@@ -135,11 +135,12 @@ message Dimension3d
135135// xy-plane. Yaw is 0 if the object's local x-axis is parallel to its parent's
136136// x-axis.
137137//
138- // <tt>Rotation_yaw_pitch_roll = Rotation_roll*Rotation_pitch*Rotation_yaw</tt>
138+ // \f$ Rotation_{yaw,pitch,roll} =
139+ // Rotation_{roll}*Rotation_{pitch}*Rotation_{yaw} \f$
139140//
140- // <tt>vector_global_coord_system :=
141- // Inverse_Rotation_yaw_pitch_roll(</tt><tt> Orientation3d</tt><tt>)*(vector_local_coord_system)
142- // + local_origin ::position</tt>
141+ // \f$ vector_{\text{global coord system}} :=
142+ // Rotation_{yaw,pitch,roll}^{-1}( \f$ \c Orientation3d \f$
143+ // )*vector_{\text{local coord system}} + local_{origin}\text{ ::position} \f$
143144//
144145// \attention This definition changed in OSI version 3.0.0. Previous OSI
145146// versions (V2.xx) had an other definition.
@@ -202,9 +203,10 @@ message MountingPosition
202203
203204 // Orientation offset relative to the specified reference coordinate system.
204205 //
205- // <tt>Origin_sensor :=
206- // Rotation_yaw_pitch_roll(#orientation)*(Origin_reference_coordinate_system
207- // - #position)</tt>
206+ // \f$ Origin_{sensor} :=
207+ // Rotation_{yaw,pitch,roll}( \f$ \c #orientation \f$
208+ // )*(Origin_{\text{reference coord system}}
209+ // - \f$ \c #position \f$ )\f$
208210 //
209211 optional Orientation3d orientation = 2 ;
210212}
@@ -222,8 +224,9 @@ message MountingPosition
222224// (around the new y-axis) to follow the definition of \c Orientation3d. For the
223225// sense of each rotation, the right-hand rule applies.
224226//
225- // <tt>vector_cartesian :=
226- // Rotation(#elevation)*Rotation(#azimuth)*Unit_vector_x*#distance</tt>
227+ // \f$ vector_{cartesian} :=
228+ // Rotation( \f$ \c #elevation \f$ )*Rotation( \f$ \c #azimuth \f$ )*
229+ // (Unit_{vector_x}* \f$ \c #distance \f$ ) \f$
227230//
228231message Spherical3d
229232{
@@ -275,9 +278,10 @@ message BaseStationary
275278 // frame, noted in the parent frame. The orientation becomes global/absolute
276279 // if the parent frame is inertial (all parent frames up to ground truth).
277280 //
278- // <tt>Origin_base_stationary_entity :=
279- // Rotation_yaw_pitch_roll(#orientation)*(Origin_parent_coordinate_system -
280- // #position)</tt>
281+ // \f$ Origin_{\text{base stationary entity}} :=
282+ // Rotation_{yaw,pitch,roll}( \f$ \c #orientation \f$ )*
283+ // (Origin_{\text{parent coord system}} -
284+ // \f$ \c #position \f$ )\f$
281285 //
282286 // \note There may be some constraints how to align the orientation w.r.t.
283287 // to some stationary object's or entity's definition.
@@ -336,9 +340,10 @@ message BaseMoving
336340 // noted in the parent frame. The orientation becomes global/absolute if
337341 // the parent frame is inertial (all parent frames up to ground truth).
338342 //
339- // <tt>Origin_base_moving_entity :=
340- // Rotation_yaw_pitch_roll(#orientation)*(Origin_parent_coordinate_system -
341- // #position)</tt>
343+ // \f$ Origin_{\text{base moving entity}} :=
344+ // Rotation_{yaw,pitch,roll}( \f$ \c #orientation \f$ )*
345+ // (Origin_{\text{parent coord system}} -
346+ // \f$ \c #position \f$ ) \f$
342347 //
343348 // \note There may be some constraints how to align the orientation w.r.t.
344349 // to some stationary object's or entity's definition.
@@ -349,18 +354,20 @@ message BaseMoving
349354 // noted in the parent frame. The velocity becomes global/absolute if
350355 // the parent frame does is inertial (all parent frames up to ground truth).
351356 //
352- // <tt>#position (t) := #position (t-dt)+ #velocity *dt</tt>
357+ // \c #position \f$ (t) := \f$ \c #position \f$ (t-dt)+ \f$ \c #velocity \f$
358+ // *dt \f$
353359 //
354360 optional Vector3d velocity = 4 ;
355361
356362 // The relative acceleration of the moving object w.r.t. its parent frame,
357363 // noted in the parent frame. The acceleration becomes global/absolute if
358364 // the parent frame is inertial (all parent frames up to ground truth).
359365 //
360- // <tt> #position (t) := #position (t-dt)+ #velocity *dt+ #acceleration
361- // /2*dt^2</tt>
366+ // \c #position \f$ (t) := \f$ \c #position \f$ (t-dt)+ \f$ \c #velocity \f$
367+ // *dt+ \f$ \c #acceleration \f$ /2*dt^2\f$
362368 //
363- // <tt> #velocity (t) := #velocity (t-dt)+ #acceleration *dt</tt>
369+ // \c #velocity \f$ (t) := \f$ \c #velocity \f$ (t-dt)+ \f$ \c #acceleration
370+ // \f$ *dt \f$
364371 //
365372 optional Vector3d acceleration = 5 ;
366373
@@ -370,14 +377,36 @@ message BaseMoving
370377 // The orientation becomes global/absolute if the parent frame is inertial
371378 // (all parent frames up to ground truth).
372379 //
373- // <tt>orientation.yaw(t) := orientation_rate.yaw(t) * dt + orientation.yaw(t-dt)</tt>
380+ // \c #orientation \f$ .yaw(t) := \f$ \c #orientation_rate \f$ .yaw(t) * dt
381+ // + \f$ \c #orientation \f$ .yaw(t-dt) \f$
374382 //
375- // <tt>orientation.pitch(t) := orientation_rate.pitch(t) * dt + orientation.pitch(t-dt)</tt>
383+ // \c #orientation \f$ .pitch(t) := \f$ \c #orientation_rate \f$ .pitch(t) *
384+ // dt + \f$ \c #orientation \f$ .pitch(t-dt) \f$
376385 //
377- // <tt>orientation.roll(t) := orientation_rate.roll(t) * dt + orientation.roll(t-dt)</tt>
386+ // \c #orientation \f$ .roll(t) := \f$ \c #orientation_rate \f$ .roll(t) *
387+ // dt + \f$ \c #orientation \f$ .roll(t-dt)\f$
378388 //
379389 optional Orientation3d orientation_rate = 6 ;
380390
391+ // The relative orientation acceleration of the moving object w.r.t. its
392+ // parent frame and parent orientation acceleration in the center point of
393+ // the bounding box (origin of the bounding box frame), noted in the parent
394+ // frame. The orientation becomes global/absolute if the parent frame is
395+ // inertial (all parent frames up to ground truth).
396+ //
397+ // \c #orientation_rate \f$ .yaw(t) := \f$ \c #orientation_acceleration \f$
398+ // .yaw(t) * dt + \f$ \c #orientation_rate \f$ .yaw(t-dt) \f$
399+ //
400+ // \c #orientation_rate \f$ .pitch(t) := \f$ \c #orientation_acceleration
401+ // \f$ .pitch(t) * dt
402+ // + \f$ \c #orientation_rate \f$ .pitch(t-dt) \f$
403+ //
404+ // \c #orientation_rate \f$ .roll(t) := \f$ \c #orientation_acceleration \f$
405+ // .roll(t) * dt +
406+ // \f$ \c #orientation_rate \f$ .roll(t-dt) \f$
407+ //
408+ optional Orientation3d orientation_acceleration = 8 ;
409+
381410 // Usage as ground truth:
382411 // The two dimensional (flat) contour of the object. This is an extension of
383412 // the concept of a bounding box as defined by \c Dimension3d. The contour
@@ -398,18 +427,4 @@ message BaseMoving
398427 // The polygon is defined counter-clockwise.
399428 //
400429 repeated Vector2d base_polygon = 7 ;
401-
402- // The relative orientation acceleration of the moving object w.r.t. its parent
403- // frame and parent orientation acceleration in the center point of the bounding box
404- // (origin of the bounding box frame), noted in the parent frame.
405- // The orientation becomes global/absolute if the parent frame is inertial
406- // (all parent frames up to ground truth).
407- //
408- // <tt>orientation_rate.yaw(t) := orientation_acceleration.yaw(t) * dt + orientation_rate.yaw(t-dt)</tt>
409- //
410- // <tt>orientation_rate.pitch(t) := orientation_acceleration.pitch(t) * dt + orientation_rate.pitch(t-dt)</tt>
411- //
412- // <tt>orientation_rate.roll(t) := orientation_acceleration.roll(t) * dt + orientation_rate.roll(t-dt)</tt>
413- //
414- optional Orientation3d orientation_acceleration = 8 ;
415430}
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