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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 matrix11 12The mounting matrix is a device tree property used to orient any device13that produce three-dimensional data in relation to the world where it is14deployed.15 16The purpose of the mounting matrix is to translate the sensor frame of17reference into the device frame of reference using a translation matrix as18defined in linear algebra.19 20The typical usecase is that where a component has an internal representation21of 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 orientation23relative to some specific device frame of reference.24 25For example a device with some kind of screen, where the user is supposed to26interact with the environment using an accelerometer, gyroscope or magnetometer27mounted on the same chassis as this screen, will likely take the screen as28reference to (x,y,z) orientation, with (x,y) corresponding to these axes on the29screen 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 left32to positive on the right, (y) from negative on the bottom to positive on top33and (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 of37reference. 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 the41external world, the environment where the device is deployed. Usually the data42from the sensor is used to figure out how the device is oriented with respect43to this world. When using the mounting matrix, the sensor and device orientation44becomes identical and we can focus on the data as it relates to the surrounding45world.46 47Device-to-world examples for some three-dimensional sensor types:48 49- Accelerometers have their world frame of reference toward the center of50 gravity, usually to the core of the planet. A reading of the (x,y,z) values51 from the sensor will give a projection of the gravity vector through the52 device relative to the center of the planet, i.e. relative to its surface at53 this point. Up and down in the world relative to the device frame of54 reference can thus be determined. and users would likely expect a value of55 9.81 m/s^2 upwards along the (z) axis, i.e. out of the screen when the device56 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 display60 is projected onto the (x,y) plane of the display panel.61 62 Example:63 64 ^ z: +g ^ z: > 065 ! /!66 ! x=y=0 / ! x: > 067 +--------+ +--------+68 ! ! ! !69 +--------+ +--------+70 ! /71 ! /72 v v73 center of center of74 gravity gravity75 76 77 If the device is tilted to the left, you get a positive x value. If you point78 its top towards surface, you get a negative y axis.79 80 (---------)81 ! ! y: -g82 ! ! ^83 ! ! !84 ! !85 ! ! x: +g <- z: +g -> x: -g86 ! 1 2 3 !87 ! 4 5 6 ! !88 ! 7 8 9 ! v89 ! * 0 # ! y: +g90 (---------)91 92 93- Magnetometers (compasses) have their world frame of reference relative to the94 geomagnetic field. The system orientation vis-a-vis the world is defined with95 respect to the local earth geomagnetic reference frame where (y) is in the96 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) is98 perpendicular to the ground plane and positive upwards.99 100 101 ^^^ North: y > 0102 103 (---------)104 ! !105 ! !106 ! !107 ! ! >108 ! ! > North: x > 0109 ! 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 come116 closer to the poles.117 118 Sensors and driver can not and should not take care of this because there119 are complex calculations and empirical data to be taken care of. We leave120 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, the125 display is readable by a person standing upright on the earth surface, this126 defines a positive y value.127 128 129- Gyroscopes detects the movement relative the device itself. The angular130 velocity is defined as orthogonal to the plane of rotation, so if you put the131 device on a flat surface and spin it around the z axis (such as rotating a132 device with a screen lying flat on a table), you should get a negative value133 along the (z) axis if rotated clockwise, and a positive value if rotated134 counter-clockwise according to the right-hand rule.135 136 137 (---------) y > 0138 ! ! v---\139 ! !140 ! !141 ! ! <--\142 ! ! ! z > 0143 ! 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 the151relative orientation of any given sensor of this type with respect to the152frame 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 means158the resulting values from the sensor, after scaling to proper units, should be159multiplied by this matrix to give the proper vectors values in three-dimensional160space, relative to the device or world point of reference.161 162For more information, consult:163https://en.wikipedia.org/wiki/Rotation_matrix164 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 * z174 y' = mxy * x + myy * y + mzy * z175 z' = mxz * x + myz * y + mzz * z176 177It is represented as an array of strings containing the real values for178producing the transformation matrix.179 180Examples:181 182Identity matrix (nothing happens to the coordinates, which means the device was183mechanically 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 we190compensate 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. mounted197upside-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 compensation204