Android 的 SensorManager.getRotation 是如何工作的（即数学）？

Question

我大致了解它的用途 ("Computes the inclination matrix I as well as the rotation matrix R transforming a vector from the device coordinate system to the world's coordinate system")，但我不明白 它是如何工作的。

javadoc is well written and the source is available here但我不懂数学（例如，mathematica/physical是什么意思的值Hx，Hy和Hz ? 例如：Hx = Ey*Az - Ez*Ay)。此外，该方法后面会发生什么。

我已经粘贴了上面 GrepCode link 中的代码，留下了源代码行号以便于参考。谢谢。

971     public static boolean More ...getRotationMatrix(float[] R, float[] I,
972             float[] gravity, float[] geomagnetic) {
973         // TODO: move this to native code for efficiency
974         float Ax = gravity[0];
975         float Ay = gravity[1];
976         float Az = gravity[2];
977         final float Ex = geomagnetic[0];
978         final float Ey = geomagnetic[1];
979         final float Ez = geomagnetic[2];
980         float Hx = Ey*Az - Ez*Ay;
981         float Hy = Ez*Ax - Ex*Az;
982         float Hz = Ex*Ay - Ey*Ax;
983         final float normH = (float)Math.sqrt(Hx*Hx + Hy*Hy + Hz*Hz);
984         if (normH < 0.1f) {
985             // device is close to free fall (or in space?), or close to
986             // magnetic north pole. Typical values are  > 100.
987             return false;
988         }
989         final float invH = 1.0f / normH;
990         Hx *= invH;
991         Hy *= invH;
992         Hz *= invH;
993         final float invA = 1.0f / (float)Math.sqrt(Ax*Ax + Ay*Ay + Az*Az);
994         Ax *= invA;
995         Ay *= invA;
996         Az *= invA;
997         final float Mx = Ay*Hz - Az*Hy;
998         final float My = Az*Hx - Ax*Hz;
999         final float Mz = Ax*Hy - Ay*Hx;
1000        if (R != null) {
1001            if (R.length == 9) {
1002                R[0] = Hx;     R[1] = Hy;     R[2] = Hz;
1003                R[3] = Mx;     R[4] = My;     R[5] = Mz;
1004                R[6] = Ax;     R[7] = Ay;     R[8] = Az;
1005            } else if (R.length == 16) {
1006                R[0]  = Hx;    R[1]  = Hy;    R[2]  = Hz;   R[3]  = 0;
1007                R[4]  = Mx;    R[5]  = My;    R[6]  = Mz;   R[7]  = 0;
1008                R[8]  = Ax;    R[9]  = Ay;    R[10] = Az;   R[11] = 0;
1009                R[12] = 0;     R[13] = 0;     R[14] = 0;    R[15] = 1;
1010            }
1011        }
1012        if (I != null) {
1013            // compute the inclination matrix by projecting the geomagnetic
1014            // vector onto the Z (gravity) and X (horizontal component
1015            // of geomagnetic vector) axes.
1016            final float invE = 1.0f / (float)Math.sqrt(Ex*Ex + Ey*Ey + Ez*Ez);
1017            final float c = (Ex*Mx + Ey*My + Ez*Mz) * invE;
1018            final float s = (Ex*Ax + Ey*Ay + Ez*Az) * invE;
1019            if (I.length == 9) {
1020                I[0] = 1;     I[1] = 0;     I[2] = 0;
1021                I[3] = 0;     I[4] = c;     I[5] = s;
1022                I[6] = 0;     I[7] =-s;     I[8] = c;
1023            } else if (I.length == 16) {
1024                I[0] = 1;     I[1] = 0;     I[2] = 0;
1025                I[4] = 0;     I[5] = c;     I[6] = s;
1026                I[8] = 0;     I[9] =-s;     I[10]= c;
1027                I[3] = I[7] = I[11] = I[12] = I[13] = I[14] = 0;
1028                I[15] = 1;
1029            }
1030        }
1031        return true;
1032    }

Answer 1

他们是cross product。假设方法中传递的参数之一是 gravity，因此是 Sky axis。另一个假设是传入的 magnetic 参数位于 North-Sky 平面中。因此，这两个向量的 cross product 是与 North-Sky 平面正交的向量，即 East。现在 Sky 和 East 的叉积是一个与这两个正交的向量，即 North。将所有这些归一化将为 World coordinate.
提供标准正交基础在上面的计算中，H 是 East 而 M 是 North.

Android 的 SensorManager.getRotation 是如何工作的（即数学）？

How does Android's SensorManager.getRotation work (i.e. the math)?

android

android-sensors

sensormanager