1For discussion. Unclear are:
2* is the definition of +/- values practical or counterintuitive?
3* are the definitions unambiguous and easy to follow?
4* are the examples correct?
5* should we have HOWTO engineer a correct matrix for a new device (without comparing to a different one)?
6
7====
8
9
10Mounting matrix
11
12The mounting matrix is a device tree property used to orient any device
13that produce three-dimensional data in relation to the world where it is
14deployed.
15
16The purpose of the mounting matrix is to translate the sensor frame of
17reference into the device frame of reference using a translation matrix as
18defined in linear algebra.
19
20The typical usecase is that where a component has an internal representation
21of the (x,y,z) triplets, such as different registers to read these coordinates,
22and thus implying that the component should be mounted in a certain orientation
23relative to some specific device frame of reference.
24
25For example a device with some kind of screen, where the user is supposed to
26interact with the environment using an accelerometer, gyroscope or magnetometer
27mounted on the same chassis as this screen, will likely take the screen as
28reference to (x,y,z) orientation, with (x,y) corresponding to these axes on the
29screen and (z) being depth, the axis perpendicular to the screen.
30
31For a screen you probably want (x) coordinates to go from negative on the left
32to positive on the right, (y) from negative on the bottom to positive on top
33and (z) depth to be negative under the screen and positive in front of it,
34toward the face of the user.
35
36A sensor can be mounted in any angle along the axes relative to the frame of
37reference. This means that the sensor may be flipped upside-down, left-right,
38or tilted at any angle relative to the frame of reference.
39
40Another frame of reference is how the device with its sensor relates to the
41external world, the environment where the device is deployed. Usually the data
42from the sensor is used to figure out how the device is oriented with respect
43to this world. When using the mounting matrix, the sensor and device orientation
44becomes identical and we can focus on the data as it relates to the surrounding
45world.
46
47Device-to-world examples for some three-dimensional sensor types:
48
49- Accelerometers have their world frame of reference toward the center of
50  gravity, usually to the core of the planet. A reading of the (x,y,z) values
51  from the sensor will give a projection of the gravity vector through the
52  device relative to the center of the planet, i.e. relative to its surface at
53  this point. Up and down in the world relative to the device frame of
54  reference can thus be determined. and users would likely expect a value of
55  9.81 m/s^2 upwards along the (z) axis, i.e. out of the screen when the device
56  is held with its screen flat on the planets surface and 0 on the other axes,
57  as the gravity vector is projected 1:1 onto the sensors (z)-axis.
58
59  If you tilt the device, the g vector virtually coming out of the display
60  is projected onto the (x,y) plane of the display panel.
61
62  Example:
63
64         ^ z: +g                   ^ z: > 0
65         !                        /!
66         ! x=y=0                 / ! x: > 0
67     +--------+             +--------+
68     !        !             !        !
69     +--------+             +--------+
70         !                    /
71         !                   /
72         v                  v
73      center of         center of
74       gravity           gravity
75
76
77  If the device is tilted to the left, you get a positive x value. If you point
78  its top towards surface, you get a negative y axis.
79
80     (---------)
81     !         !           y: -g
82     !         !             ^
83     !         !             !
84     !         !
85     !         !  x: +g <- z: +g  -> x: -g
86     ! 1  2  3 !
87     ! 4  5  6 !             !
88     ! 7  8  9 !             v
89     ! *  0  # !           y: +g
90     (---------)
91
92
93- Magnetometers (compasses) have their world frame of reference relative to the
94  geomagnetic field. The system orientation vis-a-vis the world is defined with
95  respect to the local earth geomagnetic reference frame where (y) is in the
96  ground plane and positive towards magnetic North, (x) is in the ground plane,
97  perpendicular to the North axis and positive towards the East and (z) is
98  perpendicular to the ground plane and positive upwards.
99
100
101     ^^^ North: y > 0
102
103     (---------)
104     !         !
105     !         !
106     !         !
107     !         !  >
108     !         !  > North: x > 0
109     ! 1  2  3 !  >
110     ! 4  5  6 !
111     ! 7  8  9 !
112     ! *  0  # !
113     (---------)
114
115  Since the geomagnetic field is not uniform this definition fails if we come
116  closer to the poles.
117
118  Sensors and driver can not and should not take care of this because there
119  are complex calculations and empirical data to be taken care of. We leave
120  this up to user space.
121
122  The definition we take:
123
124  If the device is placed at the equator and the top is pointing north, the
125  display is readable by a person standing upright on the earth surface, this
126  defines a positive y value.
127
128
129- Gyroscopes detects the movement relative the device itself. The angular
130  velocity is defined as orthogonal to the plane of rotation, so if you put the
131  device on a flat surface and spin it around the z axis (such as rotating a
132  device with a screen lying flat on a table), you should get a negative value
133  along the (z) axis if rotated clockwise, and a positive value if rotated
134  counter-clockwise according to the right-hand rule.
135
136
137     (---------)     y > 0
138     !         !     v---\
139     !         !
140     !         !
141     !         !      <--\
142     !         !         ! z > 0
143     ! 1  2  3 !       --/
144     ! 4  5  6 !
145     ! 7  8  9 !
146     ! *  0  # !
147     (---------)
148
149
150So unless the sensor is ideally mounted, we need a means to indicate the
151relative orientation of any given sensor of this type with respect to the
152frame of reference.
153
154To achieve this, use the device tree property "mount-matrix" for the sensor.
155
156This supplies a 3x3 rotation matrix in the strict linear algebraic sense,
157to orient the senor axes relative to a desired point of reference. This means
158the resulting values from the sensor, after scaling to proper units, should be
159multiplied by this matrix to give the proper vectors values in three-dimensional
160space, relative to the device or world point of reference.
161
162For more information, consult:
163https://en.wikipedia.org/wiki/Rotation_matrix
164
165The mounting matrix has the layout:
166
167 (mxx, myx, mzx)
168 (mxy, myy, mzy)
169 (mxz, myz, mzz)
170
171Values are intended to be multiplied as:
172
173  x' = mxx * x + myx * y + mzx * z
174  y' = mxy * x + myy * y + mzy * z
175  z' = mxz * x + myz * y + mzz * z
176
177It is represented as an array of strings containing the real values for
178producing the transformation matrix.
179
180Examples:
181
182Identity matrix (nothing happens to the coordinates, which means the device was
183mechanically mounted in an ideal way and we need no transformation):
184
185mount-matrix = "1", "0", "0",
186               "0", "1", "0",
187               "0", "0", "1";
188
189The sensor is mounted 30 degrees (Pi/6 radians) tilted along the X axis, so we
190compensate by performing a -30 degrees rotation around the X axis:
191
192mount-matrix = "1", "0", "0",
193               "0", "0.866", "0.5",
194               "0", "-0.5", "0.866";
195
196The sensor is flipped 180 degrees (Pi radians) around the Z axis, i.e. mounted
197upside-down:
198
199mount-matrix = "0.998", "0.054", "0",
200               "-0.054", "0.998", "0",
201               "0", "0", "1";
202
203???: this does not match "180 degrees" - factors indicate ca. 3 degrees compensation
204