooring surface of the Field is made of 36 (nominal size) 24 inch by 24 inch by 5/8 inch interlocking soft foam tiles. 
+      The flooring surface of the Field is made of 36 interlocking soft foam tiles.
+      The nominal size of a tile is 24 inches by 24 inches by 5/8 of an inch.
+