grid = key=master,group=grid,depth=1,widthcm=15,heightcm=11,gcell=10, \ xmarg=1,ymarg=1,shrink=false,rounded=true, \ border_thickness=very thin,border_color=menublue, \ gback_color=gray99,gline_thickness=thin,gline_color=gray96 circle = key=range,group=contact,depth=2,x=0,y=0,radius=25, \ line_color=darkblue,fill_color=invisible,line_style=solid, \ line_thickness=ultra thin panel = key=panel1_initial_pose,group=panel_1,depth=11,x=-40,y=46.8, \ widthcm=7.8,heightcm=1,rounded=true,border_thickness=thin, \ border_color=gray40,panel_color=beige panel = key=panel2_theta_gam,group=panel_2,depth=12,x=35.1,y=5.8, \ widthcm=5.6,heightcm=2.6,rounded=true,border_thickness=thin, \ border_color=gray35,panel_color=beige panel = key=panel2a,group=panel_2a,depth=12,x=42.8,y=36.6,widthcm=4.8, \ heightcm=2.1,rounded=true,border_thickness=thin, \ border_color=gray35,panel_color=beige panel = key=panel3_gamma_ranges,group=panel_3,depth=13,x=40,y=-23.1, \ widthcm=5.3,heightcm=2.4,rounded=true,border_thickness=thin, \ border_color=gray35,panel_color=beige panel = key=panel4,group=panel_4,depth=14,x=30,y=-45,widthcm=6.4, \ heightcm=1.7,rounded=true,border_thickness=thin, \ border_color=gray35,panel_color=beige panel = key=panel5_final_result,group=panel_5,depth=15,x=-24,y=-45, \ widthcm=4.55,heightcm=1.7,rounded=true,border_thickness=thin, \ border_color=gray35,panel_color=beige label = key=macro1_os_cn_pos,group=panel_1,depth=81, \ label=macro:macro1_init_pos,label_color=black, \ label_size=scriptsize,x=-2,y=51.8 label = key=macro2a,group=panel_2a,depth=82,label=macro:macro2a, \ label_color=black,label_size=scriptsize,x=67,y=47.6 label = key=macro2,group=panel_2,depth=82,label=macro:macro2_range_bng, \ label_color=black,label_size=scriptsize,x=64,y=18.5 label = key=macro3,group=panel_3,depth=83, \ label=macro:macro3_gamma_ranges,label_color=black, \ label_size=scriptsize,x=68,y=-10.6 label = key=macro4,group=panel_4,depth=84,label=macro:macro4_timedist, \ label_color=black,label_size=scriptsize,x=62,y=-36 label = key=macro5_result,group=right_side,depth=85, \ label=macro:macro5_result,label_color=black, \ label_size=scriptsize,x=-3,y=-37 line = key=beam_star,group=contact,depth=100,x1=-5,y1=34,x2=5.607, \ y2=44.607,line_color=black,line_style=dotted, \ line_thickness=very thin line = key=range_os_in_cnh,group=gamma,depth=100,x1=0,y1=0,x2=-26.87, \ y2=26.87,line_color=gray50,line_style=solid, \ line_thickness=very thin,endtype2=arrow \begin{macro}[macro5_result][macros] $\begin{aligned} r^{os}_{pcnp} &= r_{\gamma} - r^{pos}_{\gamma} \\ &= 204.788 - 84.3157 \\ &= 120.472m \\ \end{aligned}$ \end{macro} \begin{macro}[macro4_timedist][macros] $\begin{aligned} t^{os}_{\epsilon} &= \frac{r_{\epsilon}}{v^{os}_{\epsilon}} = \frac{143.394}{6.75} = 24.9381s \\ r^{pos}_{\gamma} &= t^{os}_{\epsilon} \cdot v^{os}_{\gamma} = 24.9381 \cdot 3.381 = 84.3157m \\ \end{aligned}$ \end{macro} \begin{macro}[macro1_init_pos][macros] $\begin{aligned} x_{os} &= 0, & y_{os} &=0, & \theta_{os} &=340^{\circ}, & v_{os} &= 8m/s \\ x_{cn} &= 43.4, & y_{cn} &=246.2, & \theta_{cn} &=315^{\circ}, & v_{cn} &= 1.5m/s \end{aligned}$ \end{macro} \begin{macro}[macro2a][macros] $\begin{aligned} \theta^{os}_{\gamma} &= [\theta_{cn} + 90]^{^{360}} = 45^{\circ} \\ v^{os}_{\gamma} &= cos(\theta^{os}_{\gamma} - \theta_{os}) \cdot v_{os} \\ &= cos(65) \cdot 8 = 3.381 m/s \\ bng^{os}_{cn} &= 10^{\circ} \end{aligned}$ \end{macro} \begin{macro}[macro2_range_bng][macros] $\begin{aligned} \theta^{os}_{\epsilon} &= \theta_{cn} = 315^{\circ} \\ v^{os}_{cnh} &= cos(\theta^{os} - \theta^{os}_{\epsilon}) \cdot v_{os} \\ v^{os}_{cnh} &= cos(340 - 315) \cdot 8 = 7.25m/s \\[0.06in] v^{os}_{\epsilon} &= v^{os}_{cnh} - v_{cn} \\ v^{os}_{\epsilon} &= 7.25 - 1.5 = 5.75m/s \\ \end{aligned}$ \end{macro} swarmpath = key=,group=,depth=100,begtime=0,endtime=0,nowtime=0 frame = key=framekey,group=frame,depth=100,xl=-33.284,xh=95,yl=-46, \ yh=60 vessel = key=ownship,group=ownship,depth=100,x=0,y=0,hdg=340, \ body_type=,length=4,wid_mbody=2,wid_stern=1.086,pct_mbody=0.5, \ line_color=black,line_thickness=ultra thin,fill_color=white vessel = key=ownship_atcross,group=ownship,depth=100,x=-10.4,y=28.7, \ hdg=340,body_type=,length=4,wid_mbody=2,wid_stern=1.086, \ pct_mbody=0.5,line_color=black,line_thickness=ultra thin, \ fill_color=white label = key=contact,group=contact,depth=100,label=contact, \ label_color=black,label_size=tiny,x=10,y=27 label = key=contact_beam1,group=contact,depth=100,label=contact, \ label_color=black,label_size=tiny,x=-29,y=12 label = key=contact_beam2,group=contact,depth=100,label=beam, \ label_color=black,label_size=tiny,x=-29,y=10 label = key=range_os_pcnp,group=ownship,depth=100, \ label={$r^{os}_{pcnp}$},label_color=black, \ label_size=scriptsize,x=-14,y=37 label = key=range_pos_gamma,group=ownship,depth=100, \ label={$r^{pos}_{\gamma}$},label_color=black, \ label_size=scriptsize,x=-20,y=30 label = key=range_gamma,group=contact,depth=100,label=$r_{\gamma}$, \ label_color=black,label_size=scriptsize,x=11,y=2 \begin{macro}[macro3_gamma_ranges][macros] $\begin{aligned} r &= 250m \\ r_{\gamma} &= cos(\theta^{os}_{\gamma} - bng^{os}_{cn}) \cdot r \\ &= cos(35) \cdot 250 = 204.788 m \\ r_{\epsilon} &= cos(\theta^{os}_{\epsilon} - bng^{os}_{cn}) \cdot r \\ &= cos(305) \cdot 250 = 143.394 m \end{aligned}$ \end{macro} label = key=tangent_theta,group=ownship,depth=100, \ label=$\theta^{os}_{\gamma}$,label_color=black, \ label_size=scriptsize,x=24,y=22 line = key=beam_port,group=contact,depth=100,x1=-5,y1=34,x2=-26.213, \ y2=12.787,line_color=black,line_style=dotted, \ line_thickness=very thin line = key=range_pos_gam,group=gamma,depth=100,x1=-13.691,y1=32.209, \ x2=-22.954,y2=22.946,line_color=gray50,line_style=solid, \ line_thickness=very thin,endtype1=flat,endtype2=flat line = key=range_epsilon,group=gamma,depth=100,x1=3,y1=23.2,x2=13.147, \ y2=13.053,line_color=gray50,line_style=solid, \ line_thickness=very thin,endtype1=flat,endtype2=flat line = key=range_os_pcnp,group=gamma,depth=100,x1=-8.6,y1=37.3, \ x2=-13.691,y2=32.209,line_color=gray50,line_style=solid, \ line_thickness=very thin,endtype1=flat,endtype2=flat line = key=range_gamma,group=gamma,depth=100,x1=2,y1=-2,x2=16.496, \ y2=12.496,line_color=gray50,line_style=solid, \ line_thickness=very thin,endtype1=flat,endtype2=flat label = key=range_epsilon,group=contact,depth=100,label=$r_{\epsilon}$, \ label_color=black,label_size=scriptsize,x=7,y=16 label = key=ownship_hdg_spd,group=ownship,depth=100, \ label={$\theta_{os}, v_{os}$},label_color=black, \ label_size=scriptsize,x=0,y=-8 label = key=ownship_label,group=ownship,depth=100,label=ownship, \ label_color=black,label_size=tiny,x=0,y=-5.5 label = key=contact_hdg_spd,group=contact,depth=100, \ label={$\theta_{cn}, v_{cn}$},label_color=black, \ label_size=scriptsize,x=10.5,y=30.5 line = key=panel2_3,group=panel_2,depth=101,x1=63.1,y1=5.8,x2=63.1, \ y2=0.8,line_color=black,line_style=solid,line_thickness=thick, \ endtype2=arrow line = key=panel2a_2,group=panel2a,depth=101,x1=65,y1=36.5,x2=65, \ y2=31.5,line_color=black,line_style=solid,line_thickness=thick, \ endtype2=arrow line = key=panel1_2,group=panel_1,depth=101,x1=36.5,y1=52,x2=42.6, \ y2=52,line_color=black,line_style=solid,line_thickness=thick, \ endtype2=arrow line = key=panel3_4,group=panel_3,depth=104,x1=65,y1=-23,x2=65,y2=-28, \ line_color=black,line_style=solid,line_thickness=thick, \ endtype2=arrow line = key=panel4_5,group=panel_4,depth=105,x1=30,y1=-36,x2=21,y2=-36, \ line_color=black,line_style=solid,line_thickness=thick, \ endtype2=arrow vessel = key=contact,group=contact,depth=900,x=4.34,y=24.62,hdg=315, \ body_type=kayak,length=4,wid_mbody=2,wid_stern=1.086, \ pct_mbody=0.5,line_color=black,line_thickness=ultra thin, \ fill_color=beige vessel = key=contact_atcross,group=contact,depth=900,x=-5,y=34,hdg=315, \ body_type=kayak,length=3.5,wid_mbody=1.75,wid_stern=0.95, \ pct_mbody=0.5,line_color=black,line_thickness=ultra thin, \ fill_color=beige point = key=ship_ctr_ownship_atcross,group=ownship,depth=904,x=-10.4, \ y=28.7,point_size=0.02,point_color=black point = key=ship_ctr_ownship,group=ownship,depth=904,x=0,y=0, \ point_size=0.02,point_color=black point = key=bogus_right,group=bogus,depth=904,x=95,y=0, \ point_size=0.001,point_color=white point = key=ship_ctr_contact_atcross,group=contact,depth=904,x=-5,y=34, \ point_size=0.02,point_color=black point = key=bogus_right_bottom,group=bogus,depth=904,x=90,y=-44, \ point_size=0.001,point_color=white point = key=ship_ctr_contact,group=contact,depth=904,x=4.34,y=24.62, \ point_size=0.02,point_color=black line = key=ownship_heading_to_intersect,group=ownship,depth=915,x1=0, \ y1=0,x2=-11.799,y2=32.42,line_color=gray55,line_style=solid, \ line_thickness=thin,endtype2=arrow line = key=contact_heading_to_intercept,group=contact,depth=920, \ x1=4.34,y1=24.62,x2=-7.681,y2=36.641,line_color=gray55, \ line_style=solid,line_thickness=thin,endtype2=arrow line = key=ownship_heading,group=ownship,depth=920,x1=0,y1=0,x2=-3.42, \ y2=9.397,line_color=gray10,line_style=solid, \ line_thickness=semithick,endtype2=arrow line = key=theta_gamma,group=ownship_contact,depth=920,x1=0,y1=0, \ x2=21.213,y2=21.213,line_color=gray60,line_style=solid, \ line_thickness=thin,endtype2=arrow line = key=contact_trail,group=contact,depth=920,x1=4.34,y1=24.658, \ x2=19.896,y2=9.102,line_color=gray50,line_style=dotted, \ line_thickness=thin line = key=range_line,group=ownship_contact,depth=920,x1=0,y1=0, \ x2=4.341,y2=24.62,line_color=gray25,line_style=dotted, \ line_thickness=thin line = key=contact_heading,group=contact,depth=1020,x1=4.34,y1=24.62, \ x2=0.804,y2=28.156,line_color=gray10,line_style=solid, \ line_thickness=semithick,endtype2=arrow