C#
我正在使用Eigen来计算一组点到飞机的最佳拟合。 我需要对这些数据进行处理,然后旋转一组点,使它们平放,否定旋转值。
我的代码是:
cv::Point2f plane_from_points(const std::vector<Vector3> & c)
{
// copy coordinates to matrix in Eigen format
size_t num_atoms = c.size();
Eigen::Matrix< Vector3::Scalar, Eigen::Dynamic, Eigen::Dynamic > coord(3, num_atoms);
for (size_t i = 0; i < num_atoms; ++i) coord.col(i) = c[i];
// calculate centroid
Vector3 centroid(coord.row(0).mean(), coord.row(1).mean(), coord.row(2).mean());
// subtract centroid
coord.row(0).array() -= centroid(0); coord.row(1).array() -= centroid(1); coord.row(2).array() -= centroid(2);
// we only need the left-singular matrix here
// http://math.stackexchange.com/questions/99299/best-fitting-plane-given-a-set-of-points
auto svd = coord.jacobiSvd(Eigen::ComputeThinU | Eigen::ComputeThinV);
Vector3 plane_normal = svd.matrixU().rightCols<1>();
float x = plane_normal[0];
float y = plane_normal[1];
float z = plane_normal[2];
float angle = atan2(x, z) * 180 / PI;
float angle2 = atan2(y, z) * 180 / PI;
cv::Point ret(angle, angle2);
return ret;
}
然后,在C#中,我将角度值转换为四元数来旋转我的对象:
public static Quaternion QuatFromEuler(double yaw, double pitch, double roll)
{
yaw = Deg2Rad(yaw);
pitch = Deg2Rad(pitch);
roll = Deg2Rad(roll);
double rollOver2 = roll * 0.5f;
double sinRollOver2 = (double)Math.Sin((double)rollOver2);
double cosRollOver2 = (double)Math.Cos((double)rollOver2);
double pitchOver2 = pitch * 0.5f;
double sinPitchOver2 = (double)Math.Sin((double)pitchOver2);
double cosPitchOver2 = (double)Math.Cos((double)pitchOver2);
double yawOver2 = yaw * 0.5f;
double sinYawOver2 = (double)Math.Sin((double)yawOver2);
double cosYawOver2 = (double)Math.Cos((double)yawOver2);
Quaternion result = new Quaternion();
result.W = cosYawOver2 * cosPitchOver2 * cosRollOver2 + sinYawOver2 * sinPitchOver2 * sinRollOver2;
result.X = cosYawOver2 * sinPitchOver2 * cosRollOver2 + sinYawOver2 * cosPitchOver2 * sinRollOver2;
result.Y = sinYawOver2 * cosPitchOver2 * cosRollOver2 - cosYawOver2 * sinPitchOver2 * sinRollOver2;
result.Z = cosYawOver2 * cosPitchOver2 * sinRollOver2 - sinYawOver2 * sinPitchOver2 * cosRollOver2;
return result;
}
这给了我:
angles: -177 -126
quat: -0.453834928533952,-0.890701198505913,-0.0233238317256566,0.0118840858439476
当我应用它时,它看起来不像它应该那样。 (我期望在一个轴上旋转大约45度,我会翻转180度)
我试过切换轴来检查坐标空间不匹配(可能),但我无法得到这个工作。 难道我做错了什么?
我检查了我传入算法的3d点,它们是正确的,所以我的问题是在点对面平面代码或四元数转换中。 任何帮助将非常感激。 谢谢。
如果要计算将一个平面旋转到另一个平面的四元数,只需计算旋转法向的四元数:
#include <Eigen/Geometry>
int main() {
using namespace Eigen;
// replace this by your actual plane normal:
Vector3d plane_normal = Vector3d::Random().normalized();
// Quaternion which rotates plane_normal to UnitZ, or the plane to the XY-plane:
Quaterniond rotQ = Quaterniond::FromTwoVectors(plane_normal, Vector3d::UnitZ());
std::cout << "Random plane_normal: " << plane_normal.transpose() << 'n';
std::cout << "rotated plane_normal: " << (rotQ * plane_normal).transpose() << 'n';
}
此外,不要以角度存储角度(有时以度为单位输出它们可能有意义)。
更重要的是: 停止使用欧拉角度!
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