Procedure

Sub Rotate(XInput, YInput, XCentre, YCentre, RotAngle, XNew, YNew)

Subroutine to calculate the new coordinates (XNew, YNew) of a point (XInput, YInput) that is rotated through an angle in radians RotAngle about a centre point (XCentre, YCentre).

Function RotatedX(XOrd, YOrd, XCentre, YCentre, AngleDeg)

[RotatedY is similar]

Returns the rotated X-ordinate when a point (XOrd, YOrd) is rotated about a centre point (XCentre, YCentre) through an angle in degrees AngleDeg.

Sub Trailing(LinkLen, HeadX, HeadY, HeadXPrev, HeadYPrev, TailXPrev, TailYPrev, TailX, TailY, DirDeg)

Subroutine to calculate the current coordinates (TailX, TailY) of the tail end of a trailing link of length LinkLen when the head of the trailing link has moved in a straight line to its current position (HeadX, HeadY) from its previous position (HeadXPrev, HeadYPrev) and the previous position of the tail end of the trailing link is known (TailXPrev,TailYPrev). The subroutine also calculates the current direction of the trailing link in degrees DirDeg.

The curved path of the tail end of the trailing link is generated by an iterative process for a succession of very small displacements of the head of the link. An incremental distance of 0.01 metres is used.

Sub RotationByRadius(Dist, InvRadius, XInput, YInput, InputDirectionDeg, XCentre, YCentre, XNew, YNew, OutputDirectionDeg)

Subroutine to calculate the new coordinates of a point (XNew, YNew) where the initial coordinates (XInput, YInput) are given and where the point is rotated left or right through a specified path-length distance Dist with a specified turning radius (expressed as an inverse radius InvRadius) and where the initial or input direction InputDirectionDeg of the path is specified in degrees. The sign of the inverse radius InvRadius determines whether the path will proceed to the left or to the right with respect to the initial point and the initial direction. A positive input value of InvRadius will give a left-hand turn while a negative value will give a right-hand turn. The subroutine also calculates the final or output direction of the path in degrees OutputDirectionDeg and the coordinates of the centre of rotation (XCentre, YCentre).

Function RotationByRadiusX(Dist, InvRadius, XInput, YInput, InputDirectionDeg)

[RotationByRadiusY, RotationByRadiusXCentre, RotationByRadiusYCentre and RotationByRadiusOutDir are similar]

Returns the new X-ordinate of a point where the initial coordinates (XInput, YInput) are given and where the point is rotated as described for Sub RotationByRadius.

Sub Steer(Dist, InvRadius1, InvRadius2, XInput, YInput, InputDirectionDeg, XNew, YNew, XCentre, YCentre, OutputDirectionDeg)

Subroutine to calculate the new coordinates of a point (XNew, YNew) where the initial coordinates of the point (XInput, YInput) are given and where the point is steered left or right through a specified path-length distance Dist with a variable turning radius (expressed as an inverse radius that varies linearly with path distance from InvRadius1 to InvRadius2) and where the initial or input direction InputDirectionDeg of the path is specified in degrees. The sign of the inverse radius determines whether the path will proceed to the left or to the right as for Sub RotationByRadius. The subroutine also calculates the new coordinates of the centre of rotation (XCentre, YCentre) and the output direction OutputDirectionDeg (at the end of the path).

Function SteerX(Dist, InvRadius1, InvRadius2, XInput, YInput, InputDirectionDeg)

[SteerY, SteerXCentre, SteerYCentre and SteerOutDir are similar]

Returns the new X-ordinate of a point where the initial coordinates of the point (XInput, YInput) are given and where the point is steered left or right as described for Sub Steer.

Public Sub SteerAndTrail(Dist, InvRadius1, InvRadius2, HeadXPrev, HeadYPrev, TailXPrev, TailYPrev, InputDirectionDeg, LinkLen, HeadX, HeadY, TailX, TailY, XCentre, YCentre, OutputDirectionDeg, TrailerDirectionDeg)

Subroutine to calculate the new coordinates of the head and tail endpoints (HeadX, HeadY) and (TailX, TailY) of a trailing link of length LinkLen where the previous coordinates of the head and tail endpoints (HeadXPrev, HeadYPrev) and (TailXPrev, TailYPrev) are given and where the head of the trailing link is steered as described for Sub Steer. The subroutine also calculates the coordinates of the centre of rotation (XCentre, YCentre) at the end of the path of the head, the final or output direction of the path of the head in degrees OutputDirectionDeg and the direction of the trailer at the end of the movement TrailerDirectionDeg.

Function TrailingX(Dist, InvRadius1, InvRadius2, HeadXPrev, HeadYPrev, TailXPrev, TailYPrev, InputDirectionDeg, LinkLen)

[TrailingY and TrailingDirDeg are similar]

Returns the new X-ordinate of the tail endpoint of a trailing link of length LinkLen where the previous coordinates of the head and tail endpoints of the link (HeadXPrev, HeadYPrev) and (TailXPrev, TailYPrev) are given and where the head of the trailing link is steered as described for Sub Steer.

Public Sub TimeTick()

This subroutine allows other procedures to run until the step time has elapsed. The step time is set at 0.1 seconds.