/// <summary> /// /// </summary> /// <param name="xv">position and orientation of the camera</param> /// <param name="u">Control vector of accelerations</param> /// <param name="delta_t">time step in seconds</param> public override void func_fv_and_dfv_by_dxv(Vector xv, Vector u, float delta_t) { Vector3D rold, vold, omegaold, rnew, vnew, omeganew; Quaternion qold, qnew; // Separate things out to make it clearer rold = new Vector3D(0, 0, 0); vold = new Vector3D(0, 0, 0); omegaold = new Vector3D(0, 0, 0); qold = new Quaternion(); extract_r_q_v_omega(xv, rold, qold, vold, omegaold); Vector3D acceleration = new Vector3D(u); // rnew = r + v * delta_t //rnew = (Vector3D)((Point3D)rold + (Point3D)vold * delta_t); rnew = new Vector3D(rold + vold * delta_t); // qnew = q x q(omega * delta_t) // Keep qwt ( = q(omega * delta_t)) for later use Quaternion qwt = new Quaternion(omegaold * delta_t); qnew = qold.Multiply(qwt); // vnew = v vnew = new Vector3D(vold + acceleration * delta_t); // omeganew = omega omeganew = omegaold; // Put it all together compose_xv(ref rnew, ref qnew, ref vnew, ref omeganew, ref fvRES); // cout << "rold qold vold omegaold" << rold << qold // << vold << omegaold; // cout << "rnew qnew vnew omeganew" << rnew << qnew // << vnew << omeganew; // Now on to the Jacobian... // Identity is a good place to start since overall structure is like this // I 0 I * delta_t 0 // 0 dqnew_by_dq 0 dqnew_by_domega // 0 0 I 0 // 0 0 0 I dfv_by_dxvRES.SetIdentity(); // Fill in dxnew_by_dv = I * delta_t MatrixFixed Temp33A = new MatrixFixed(3, 3); Temp33A.SetIdentity(); Temp33A *= delta_t; dfv_by_dxvRES.Update(Temp33A, 0, 7); // Fill in dqnew_by_dq // qnew = qold x qwt ( = q3 = q2 x q1 in Scene/newbits.cc language) MatrixFixed Temp44A = MatrixFixed.dq3_by_dq2(qwt); //4,4 dfv_by_dxvRES.Update(Temp44A, 3, 3); // Fill in dqnew_by_domega = d(q x qwt)_by_dqwt . dqwt_by_domega Temp44A = MatrixFixed.dq3_by_dq1(qold); // Temp44A is d(q x qwt) by dqwt // Use function below for dqwt_by_domega MatrixFixed Temp43A = new MatrixFixed(4, 3); dqomegadt_by_domega(omegaold, delta_t, Temp43A); // Multiply them together MatrixFixed Temp43B = Temp44A * Temp43A; // And plug it in dfv_by_dxvRES.Update(Temp43B, 3, 10); // cout << "dfv_by_dxvRES" << dfv_by_dxvRES; }