1 For 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 10 Mounting matrix 11 12 The mounting matrix is a device tree property used to orient any device 13 that produce three-dimensional data in relation to the world where it is 14 deployed. 15 16 The purpose of the mounting matrix is to translate the sensor frame of 17 reference into the device frame of reference using a translation matrix as 18 defined in linear algebra. 19 20 The typical usecase is that where a component has an internal representation 21 of the (x,y,z) triplets, such as different registers to read these coordinates, 22 and thus implying that the component should be mounted in a certain orientation 23 relative to some specific device frame of reference. 24 25 For example a device with some kind of screen, where the user is supposed to 26 interact with the environment using an accelerometer, gyroscope or magnetometer 27 mounted on the same chassis as this screen, will likely take the screen as 28 reference to (x,y,z) orientation, with (x,y) corresponding to these axes on the 29 screen and (z) being depth, the axis perpendicular to the screen. 30 31 For a screen you probably want (x) coordinates to go from negative on the left 32 to positive on the right, (y) from negative on the bottom to positive on top 33 and (z) depth to be negative under the screen and positive in front of it, 34 toward the face of the user. 35 36 A sensor can be mounted in any angle along the axes relative to the frame of 37 reference. This means that the sensor may be flipped upside-down, left-right, 38 or tilted at any angle relative to the frame of reference. 39 40 Another frame of reference is how the device with its sensor relates to the 41 external world, the environment where the device is deployed. Usually the data 42 from the sensor is used to figure out how the device is oriented with respect 43 to this world. When using the mounting matrix, the sensor and device orientation 44 becomes identical and we can focus on the data as it relates to the surrounding 45 world. 46 47 Device-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 (---------) 148 149 150 So unless the sensor is ideally mounted, we need a means to indicate the 151 relative orientation of any given sensor of this type with respect to the 152 frame of reference. 153 154 To achieve this, use the device tree property "mount-matrix" for the sensor. 155 156 This supplies a 3x3 rotation matrix in the strict linear algebraic sense, 157 to orient the senor axes relative to a desired point of reference. This means 158 the resulting values from the sensor, after scaling to proper units, should be 159 multiplied by this matrix to give the proper vectors values in three-dimensional 160 space, relative to the device or world point of reference. 161 162 For more information, consult: 163 https://en.wikipedia.org/wiki/Rotation_matrix 164 165 The mounting matrix has the layout: 166 167 (mxx, myx, mzx) 168 (mxy, myy, mzy) 169 (mxz, myz, mzz) 170 171 Values 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 176 177 It is represented as an array of strings containing the real values for 178 producing the transformation matrix. 179 180 Examples: 181 182 Identity matrix (nothing happens to the coordinates, which means the device was 183 mechanically mounted in an ideal way and we need no transformation): 184 185 mount-matrix = "1", "0", "0", 186 "0", "1", "0", 187 "0", "0", "1"; 188 189 The sensor is mounted 30 degrees (Pi/6 radians) tilted along the X axis, so we 190 compensate by performing a -30 degrees rotation around the X axis: 191 192 mount-matrix = "1", "0", "0", 193 "0", "0.866", "0.5", 194 "0", "-0.5", "0.866"; 195 196 The sensor is flipped 180 degrees (Pi radians) around the Z axis, i.e. mounted 197 upside-down: 198 199 mount-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
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