function

Planning.Bezier.cubicControlPoints

Construct a degree-three curve from endpoint value and rate

The four endpoint constraints uniquely determine a cubic curve. This package uses it for yaw because flatness reconstruction requires yaw through its second derivative.

Public declarations

Explicit source declarations; dimensions, modifications and defaults are shown as written, without evaluation.

Role	Name	Type	Dimensions / attributes / default	Description
input	`startDerivative`	`Real`	`[:, 2]`	Value and rate at t=0
input	`endDerivative`	`Real`	`[size(startDerivative, 1), 2]`	Value and rate at t=duration
input	`duration`	`Real`	`(unit = "s")`	Curve duration
output	`controlPoint`	`Real`	`[size(startDerivative, 1), 4]`	Degree-three Bezier control points

Modelica declarations and implementation

Show parameters, interfaces and source

Parameters, inputs, outputs, defaults and equations from the source file.

function cubicControlPoints
    "Construct a degree-three curve from endpoint value and rate"
    input Real startDerivative[:, 2] "Value and rate at t=0";
    input Real endDerivative[size(startDerivative, 1), 2]
      "Value and rate at t=duration";
    input Real duration(unit = "s") "Curve duration";
    output Real controlPoint[size(startDerivative, 1), 4]
      "Degree-three Bezier control points";
  algorithm
    assert(duration > 0.0, "Bezier duration must be positive");
    controlPoint[:, 1] := startDerivative[:, 1];
    controlPoint[:, 2] := controlPoint[:, 1]
      + duration * startDerivative[:, 2] / 3.0;
    controlPoint[:, 4] := endDerivative[:, 1];
    controlPoint[:, 3] := controlPoint[:, 4]
      - duration * endDerivative[:, 2] / 3.0;
    annotation(Documentation(info="<html>
      <p>The four endpoint constraints uniquely determine a cubic curve.
      This package uses it for yaw because flatness reconstruction requires
      yaw through its second derivative.</p>
    </html>"));
  end cubicControlPoints;