Efficient C++ quaternion multiplication using cv::Mat

问题

I want to multiply 2 quaternions, which are stored in a cv::Mat structure. I want the function to be as efficient as possible. I have the following code so far:

/** Quaternion multiplication
 *
 */
void multiplyQuaternion(const Mat& q1,const Mat& q2, Mat& q)
{
    // First quaternion q1 (x1 y1 z1 r1)
    const float x1=q1.at<float>(0);
    const float y1=q1.at<float>(1);
    const float z1=q1.at<float>(2);
    const float r1=q1.at<float>(3);

    // Second quaternion q2 (x2 y2 z2 r2)
    const float x2=q2.at<float>(0);
    const float y2=q2.at<float>(1);
    const float z2=q2.at<float>(2);
    const float r2=q2.at<float>(3);


    q.at<float>(0)=x1*r2 + r1*x2 + y1*z2 - z1*y2;   // x component
    q.at<float>(1)=r1*y2 - x1*z2 + y1*r2 + z1*x2;   // y component
    q.at<float>(2)=r1*z2 + x1*y2 - y1*x2 + z1*r2;   // z component
    q.at<float>(3)=r1*r2 - x1*x2 - y1*y2 - z1*z2;   // r component
}

Is this the fastest way with OpenCV? Would it be fastest using fixed-point arithmetic?

回答1:

In this tutorial different ways to access different pixels are covered. The Mat::at function was found to be about 10% slower in comparison to direct pixel access, probably due to the extra check in debug mode.

If you are really off for performance, you should rewrite your method with the 3 different methods mentioned in the text and then profile to find the one which is best in your situation.

回答2:

There -had- been an ARM vector floating point quaternion multiply out there I can not find now. I could find this SIMD library:

Bullet 3D Game Multiphysics Library

回答3:

Quaternions are often used to rotate 3D vectors so you might consider checking that one quaternion is a pure vector (i.e., the scalar or real part is zero). This could cut your work to 12 multiplies, 8 adds/subtracts and one sign flip.

You can also use quaternion multiplication on two pure vectors to compute their dot and cross products simultaneously, so testing for this special case may also be worth it. If both quaternions are pure vectors, you only need do 9 multiplies, 5 add/subtracts and one sign flip.

来源：https://stackoverflow.com/questions/10781033/efficient-c-quaternion-multiplication-using-cvmat

标签

c++

OpenCV

quaternions