Temporal Rigid Geometries

Input and Output

Constructors

  • trgeometry: Construct a temporal rigid geometry from a reference geometry and a temporal pose

Conversions

  • tpose: Return the underlying temporal pose

  • tgeompoint: Return the centroid (antenna) trajectory as a temporal point

Accessors

Traversed Area

  • traversedArea: Return the area traversed by the temporal rigid geometry

Spatial Functions

  • centroid: Return the centroid of the moving body as a temporal point

  • convexHull: Return the convex hull of the area traversed by the moving body

  • bodyPointTrajectory: Return the world-frame trajectory of a body-frame point carried by the moving rigid geometry

Motion Metrics

  • length, cumulativeLength: Return the total length traversed by the centroid, or its cumulative length over time

  • speed: Return the speed of the centroid as a temporal float

  • angularSpeed: Return the angular speed as a temporal float

  • twCentroid: Return the time-weighted centroid of the centroid trajectory as a geometry

Transformations

  • round: Round all numeric components to a given number of decimal places

  • setInterp: Convert between linear and step interpolations

  • shiftTime, scaleTime, shiftScaleTime: Shift, scale, or both shift and scale the time domain of a trgeometry

  • unnest: Transform a nonlinear trgeometry into a set of rows, one per distinct pose, each one is a pair composed of the reference geometry with the pose applied and the period set during which the trgeometry takes that pose

  • translate: Return a temporal value translated by given offsets

  • rotate: Return a temporal value rotated counter-clockwise about the origin or about a point

  • rotateX: Return a temporal value rotated counter-clockwise about the x axis

  • rotateY: Return a temporal value rotated counter-clockwise about the y axis

  • rotateZ: Return a temporal value rotated counter-clockwise about the z axis

Modifications

  • appendInstant: Append a single instant to an existing trgeometry, growing the underlying pose path

  • appendSequence: Append an entire sequence to an existing trgeometry

  • merge: Combine two trgeometries with the same reference geometry into a single sequence-set

Restrictions

Distance Operations

  • <->: Return the temporal distance

  • |=|: Return the nearest approach distance

  • nearestApproachInstant: Return the instant of the first argument at which the two arguments are nearest

  • shortestLine: Return the line between the nearest points of the two arguments at their nearest approach instant

Bounding Box Operations

Ever and Always Relationships

Spatiotemporal Relationships

Comparisons

Tiles

Bounding Boxes

Aggregations

  • tCount: Number of overlapping temporal rigid geometries at each instant, equivalent to tCount on the underlying tpose

  • extent: Aggregate bounding box of a column of temporal rigid geometries