var measurementData = [
  {
    "id": "Distance_First_Second",
    "name": "Distance between 1st point - 2nd point",
    "imageFile": "measurement_distance_between_two_points-frontal.png",
    "description": "To measure the distance between 2 points that are not listed as feature points in the list: Select '1st Point' then mark the point on the model. Then select '2nd Point' and mark the point on the model. The distance will be calculated.",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(FirstPoint.x-SecondPoint.x\\right)^2+\\left(FirstPoint.y-SecondPoint.y\\right)^2+\\left(FirstPoint.z-SecondPoint.z\\right)^2}$$"
  },
  {
    "id": "Angle_First_Second_Third",
    "name": "Angle between 1st, 2nd & 3rd points",
    "imageFile": "measurement_angle_between_three_points-basal.png",
    "description": "To measure the angle between 3 points that form an angle at the 2nd point: Select '1st Point' then mark the point on the model. Then do the same for '2nd & 3rd Point'. The angle will be calculated.",
    "type": "Angles",
    "formula": "V1=$$<\\left(SecondPoint.x-FirstPoint.x\\right),\\left(SecondPoint.y-FirstPoint.y\\right),\\left(SecondPoint.z-FirstPoint.z\\right)>$$ V2=$$<\\left(SecondPoint.x-ThirdPoint.x\\right),\\left(SecondPoint.y-ThirdPoint.y\\right),\\left(SecondPoint.z-ThirdPoint.z\\right)>$$$$\\theta=\\cos^{-1}(\\frac{V1\\bullet V2}{|V1||V2|})$$"
  },
  {
    "id": "Ratio_First_Second_Third_Fourth",
    "name": "Ratio of two distances [1st to 2nd] / [3rd to 4th]",
    "imageFile": "measurement_ratio_between_two_distances.png",
    "description": "To measure the ratio of two distances. The first distance is between 1st and 2nd points and the second distance is between the 3rd and 4th points.",
    "type": "Ratios",
    "formula": "$$\\frac{\\sqrt{\\left(FirstPoint.x-SecondPoint.x\\right)^2+\\left(FirstPoint.y-SecondPoint.y\\right)^2+\\left(FirstPoint.z-SecondPoint.z\\right)^2}}{\\sqrt{\\left(ThirdPoint.x-FourthPoint.x\\right)^2+\\left(ThirdPoint.y-FourthPoint.y\\right)^2+\\left(ThirdPoint.z-FourthPoint.z\\right)^2}}$$"
  },
  {
    "id": "Ala/Alar_Length_(left)",
    "name": "Ala/Alar Length (left)",
    "imageFile": "measurement_distance_left_alar_length-basal.png",
    "description": "Distance between 'Pronasale/Tip (prn)' and 'Alar Curvature - left (ac_l)'",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(Prn.x-Ac_l.x\\right)^2+\\left(Prn.y-Ac_l.y\\right)^2+\\left(Prn.z-Ac_l.z\\right)^2}$$"
  },
  {
    "id": "Ala/Alar_Length_(right)",
    "name": "Ala/Alar Length (right)",
    "imageFile": "measurement_distance_right_alar_length-basal.png",
    "description": "Distance between 'Pronasale/Tip (prn)' and 'Alar Curvature - right (ac_r)' ",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(Prn.x-Ac_r.x\\right)^2+\\left(Prn.y-Ac_r.y\\right)^2+\\left(Prn.z-Ac_r.z\\right)^2}$$"
  },
  {
    "id": "Alar_Base_Width",
    "name": "Alar Base Width",
    "imageFile": "measurement_distance_alar_base_width-basal.png",
    "description": "Distance from 'Alar Curvature/Alar Base Junction - left (ac_l)' to 'Alar Curvature/Alar Base Junction - right (ac_r)'",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(Ac_l.x-Ac_r.x\\right)^2+\\left(Ac_l.y-Ac_r.y\\right)^2+\\left(Ac_l.z-Ac_r.z\\right)^2}$$"
  },
  {
    "id": "Base_Bony_Width",
    "name": "Base Bony Width",
    "imageFile": "measurement_distance_base_bony_width-frontal.png",
    "description": "Distance between 'Nasal Parenthesis - left (np_l)' and 'Nasal Parenthesis - right (np_r)'",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(Np_l.x-Np_r.x\\right)^2+\\left(Np_l.y-Np_r.y\\right)^2+\\left(Np_l.z-Np_r.z\\right)^2}$$"
  },
  {
    "id": "Chin_Projection",
    "name": "Chin Projection",
    "imageFile": "measurement_distance_chin_projection1-lateral(l).png",
    "description": "Distance from 'Pogonion (pg)' to the 'Vertical Facial Plane (vfp)'",
    "type": "Distance",
    "formula": "MISSING"
  },
  {
    "id": "Columella_Length",
    "name": "Columella Length",
    "imageFile": "measurement_distance_columella_length-lateral(l).png",
    "description": "Distance between 'Subnasale (sn)' and 'Columella Breakpoint (c)'",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(Sn.x-C.x\\right)^2+\\left(Sn.y-C.y\\right)^2+\\left(Sn.z-C.z\\right)^2}$$"
  },
  {
    "id": "Columella_Width",
    "name": "Columella Width",
    "imageFile": "measurement_distance_columella_width-basal.png",
    "description": "Distance from 'Subnasale' left (sn'_l)' to 'Subnasale' right (sn'_r)'",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(Sn’_l.x-Sn’_r.x\\right)^2+\\left(Sn’_l.y-Sn’_r.y\\right)^2+\\left(Sn’_l.z-Sn’_r.z\\right)^2}$$"
  },
  {
    "id": "Columella-Alar_Distance_-_left",
    "name": "Columella-Alar Distance - left",
    "imageFile": "measurement_distance_columella-alar_distance_left-lateral.png",
    "description": "Distance between 'Alar Ridge's Highest Point - left (armax_l)' and 'Columella's Lowest Point - left (cmin_l)'",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(Armax_l.x-Cmin_l.x\\right)^2+\\left(Armax_l.y-Cmin_l.y\\right)^2+\\left(Armax_l.z-Cmin_l.z\\right)^2}$$"
  },
  {
    "id": "Columella-Alar_Distance_-_right",
    "name": "Columella-Alar Distance - right",
    "imageFile": "measurement_distance_columella-alar_distance_right-lateral.png",
    "description": "Distance between 'Alar Ridge's Highest Point - right (armax_r)' and 'Columella's Lowest Point - right (cmin_r)'",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(Armax_r.x-Cmin_r.x\\right)^2+\\left(Armax_r.y-Cmin_r.y\\right)^2+\\left(Armax_r.z-Cmin_r.z\\right)^2}$$"
  },
  {
    "id": "Face_Length/Height",
    "name": "Face Length/Height",
    "imageFile": "measurement_distance_facial_height-frontal.png",
    "description": "Distance between 'Trichion (tr)' and 'Menton/Gnathion (me)'",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(Tr.x-Me.x\\right)^2+\\left(Tr.y-Me.y\\right)^2+\\left(Tr.z-Me.z\\right)^2}$$"
  },
  {
    "id": "Face_Width",
    "name": "Face Width",
    "imageFile": "measurement_distance_face_width-frontal.png",
    "description": "Distance from 'Zygion - left (zy_l)' to 'Zygion - right (zy_r)'",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(Zy_l.x-Zy_r.x\\right)^2+\\left(Zy_l.y-Zy_r.y\\right)^2+\\left(Zy_l.z-Zy_r.z\\right)^2}$$"
  },
  {
    "id": "Height_of_the_Mandible/Chin_Height",
    "name": "Height of the Mandible/Chin Height",
    "imageFile": "measurement_distance_chin_height-lateral(l).png",
    "description": "Distance between 'Menton/Gnathion (me)' and 'Stomion (sto)'",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(Me.x-Sto.x\\right)^2+\\left(Me.y-Sto.y\\right)^2+\\left(Me.z-Sto.z\\right)^2}$$"
  },
  {
    "id": "Infratip_Lobule/Infralobule",
    "name": "Infratip Lobule/Infralobule",
    "imageFile": "measurement_distance_infratip_lobule-lateral(l).png",
    "description": "Distance between 'Pronasale/Tip (prn)' and 'Columella Break Point (c)'",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(Prn.x-C.x\\right)^2+\\left(Prn.y-C.y\\right)^2+\\left(Prn.z-C.z\\right)^2}$$"
  },
  {
    "id": "Interalar_Distance",
    "name": "Interalar Distance",
    "imageFile": "measurement_distance_interalar_distance-frontal.png",
    "description": "Distance between 'Alare/Alar Flare - left (al_l)' and 'Alar/Alar Flare - right (al_r)'",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(Al_l.x-Al_r.x\\right)^2+\\left(Al_l.y-Al_r.y\\right)^2+\\left(Al_l.z-Al_r.z\\right)^2}$$"
  },
  {
    "id": "(Inner)_Intercanthal_Distance/Width",
    "name": "(Inner) Intercanthal Distance/Width",
    "imageFile": "measurement_distance_intercanthal_distance-frontal.png",
    "description": "Distance between 'Endocanthion/Medial Canthus - left (en_l)' and 'Endocanthion/Medial Canthus - right (en_r)'",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(En_l.x-En_r.x\\right)^2+\\left(En_l.y-En_r.y\\right)^2+\\left(En_l.z-En_r.z\\right)^2}$$"
  },
  {
    "id": "Interpupillary/Interocular_Distance",
    "name": "Interpupillary/Interocular Distance",
    "imageFile": "measurement_distance_interpupillary_distance-frontal.png",
    "description": "Distance from 'Pupil - left (p_l)' to 'Pupil - right (p_r)'",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(P_l.x-P_r.x\\right)^2+\\left(P_l.y-P_r.y\\right)^2+\\left(P_l.z-P_r.z\\right)^2}$$"
  },
  {
    "id": "Left_Eye_Width",
    "name": "Left Eye Width",
    "imageFile": "measurement_distance_left_eye_length-frontal.png",
    "description": "Distance from 'Endocanthion/Medial Canthus - left (en_l)' to 'Exocanthion/Lateral Canthus – left (ex_l)'",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(En_l.x-Ex_l.x\\right)^2+\\left(En_l.y-Ex_l.y\\right)^2+\\left(En_l.z-Ex_l.z\\right)^2}$$"
  },
  {
    "id": "Lower_Facial_Height",
    "name": "Lower Facial Height",
    "imageFile": "measurement_distance_lower_facial_height-frontal.png",
    "description": "Distance between 'Subnasale (sn)' and 'Menton/Gnathion (me)'",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(Me.x-Sn.x\\right)^2+\\left(Me.y-Sn.y\\right)^2+\\left(Me.z-Sn.z\\right)^2}$$"
  },
  {
    "id": "Lower_Lip_Height",
    "name": "Lower Lip Height",
    "imageFile": "measurement_distance_lower_lip_height-frontal.png",
    "description": "Distance from 'Sublabiale (sl)' to 'Stomion (sto)', when the mouth is in a neutral position",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(Sl.x-Sto.x\\right)^2+\\left(Sl.y-Sto.y\\right)^2+\\left(Sl.z-Sto.z\\right)^2}$$"
  },
  {
    "id": "Mid-Facial_Height",
    "name": "Mid-Facial Height",
    "imageFile": "measurement_distance_mid_facial_height-frontal.png",
    "description": "Distance between 'Subnasale (sn)' and 'Glabella (g)'",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(G.x-Sn.x\\right)^2+\\left(G.y-Sn.y\\right)^2+\\left(G.z-Sn.z\\right)^2}$$"
  },
  {
    "id": "Mouth/Lips_Width",
    "name": "Mouth/Lips Width",
    "imageFile": "measurement_distance_mouth_width-basal.png",
    "description": "Distance from 'Cheilion - left (ch_l)' to 'Cheilion - right (ch_r)', when the mouth is in a neutral position.",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(Ch_l.x-Ch_r.x\\right)^2+\\left(Ch_l.y-Ch_r.y\\right)^2+\\left(Ch_l.z-Ch_r.z\\right)^2}$$"
  },
  {
    "id": "Nasal_Bridge_Length",
    "name": "Nasal Bridge Length",
    "imageFile": "measurement_distance_nasal_bridge_length-lateral(l).png",
    "description": "Distance between 'Pronasale/Tip (prn)' and 'Nasion (n)'",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(Prn.x-N.x\\right)^2+\\left(Prn.y-N.y\\right)^2+\\left(Prn.z-N.z\\right)^2}$$"
  },
  {
    "id": "Nasal_Root_Width",
    "name": "Nasal Root Width",
    "imageFile": "measurement_distance_nasal_root_width-frontal.png",
    "description": "Distance between 'Maxilloanteriorale - left (mf_l)' and 'Maxilloanteriorale - right (mf_r)'",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(Mf_l.x-Mf_r.x\\right)^2+\\left(Mf_l.y-Mf_r.y\\right)^2+\\left(Mf_l.z-Mf_r.z\\right)^2}$$"
  },
  {
    "id": "Nasal_Tip_Projection",
    "name": "Nasal Tip Projection",
    "imageFile": "measurement_distance_nasal_tip_projection_I-lateral(l).png",
    "description": "Distance between 'Subnasale (sn)' and 'Pronasale/Tip (prn)'",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(Prn.x-Sn.x\\right)^2+\\left(Prn.y-Sn.y\\right)^2+\\left(Prn.z-Sn.z\\right)^2}$$"
  },
  {
    "id": "Nose_Height",
    "name": "Nose Height",
    "imageFile": "measurement_distance_nose_height-lateral(l).png",
    "description": "Distance between 'Subnasale (sn)' and 'Nasion (n)'",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(Sn.x-N.x\\right)^2+\\left(Sn.y-N.y\\right)^2+\\left(Sn.z-N.z\\right)^2}$$"
  },
  {
    "id": "Nostril_Floor_Width_(left)",
    "name": "Nostril Floor Width (left)",
    "imageFile": "measurement_distance_left_nostril_floor_width-basal.png",
    "description": "Distance between 'Subnasale (sn)' to 'Subalare - left (sbal_l)'",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(Sn.x-Sbal_l.x\\right)^2+\\left(Sn.y-Sbal_l.y\\right)^2+\\left(Sn.z-Sbal_l.z\\right)^2}$$"
  },
  {
    "id": "Nostril_Floor_Width_(right)",
    "name": "Nostril Floor Width (right)",
    "imageFile": "measurement_distance_right_nostril_floor_width-basal.png",
    "description": "Distance between 'Subnasale (sn)' to 'Subalare - right (sbal_r)'",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(Sn.x-Sbal_r.x\\right)^2+\\left(Sn.y-Sbal_r.y\\right)^2+\\left(Sn.z-Sbal_r.z\\right)^2}$$"
  },
  {
    "id": "Outer_Intercanthal_Distance",
    "name": "Outer Intercanthal Distance",
    "imageFile": "measurement_distance_outercanthal_distance-frontal.png",
    "description": "Distance between 'Exocanthion/Lateral Canthus – left (ex_l)' and 'Exocanthion/Lateral Canthus – right (ex_r)'",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(Ex_l.x-Ex_r.x\\right)^2+\\left(Ex_l.y-Ex_r.y\\right)^2+\\left(Ex_l.z-Ex_r.z\\right)^2}$$"
  },
  {
    "id": "Philtrum_Width/Interphiltral_Distance",
    "name": "Philtrum Width/Interphiltral Distance",
    "imageFile": "measurement_distance_philtrum_width-basal.png",
    "description": "Distance from 'Crista Philtri - left (cph_l)' to 'Crista Philtri - right (cph_r)' , when the mouth is in a neutral position",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(Cph_l.x-Cph_r.x\\right)^2+\\left(Cph_l.y-Cph_r.y\\right)^2+\\left(Cph_l.z-Cph_r.z\\right)^2}$$"
  },
  {
    "id": "Premaxilla_-_left",
    "name": "Premaxilla - left",
    "imageFile": "measurement_distance_left_premaxilla-lateral(l).png",
    "description": "Distance between 'Subnasale (sn)' and 'Alar Base Junction Left (ac_l)'",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(Sn.x-Ac_l.x\\right)^2+\\left(Sn.y-Ac_l.y\\right)^2+\\left(Sn.z-Ac_l.z\\right)^2}$$"
  },
  {
    "id": "Premaxilla_-_right",
    "name": "Premaxilla - right",
    "imageFile": "measurement_distance_right_premaxilla-lateral(r).png",
    "description": "Distance between 'Subnasale (sn)' and 'Alar Base Junction Right (ac_r)'",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(Sn.x-Ac_r.x\\right)^2+\\left(Sn.y-Ac_r.y\\right)^2+\\left(Sn.z-Ac_r.z\\right)^2}$$"
  },
  {
    "id": "Radix_Depth",
    "name": "Radix Depth",
    "imageFile": "measurement_distance_radix_depth-lateral(l).png",
    "description": "Distance between 'Nasal/Radix (n)' and 'Supratarsal Crease (sc_l)'",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(Sc_l.x-N.x\\right)^2+\\left(Sc_l.y-N.y\\right)^2+\\left(Sc_l.z-N.z\\right)^2}$$"
  },
  {
    "id": "Radix_Projection",
    "name": "Radix Projection",
    "imageFile": "measurement_distance_radix_projection-lateral(l).png",
    "description": "Distance between 'Corneal Plane (cp)' and 'Nasion/Radix (n)'",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(Cp.x-N.x\\right)^2+\\left(Cp.y-N.y\\right)^2+\\left(Cp.z-N.z\\right)^2}$$"
  },
  {
    "id": "Right_Eye_Width",
    "name": "Right Eye Width",
    "imageFile": "measurement_distance_right_eye_length-frontal.png",
    "description": "Distance from 'Endocanthion/Medial Canthus - right (en_r)' to 'Exocanthion/Lateral Canthus – right (ex_r)'",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(En_r.x-Ex_r.x\\right)^2+\\left(En_r.y-Ex_r.y\\right)^2+\\left(En_r.z-Ex_r.z\\right)^2}$$"
  },
  {
    "id": "Subnasal_Width",
    "name": "Subnasal Width",
    "imageFile": "measurement_distance_subnasal_width-basal.png",
    "description": "Distance between 'Subalare - right (sbal_r)' and 'Subalare - left (sbal_l)'",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(Sbal_r.x-Sbal_l.x\\right)^2+\\left(Sbal_r.y-Sbal_l.y\\right)^2+\\left(Sbal_r.z-Sbal_l.z\\right)^2}$$"
  },
  {
    "id": "Supratip_Lobule",
    "name": "Supratip Lobule",
    "imageFile": "measurement_distance_supratip_lobule-lateral(l).png",
    "description": "Distance between 'Pronasale/Tip (prn)' and 'Supratip Break Point (s)'",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(Prn.x-S.x\\right)^2+\\left(Prn.y-S.y\\right)^2+\\left(Prn.z-S.z\\right)^2}$$"
  },
  {
    "id": "Tip/Lobule_Width",
    "name": "Tip/Lobule Width",
    "imageFile": "measurement_distance_lobule_width-frontal.png",
    "description": "Distance from 'Tip Defining Point - left (td_l)' to 'Tip Defining Point - right (td_r)'",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(Td_l.x-Td_r.x\\right)^2+\\left(Td_l.y-Td_r.y\\right)^2+\\left(Td_l.z-Td_r.z\\right)^2}$$"
  },
  {
    "id": "Upper_Facial_Height",
    "name": "Upper Facial Height",
    "imageFile": "measurement_distance_upper_facial_height-frontal.png",
    "description": "Distance between 'Trichion (tr)' and 'Glabella (g)'",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(G.x-Tr.x\\right)^2+\\left(G.y-Tr.y\\right)^2+\\left(G.z-Tr.z\\right)^2}$$"
  },
  {
    "id": "Upper_Lip_Height",
    "name": "Upper Lip Height",
    "imageFile": "measurement_distance_upper_lip_height-frontal.png",
    "description": "Distance between 'Subnasale (sn)' and 'Stomion (sto)'",
    "type": "Distance",
    "formula": "$$\\sqrt{\\left(Sn.x-Sto.x\\right)^2+\\left(Sn.y-Sto.y\\right)^2+\\left(Sn.z-Sto.z\\right)^2}$$"
  },
  {
    "id": "Columellar_Labial_Angle",
    "name": "Columellar Labial Angle",
    "imageFile": "measurement_angle_columellar_labial_angle-lateral(l).png",
    "description": " The columellar-labial angle is formed by the columella and the upper lip.",
    "type": "Angles",
    "formula": "V1=$$<\\left(Sn.x-Ls.x\\right),\\left(Sn.y-Ls.y\\right),\\left(Sn.z-Ls.z\\right)>$$ V2=$$<\\left(Sn.x-C.x\\right),\\left(Sn.y-C.y\\right),\\left(Sn.z-C.z\\right)>$$$$\\theta=\\cos^{-1}(\\frac{V1\\bullet V2}{|V1||V2|})$$"
  },
  {
    "id": "Columellar_Lobular_Angle",
    "name": "Columellar Lobular Angle",
    "imageFile": "measurement_angle_columellar_lobular_angle-lateral(l).png",
    "description": "This angle is formed at the junction of the columella and the infratip lobule, and indicates the junction of the middle and medial crura.",
    "type": "Angles",
    "formula": "V1=$$<\\left(C.x-Prn.x\\right),\\left(C.y-Prn.y\\right),\\left(C.z-Prn.z\\right)>$$ V2=$$<\\left(C.x-Sn.x\\right),\\left(C.y-Sn.y\\right),\\left(C.z-Sn.z\\right)>$$$$\\theta=\\cos^{-1}(\\frac{V1\\bullet V2}{|V1||V2|})$$"
  },
  {
    "id": "Degree_of_Deviation_(C-type)",
    "name": "Degree of Deviation (C-type)",
    "imageFile": "measurement_angle_degree_of_deviation_c_type-frontal.png",
    "description": "(A) glabella, (B) nasion, (C) nasal tip, (D) middle point of upper lip, (E) most prominent point of the convexity, C - type crooked nose angle: the angle between BE and EC lines.",
    "type ": "Angles",
    "formula": "V1=$$<\\left(N.x-Pc.x\\right),\\left(N.y-Pc.y\\right),\\left(N.z-Pc.z\\right)>$$ V2=$$<\\left(Pc.x-Prn.x\\right),\\left(Pc.y-Prn.y\\right),\\left(Pc.z-Prn.z\\right)>$$$$\\theta=\\cos^{-1}(\\frac{V1\\bullet V2}{|V1||V2|})$$"
  },
  {
    "id": "Degree_of_Deviation_(I-type)",
    "name": "Degree of Deviation (I-type)",
    "imageFile": "measurement_angle_degree_of_deviation_i_type-frontal.png",
    "description": "(A) glabella, (B) nasion, (C) most prominent point of the nasal tip, (D) middle point of upper lip, I - type crooked nose angle: the angle between BD and BC lines.",
    "type ": "Angles",
    "formula": "V1=$$<\\left(N.x-Ls.x\\right),\\left(N.y-Ls.y\\right),\\left(N.z-Ls.z\\right)>$$ V2=$$<\\left(N.x-Prn.x\\right),\\left(N.y-Prn.y\\right),\\left(N.z-Prn.z\\right)>$$$$\\theta=\\cos^{-1}(\\frac{V1\\bullet V2}{|V1||V2|})$$"
  },
  {
    "id": "Interalar_Angle",
    "name": "Interalar Angle",
    "imageFile": "measurement_angle_interalar_angle-basal.png",
    "description": "Angle between 'Alare - left (al_l)' to 'Pronasale/Tip (prn)' and 'Pronasale/Tip (prn)' to Alare - right (al_r))' Formed near the nose tip by the two tangents touching the alar on either side. Used to classify the nose shape into different morphological types.",
    "type": "Angles",
    "formula": "V1=$$<\\left(Al_l.x-Prn.x\\right),\\left(Al_l.y-Prn.y\\right),\\left(Al_l.z-Prn.z\\right)>$$ V2=$$<\\left(Prn.x-Al_r.x\\right),\\left(Prn.y-Al_r.y\\right),\\left(Prn.z-Al_r.z\\right)>$$$$\\theta=\\cos^{-1}(\\frac{V1\\bullet V2}{|V1||V2|})$$"
  },
  {
    "id": "Interaxial_Angle_(Nostril_Inclination)",
    "name": "Interaxial Angle (Nostril Inclination)",
    "imageFile": "measurement_angle_nostril_inclination_with_midline-basal.png",
    "description": "Angle between 'Superior/Highest Point of Nostril - left (stn_l)' to 'Inferior/Lowest Point of Nostril - left (itn_l)' and 'Superior/Highest Point of Nostril - right (stn_r)' to 'Inferior/Lowest Point of Nostril - right (itn_r)' Formed at the apex where the two nostril axes meet; it is closely related to the nostril inclination",
    "type": "Angles",
    "formula": "V1=$$<\\left(Stn_l.x-Itn_l.x\\right),\\left(Stn_l.y-Itn_l.y\\right),\\left(Stn_l.z-Itn_l.z\\right)>$$ V2=$$<\\left(Stn_r.x-Itn_r.x\\right),\\left(Stn_r.y-Itn_r.y\\right),\\left(Stn_r.z-Itn_r.z\\right)>$$$$\\theta=\\cos^{-1}(\\frac{V1\\bullet V2}{|V1||V2|})$$"
  },
  {
    "id": "Mentocervical_Angle",
    "name": "Mentocervical Angle",
    "imageFile": "measurement_angle_mentocervical_angle-lateral(l).png",
    "description": "The angle between 'Pronasale/Tip (prn)' to 'Pogonion (pg)' and 'Menton/Gnathion (me)' to 'Cervical Point (c)'",
    "type": "Angles",
    "formula": "V1=$$<\\left(Prn.x-Pg.x\\right),\\left(Prn.y-Pg.y\\right),\\left(Prn.z-Pg.z\\right)>$$ V2=$$<\\left(Me.x-C.x\\right),\\left(Me.y-C.y\\right),\\left(Me.z-C.z\\right)>$$$$\\theta=\\cos^{-1}(\\frac{V1\\bullet V2}{|V1||V2|})$$"
  },
  {
    "id": "Nasal_Tip_Angle",
    "name": "Nasal Tip Angle",
    "imageFile": "measurement_angle_nasal_tip_angle-lateral(l).png",
    "description": " The angle between 'Nasion (n)' to 'Pronasale/Tip (prn)' and 'Pronasale/Tip (prn)' to 'Subnasale (sn)'",
    "type": "Angles",
    "formula": "V1=$$<\\left(N.x-Prn.x\\right),\\left(N.y-Prn.y\\right),\\left(N.z-Prn.z\\right)>$$ V2=$$<\\left(Prn.x-Sn.x\\right),\\left(Prn.y-Sn.y\\right),\\left(Prn.z-Sn.z\\right)>$$$$\\theta=\\cos^{-1}(\\frac{V1\\bullet V2}{|V1||V2|})$$"
  },
  {
    "id": "Nasofacial_Angle",
    "name": "Nasofacial Angle",
    "imageFile": "measurement_angle_nasofacial_angle-lateral(l).png",
    "description": "The angle between 'Nasion (n)' to 'Tip/Pronasale (prn)' and 'Nasion (n)' to 'Pogonion (pg)'",
    "type": "Angles",
    "formula": "V1=$$<\\left(N.x-Pg.x\\right),\\left(N.y-Pg.y\\right),\\left(N.z-Pg.z\\right)>$$ V2=$$<\\left(N.x-Prn.x\\right),\\left(N.y-Prn.y\\right),\\left(N.z-Prn.z\\right)>$$$$\\theta=\\cos^{-1}(\\frac{V1\\bullet V2}{|V1||V2|})$$"
  },
  {
    "id": "Nasofrontal_Angle",
    "name": "Nasofrontal Angle",
    "imageFile": "measurement_angle_nasofrontal_angle-lateral(l).png",
    "description": "The angle between 'Glabella (g)' to 'Nasion (n)' and 'Nasion (n)' to 'Pronasale/Tip (prn)'",
    "type": "Angles",
    "formula": "V1=$$<\\left(N.x-G.x\\right),\\left(N.y-G.y\\right),\\left(N.z-G.z\\right)>$$ V2=$$<\\left(N.x-G.x\\right),\\left(N.y-G.y\\right),\\left(N.z-G.z\\right)>$$$$\\theta=\\cos^{-1}(\\frac{V1\\bullet V2}{|V1||V2|})$$"
  },
  {
    "id": "Nasolabial_Angle_1",
    "name": "Nasolabial Angle 1",
    "imageFile": "measurement_angle_nasolabial_angle-lateral(l).png",
    "description": "The angle between 'Pronasale/Tip (prn)' to 'Subnasale (sn)' and 'Subnasale (sn)' to 'Labrale Superius (ls)'",
    "type": "Angles",
    "formula": "V1=$$<\\left(Prn.x-Sn.x\\right),\\left(Prn.y-Sn.y\\right),\\left(Prn.z-Sn.z\\right)>$$ V2=$$<\\left(Sn.x-Ls.x\\right),\\left(Sn.y-Ls.y\\right),\\left(Sn.z-Ls.z\\right)>$$$$\\theta=\\cos^{-1}(\\frac{V1\\bullet V2}{|V1||V2|})$$"
  },
  {
    "id": "Nasolabial_Angle_2",
    "name": "Nasolabial Angle 2",
    "imageFile": "measurement_angle_nasolabial_angle_II-lateral(r).png",
    "description": "The angle between the Columella and the line tangent to the cutaneous upper lip proper.",
    "type": "Angles",
    "formula": "$$$$"
  },
  {
    "id": "Nasolabial_Angle_3",
    "name": "Nasolabial Angle 3",
    "imageFile": "measurement_angle_nasolabial_angle_III-lateral(r).png",
    "description": "The angle between the long axis of the nostril and the line perpendicular to the Frankfort horizontal.",
    "type": "Angles",
    "formula": "$$$$"
  },
  {
    "id": "Nasolabial_Angle_4",
    "name": "Nasolabial Angle 4",
    "imageFile": "measurement_angle_nasolabial_angle_IV-lateral(r).png",
    "description": "The angle between the long axis of the nostril and the line perpendicular to the Frankfort horizontal.",
    "type": "Angles",
    "formula": "V1=$$<\\left(Itn_r.x-Itn_l.x\\right),\\left(Itn_r.y-Itn_l.y\\right),\\left(Itn_r.z-Itn_l.z\\right)>$$ V2=$$<\\left(G.x-Pg.x\\right),\\left(G.y-Pg.y\\right),\\left(G.z-Pg.z\\right)>$$$$\\theta=\\cos^{-1}(\\frac{V1\\bullet V2}{|V1||V2|})$$"
  },
  {
    "id": "Nasomental_Angle",
    "name": "Nasomental Angle",
    "imageFile": "measurement_angle_nasomental_angle-lateral(l).png",
    "description": "The angle between 'Nasion (n)' to 'Pronasale/Tip (prn)' and 'Pronasale/Tip (prn)' to 'Pogonion (pg)'",
    "type": "Angles",
    "formula": "V1=$$<\\left(Prn.x-N.x\\right),\\left(Prn.y-N.y\\right),\\left(Prn.z-N.z\\right)>$$ V2=$$<\\left(Prn.x-Pg.x\\right),\\left(Prn.y-Pg.y\\right),\\left(Prn.z-Pg.z\\right)>$$$$\\theta=\\cos^{-1}(\\frac{V1\\bullet V2}{|V1||V2|})$$"
  },
  {
    "id": "Total_Facial_Convexity_Angle",
    "name": "Total Facial Convexity Angle",
    "imageFile": "measurement_angle_total_facial_convexity_angle-lateral(l).png",
    "description": "Angle between 'Glabella (g)' to 'Pronasale/Tip (prn)' and 'Pronasale/Tip (prn)' to 'Pogonion (pg)'",
    "type": "Angles",
    "formula": "V1=$$<\\left(G.x-Prn.x\\right),\\left(G.y-Prn.y\\right),\\left(G.z-Prn.z\\right)>$$ V2=$$<\\left(Pg.x-Prn.x\\right),\\left(Pg.y-Prn.y\\right),\\left(Pg.z-Prn.z\\right)>$$$$\\theta=\\cos^{-1}(\\frac{V1\\bullet V2}{|V1||V2|})$$"
  },
  {
    "id": "Lobule_-_Base_Ratio",
    "name": "Lobule - Base Ratio",
    "imageFile": "measurement_ratio_lobule_base_ratio-basal.png",
    "description": "Calculated by dividing the width of the lobule by the width of the base of the nose.",
    "type": "Ratios",
    "formula": "$$\\frac{\\sqrt{\\left(Td_r.x-Td_l.x\\right)^2+\\left(Td_r.y-Td_l.y\\right)^2+\\left(Td_r.z-Td_l.z\\right)^2}}{\\sqrt{\\left(Ac_r.x-Ac_l.x\\right)^2+\\left(Ac_r.y-Ac_l.y\\right)^2+\\left(Ac_r.z-Ac_l.z\\right)^2}}$$"
  },
  {
    "id": "Nasal_Tip_Projection:_Baum",
    "name": "Nasal Tip Projection: Baum",
    "imageFile": "measurement_ratio_nasal_tip_projection_baum-lateral(l).png",
    "description": "Unfortunately, there is currently no well-defined approach to the measurement of NTP, although several have been described. Baum is given credit for describing a 2:1 ratio of a vertical line from the nasofrontal angle to the vertex of the nasolabial angle, and a prependicular line drawn from this superior line to the tip defining point. However, the true parameters of this relationship as described by Baum are some what ambiguous.",
    "type": "Ratios",
    "formula": "BD=$$\\frac{|Prn-Sn|\\times|Prn-N|}{|N-Sn|}$$ AD=$$\\sqrt{\\left(N.x-Prn.x\\right)^2+\\left(N.y-Prn.y\\right)^2+\\left(N.z-Prn.z\\right)^2}$$ $$BD^2+AB^2=AD^2$$ AB=$$\\sqrt{AD^2-BD^2}$$ Projection=$$\\frac{AB}{BD}$$"
  },
  {
    "id": "Nasal_Tip_Projection:_Byrd_and_Hobar",
    "name": "Nasal Tip Projection: Byrd and Hobar",
    "imageFile": "measurement_ratio_nasal_tip_projection_byrd&hobar-lateral(l).png",
    "description": "Byrd proposed that ideal nasal length is two thirds of the midfacial height, and that ideal tip projection is two thirds of the ideal nasal length. This method depends on the percentage of the nose that lies anterior to the upper lip line. To calculate the NTP by Byrd’s method, four points and two lines have to be marked. The four points included the previous three points used in Goode’s method, in addition to a point marked on the most projecting point of the upper lip.",
    "type": "Ratios",
    "formula": "AT=$$\\sqrt{\\left(Prn.x-Ac_l.x\\right)^2+\\left(Prn.y-Ac_l.y\\right)^2+\\left(Prn.z-Ac_l.z\\right)^2}$$ 2A=$$\\frac{|Prn-Ls|\\times|Prn-N|}{|N-Ls|}$$ Projection=$$\\frac{2A}{AT}$$"
  },
  {
    "id": "Nasal_Tip_Projection:_Crumley_and_Lanser_I",
    "name": "Nasal Tip Projection: Crumley and Lanser I",
    "imageFile": "measurement_ratio_nasal_tip_projection_crumley&lanser1-lateral(l).png",
    "description": "This technique was derived as a combination of the Powell Analysis and the Simons method. The vertical vector (AE) combines nasal length plus upper lip length to the vermilion-cutaneous junction.",
    "type": "Ratios",
    "formula": "AE=$$\\sqrt{\\left(N.x-Ls.x\\right)^2+\\left(N.y-Ls.y\\right)^2+\\left(N.z-Ls.z\\right)^2}$$ BD=$$\\frac{|Prn-Ls|\\times|Prn-N|}{|N-Ls|}$$ Projection=$$\\frac{AE}{BD}$$"
  },
  {
    "id": "Nasal_Tip_Projection:_Crumley_and_Lanser_II",
    "name": "Nasal Tip Projection: Crumley and Lanser II",
    "imageFile": "measurement_ratio_nasal_tip_projection_crumley&lanser2-lateral(l).png",
    "description": "This technique uses facial height as a parameter by which to measure tip projection. The same vertical line as used in the Goode analysis is drawn inferiorly until it transects the mandibular profile line (point Z). AZ is then compared with YD.",
    "type": "Ratios",
    "formula": "AZ=$$\\sqrt{\\left(N.x-Me.x\\right)^2+\\left(N.y-Me.y\\right)^2+\\left(N.z-Me.z\\right)^2}$$ YD=$$\\frac{|Prn-Me|\\times|Prn-N|}{|N-Me|}$$ Projection=$$\\frac{AZ}{YD}$$"
  },
  {
    "id": "Nasal_Tip_Projection:_Goode",
    "name": "Nasal Tip Projection: Goode",
    "imageFile": "measurement_ratio_nasal_tip_projection_goode-lateral(l).png",
    "description": "A fourth method attributed to Goode uses a 3-4-5 triangle. One side of the triangle is from the nasofrontal angle through the alar crease, the second a perpendicular line going through the tip defining point, and the third is a line drawn to complete the right triangle using the nasal dorsum. Goode’s analysis states that when the nasofacial angle is between 36 and 40 degrees, the length of the perpendicular line through the tip defining point will be 0.55 to 0.60 the length of the nasal dorsum. This method depends on a ratio between the length of the nose (as determined by a line from the root to the tip) and its height (as determined by a line from the ala to the tip).",
    "type": "Ratios",
    "formula": "$$\\frac{\\sqrt{\\left(Ac_l.x-Prn.x\\right)^2+\\left(Ac_l.y-Prn.y\\right)^2+\\left(Ac_l.z-Prn.z\\right)^2}}{\\sqrt{\\left(Prn.x-N.x\\right)^2+\\left(Prn.y-N.y\\right)^2+\\left(Prn.z-N.z\\right)^2}}$$"
  },
  {
    "id": "Nasal_Tip_Projection:_Powell_and_Humphries",
    "name": "Nasal Tip Projection: Powell and Humphries",
    "imageFile": "measurement_ratio_nasal_tip_projection_powell&humphries-lateral(l).png",
    "description": "Powell and Humphreys correctly questioned this 2:1 ratio. They found that a 2.8:1 ratio provided a more aesthetic amount of NTP, pointing out that using the 2:1 ratio produced a somewhat overprotected tip. Their analysis used the line from nasofrontal angle to the nasolabial angle. Powell and Humphreys (citing Goode) stated that the visual effect of tip projection was due to the length from alar crease to tip. This method is based on a right triangle drawn using the nasal dorsum as the hypotenuse, a line from the nasofrontal angle through the alar crease as the second side, and a perpendicular from this letter line through the tip defining point.",
    "type": "Ratios",
    "formula": "AC=$$\\sqrt{\\left(N.x-Sn.x\\right)^2+\\left(N.y-Sn.y\\right)^2+\\left(N.z-Sn.z\\right)^2}$$ BD=$$\\frac{|Prn-Sn|\\times|Prn-N|}{|N-Sn|}$$ Projection=$$\\frac{AC}{BD}$$"
  },
  {
    "id": "Nasal_Tip_Projection:_Simons",
    "name": "Nasal Tip Projection: Simons",
    "imageFile": "measurement_ratio_nasal_tip_projection_simons-lateral(l).png",
    "description": "Simons in 1982 states that upper lip length should equal the nose’s basal length. This method is appealing since it is quite simple. (1:1 ratio) and easy to use on the operating table. It has been criticized because upper lip lengths are widely variable but heretofore had not been objectively evaluated.",
    "type": "Ratios",
    "formula": "$$\\frac{\\sqrt{\\left(Sn.x-Prn.x\\right)^2+\\left(Sn.y-Prn.y\\right)^2+\\left(Sn.z-Prn.z\\right)^2}}{\\sqrt{\\left(Sn.x-Ls.x\\right)^2+\\left(Sn.y-Ls.y\\right)^2+\\left(Sn.z-Ls.z\\right)^2}}$$"
  },
  {
    "id": "Nasal_Width–Intercanthal_Distance_Ratio",
    "name": "Nasal Width–Intercanthal Distance Ratio",
    "imageFile": "measurement_ratio_nasal_width_intercanthal_distance_ratio-frontal.png",
    "description": "Nasal Width (interalar distance) divided by intercanthal distance.",
    "type": "Ratios",
    "formula": "$$\\frac{Interalar Distance}{(Inner) Intercanthal Distance}$$ $$\\frac{\\sqrt{\\left(Al_r.x-Al_l.x\\right)^2+\\left(Al_r.y-Al_l.y\\right)^2+\\left(Al_r.z-Al_l.z\\right)^2}}{\\sqrt{\\left(En_r.x-En_l.x\\right)^2+\\left(En_r.y-En_l.y\\right)^2+\\left(En_r.z-En_l.z\\right)^2}}$$"
  },
  {
    "id": "Nasal_Width-Length_Ratio",
    "name": "Nasal Width-Length Ratio",
    "imageFile": "measurement_ratio_nasal_width_length_ratio-frontal.png",
    "description": "The alar width divided by the nasal bridge length. Nasal width (ala to ala) divided by the length of the nose (nasion to pronasion)",
    "type": "Ratios",
    "formula": "$$\\frac{Interalar Distance}{Nasal Bridge Length}$$ $$\\frac{\\sqrt{\\left(Al_r.x-Al_l.x\\right)^2+\\left(Al_r.y-Al_l.y\\right)^2+\\left(Al_r.z-Al_l.z\\right)^2}}{\\sqrt{\\left(Prn.x-N.x\\right)^2+\\left(Prn.y-N.y\\right)^2+\\left(Prn.z-N.z\\right)^2}}$$"
  }

]