iphone - 如何在没有陀螺仪的设备上创建 CMRotationMatrix

Question

我想在 iPhone 上创建增强现实 View 。首先，我查看了 Apple 的 Park 演示项目。然而，deviceMotion 属性用于获取旋转矩阵来进行相机变换。但由于 deviceMotion 使用陀螺仪(iPhone 4 及更新版本上可用)并且我也想支持 3GS(事实上，3GS 是我唯一的开发设备)，因此我无法使用这种方法。因此，我想使用加速度计和指南针提供的数据自己创建旋转矩阵。

不幸的是，我自己缺乏数学技能。环顾四周，在我看来this是与我的问题最相关的实践指南，但在实现之后似乎并不适合我的问题(POI View 仅暂时出现，并且似乎更多是由于设备移动而不是其标题；我已经发布我的 onDisplayLink 方法(唯一有重大变化的方法)如下)。我尝试阅读相关的数学知识，但目前我对它的了解还不够，无法自己找到一种方法或找到代码中的错误。请问有什么帮助吗？

编辑:我从那时起就认识到传感器数据应该更好地存储在 double 中而不是整数中，并添加了一些平滑处理。现在，我可以更清楚地看到 POI 在设备旋转时应如何从侧面出现，而不是从上方向下显示。也许这有助于指出问题所在。

CMAccelerometerData* orientation = motionManager.accelerometerData;
CMAcceleration acceleration = orientation.acceleration;

vec4f_t normalizedAccelerometer;
vec4f_t normalizedMagnetometer;

xG = (acceleration.x * kFilteringFactor) + (xG * (1.0 - kFilteringFactor));
yG = (acceleration.y * kFilteringFactor) + (yG * (1.0 - kFilteringFactor));
zG = (acceleration.z * kFilteringFactor) + (zG * (1.0 - kFilteringFactor));

xB = (heading.x * kFilteringFactor) + (xB * (1.0 - kFilteringFactor));
yB = (heading.y * kFilteringFactor) + (yB * (1.0 - kFilteringFactor));
zB = (heading.z * kFilteringFactor) + (zB * (1.0 - kFilteringFactor));

double accelerometerMagnitude = sqrt(pow(xG, 2) + pow(yG, 2) + pow(zG, 2));
double magnetometerMagnitude = sqrt(pow(xB, 2) + pow(yB, 2) + pow(zB, 2));

normalizedAccelerometer[0] = xG/accelerometerMagnitude;
normalizedAccelerometer[1] = yG/accelerometerMagnitude;
normalizedAccelerometer[2] = zG/accelerometerMagnitude;
normalizedAccelerometer[3] = 1.0f;

normalizedMagnetometer[0] = xB/magnetometerMagnitude;
normalizedMagnetometer[1] = yB/magnetometerMagnitude;
normalizedMagnetometer[2] = zB/magnetometerMagnitude;
normalizedMagnetometer[3] = 1.0f;

vec4f_t eastDirection;

eastDirection[0] = normalizedAccelerometer[1] * normalizedMagnetometer[2] - normalizedAccelerometer[2] * normalizedMagnetometer[1];
eastDirection[1] = normalizedAccelerometer[0] * normalizedMagnetometer[2] - normalizedAccelerometer[2] * normalizedMagnetometer[0];
eastDirection[2] = normalizedAccelerometer[0] * normalizedMagnetometer[1] - normalizedAccelerometer[1] * normalizedMagnetometer[0];
eastDirection[3] = 1.0f;

double eastDirectionMagnitude = sqrt(pow(eastDirection[0], 2) + pow(eastDirection[1], 2) + pow(eastDirection[2], 2));

vec4f_t normalizedEastDirection;

normalizedEastDirection[0] = eastDirection[0]/eastDirectionMagnitude;
normalizedEastDirection[1] = eastDirection[1]/eastDirectionMagnitude;
normalizedEastDirection[2] = eastDirection[2]/eastDirectionMagnitude;
normalizedEastDirection[3] = 1.0f;

vec4f_t northDirection;

northDirection[0] = (pow(normalizedAccelerometer[0], 2) + pow(normalizedAccelerometer[1],2) + pow(normalizedAccelerometer[2],2)) * xB - (normalizedAccelerometer[0] * xB + normalizedAccelerometer[1] * yB + normalizedAccelerometer[2] * zB)*normalizedAccelerometer[0];
northDirection[1] = (pow(normalizedAccelerometer[0], 2) + pow(normalizedAccelerometer[1],2) + pow(normalizedAccelerometer[2],2)) * yB - (normalizedAccelerometer[0] * xB + normalizedAccelerometer[1] * yB + normalizedAccelerometer[2] * zB)*normalizedAccelerometer[1];
northDirection[2] = (pow(normalizedAccelerometer[0], 2) + pow(normalizedAccelerometer[1],2) + pow(normalizedAccelerometer[2],2)) * zB - (normalizedAccelerometer[0] * xB + normalizedAccelerometer[1] * yB + normalizedAccelerometer[2] * zB)*normalizedAccelerometer[2];
northDirection[3] = 1.0f;

double northDirectionMagnitude;

northDirectionMagnitude = sqrt(pow(northDirection[0], 2) + pow(northDirection[1], 2) + pow(northDirection[2], 2));

vec4f_t normalizedNorthDirection;

normalizedNorthDirection[0] = northDirection[0]/northDirectionMagnitude;
normalizedNorthDirection[1] = northDirection[1]/northDirectionMagnitude;
normalizedNorthDirection[2] = northDirection[2]/northDirectionMagnitude;
normalizedNorthDirection[3] = 1.0f;

CMRotationMatrix r;
r.m11 = normalizedEastDirection[0];
r.m21 = normalizedEastDirection[1];
r.m31 = normalizedEastDirection[2];
r.m12 = normalizedNorthDirection[0];
r.m22 = normalizedNorthDirection[1];
r.m32 = normalizedNorthDirection[2];
r.m13 = normalizedAccelerometer[0];
r.m23 = normalizedAccelerometer[1];
r.m33 = normalizedAccelerometer[2];

transformFromCMRotationMatrix(cameraTransform, &r);

[self setNeedsDisplay];

当设备放置在 table 上并大致(使用 Compass.app)指向北时，我记录以下数据:

Accelerometer: x: -0.016692, y: 0.060852, z: -0.998007
Magnetometer: x: -0.016099, y: 0.256711, z: -0.966354
North Direction x: 0.011472, y: 8.561041, z:0.521807
Normalized North Direction x: 0.001338, y: 0.998147, z:0.060838
East Direction x: 0.197395, y: 0.000063, z:-0.003305
Normalized East Direction x: 0.999860, y: 0.000319, z:-0.016742

这看起来理智吗？

编辑 2:我已将 r 的分配更新为一个显然可以引导我实现目标的一半:当设备直立时，我现在可以看到水平面附近的地标；当设备直立时，我现在可以看到水平面附近的地标；然而，它们与预期位置的时钟方向相差约 90 度。另外，Beta建议的移动后的输出:

Accelerometer: x: 0.074289, y: -0.997192, z: -0.009475
Magnetometer: x: 0.031341, y: -0.986382, z: -0.161458
North Direction x: -1.428996, y: -0.057306, z:-5.172881
Normalized North Direction x: -0.266259, y: -0.010678, z:-0.963842
East Direction x: 0.151658, y: -0.011698, z:-0.042025
Normalized East Direction x: 0.961034, y: -0.074126, z:-0.266305

Answer 1

拿到 iPhone 4 后，我能够将上述代码生成的数据与 CoreMotion 姿态数据的输出进行比较。有了这个，我发现我应该按以下方式将值分配给我的旋转矩阵:

CMRotationMatrix r;
r.m11 = normalizedNorthDirection[0];
r.m21 = normalizedNorthDirection[1];
r.m31 = normalizedNorthDirection[2];
r.m12 = 0 - normalizedEastDirection[0];
r.m22 = normalizedEastDirection[1];
r.m32 = 0 - normalizedEastDirection[2];
r.m13 = 0 - normalizedAccelerometer[0];
r.m23 = 0 - normalizedAccelerometer[1];
r.m33 = 0 - normalizedAccelerometer[2];

这给出了大致相似的值，但当然，CoreMotion 使用陀螺仪生成的数据要好得多。不管怎样，这是合理支持3GS的一个起点。也许可以通过某种过滤获得额外的质量，但我还没有决定这是否值得付出努力。