A Frame ("TNBFrame") describes a location in 3d space and an orientation using a right handed coordinate cross of vectors. More...

#include <C:/Trend/Development/Trax3/Code/spat/Frame.h>

Inheritance diagram for spat::Frame< Valtype, ValtypeT >:

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Public Member Functions

Valtype * ptr () noexcept

Pointer accessor for direct copying.

const Valtype * ptr () const noexcept

Pointer accessor for direct copying.

Frame & Init (const VectorBundle< Valtype, ValtypeT > &vb, const Vector< ValtypeT > &up) noexcept

Initializes the Frame structure to vb and calculates nor as to be orthogonal to up.

Frame & Init (const VectorBundle2< Valtype, ValtypeT > &vb2) noexcept

Initializes the Frame structure.

Frame & Normalize () noexcept

Makes the vectors unit vectors.

Frame & OrthoNormalize () noexcept

Normalizes the vectors preserving the direction of T as is. It then adjusts Nor and Bin in a way to form an orthogonal frame.

bool IsOrthoNormal (ValtypeT epsilon_length=2 *std::numeric_limits< ValtypeT >::epsilon(), ValtypeT epsilon_angle=2 *std::numeric_limits< ValtypeT >::epsilon()) const noexcept

Frame & TransportTo (Valtype d) noexcept

Moves the Frame by d in direction T.

Frame & TransportBy (const Vector< Valtype > &v) noexcept

Moves the Frame by v.

Frame & TransportTo (const Position< Valtype > &p) noexcept

Transport this Frame to p.

Frame & TransportTan (Valtype d) noexcept

Moves the Frame by d in direction T.

Frame & TransportNor (Valtype d) noexcept

Moves the Frame by d in direction N.

Frame & TransportBin (Valtype d) noexcept

Moves the Frame by d in direction B.

Frame & FlipTan () noexcept

Rotates the Frame by pi around T.

Frame & FlipNor () noexcept

Rotates the Frame by pi around N.

Frame & FlipBin () noexcept

Rotates the Frame by pi around B.

Frame & Rotate (const Vector< ValtypeT > &nr, ValtypeT angle) noexcept

Rotate the vectors around nr with angle in radiants.

Frame & Rotate (const Vector< ValtypeT > &r) noexcept

Rotate the vectors around r with angle r.Length() in radiants.

template<typename Valtype2>

Frame & Rotate (const VectorBundle< Valtype, Valtype2 > &axis) noexcept

Rotates the frame by axis (length of axis.T make angle in radiants).

template<typename Valtype2>

Frame & Rotate (const VectorBundle< Valtype, Valtype2 > &axis, Valtype2 angle) noexcept

Rotates the frame by axis and angle in radiants.

Frame & RotateTan (ValtypeT angle) noexcept

Rotates the vectors around the tan vector (roll).

Frame & RotateTan (const Vector< ValtypeT > &up) noexcept

Brings B as close as possible to up by rotating around T.

Frame & RotateNor (ValtypeT angle) noexcept

Rotates the vectors around the nor vector (-pitch).

Frame & RotateBin (ValtypeT angle) noexcept

Rotates the vectors around the bin vector (-yaw).

constexpr bool Equals (const Frame &frame, Valtype epsilon_length=std::numeric_limits< Valtype >::epsilon(), ValtypeT epsilon_lengthT=std::numeric_limits< ValtypeT >::epsilon()) const noexcept

Comparison within some ranges.

Frame & Round (int toDigit) noexcept

Rounds the frames position and vectors to a certain digit after the point.

template<typename Valtype2>

Frame< Valtype, ValtypeT > & operator= (const Matrix< Valtype2, 4, 4 > &trans) noexcept

template<typename Valtype2>

Frame< Valtype, ValtypeT > & operator= (const Valtype2 *pVal) noexcept

template<typename Valtype2>

Frame< Valtype, ValtypeT > & Rotate (const VectorBundle< Valtype, Valtype2 > &axis) noexcept

template<typename Valtype2>

Frame< Valtype, ValtypeT > & Rotate (const VectorBundle< Valtype, Valtype2 > &axis, Valtype2 angle) noexcept

Construction

Parameters

vb2	VectorBundle2 object giving the P,T,N part; B gets computed.
vb	VectorBundle object giving the P,T part; N and B get computed.
up	Up direction. N gets calculated so that it is perpendicular to this.
pos	Position object giving the P part.
tan	Vector object giving the T part.
nor	Vector object giving the N part.
bin	Vector object giving the B part.
rot	Rotation object giving the T,N and B part.
trans	Transformation object. Compute the Frame so that it is the frame of reference corresponding to the transformation.
pHTrans	Pointer to homogenuous transformation matrix. The first three columns of the transformation matrix are the transformed global axis vectors. The position is the transformed homogen origin (0,0,0,1).

constexpr Frame () noexcept=default

Does not initialize the members.

constexpr Frame (Valtype px, Valtype py, Valtype pz, ValtypeT tx, ValtypeT ty, ValtypeT tz, ValtypeT nx, ValtypeT ny, ValtypeT nz, ValtypeT bx, ValtypeT by, ValtypeT bz) noexcept

Does not initialize the members.

constexpr Frame (const VectorBundle2< Valtype, ValtypeT > &vb2) noexcept

Does not initialize the members.

Frame (const VectorBundle< Valtype, ValtypeT > &vb, const Vector< ValtypeT > &up) noexcept

Does not initialize the members.

constexpr Frame (const Position< Valtype > &pos) noexcept

Does not initialize the members.

constexpr Frame (const Position< Valtype > &pos, const Vector< ValtypeT > &tan, const Vector< ValtypeT > &nor, const Vector< ValtypeT > &bin) noexcept

Does not initialize the members.

Frame (const Position< Valtype > &pos, const Rotation< ValtypeT > &rot) noexcept

Does not initialize the members.

Frame (const Rotation< ValtypeT > &rot) noexcept

Does not initialize the members.

template<typename Valtype2>

Frame (const Matrix< Valtype2, 4, 4 > &trans) noexcept

Does not initialize the members.

template<typename Valtype2>

Frame (const Valtype2 *pVal) noexcept

Does not initialize the members.

Assignment

Parameters

vb2	VectorBundle2 object giving the P,T,N part; B gets computed.
rot	Rotation object giving the T,N and B part.
trans	Transformation object. Compute the Frame so that it is the frame of reference corresponding to the transformation.

Frame & operator= (const VectorBundle2< Valtype, ValtypeT > &vb2) noexcept

Frame & operator= (const Rotation< ValtypeT > &rot) noexcept

template<typename Valtype2>

Frame & operator= (const Matrix< Valtype2, 4, 4 > &trans) noexcept

template<typename Valtype2>

Frame & operator= (const Valtype2 *pVal) noexcept

Implicit conversion

Returns: A Vector2 bundle with the P, T and N values.

operator VectorBundle2< Valtype, ValtypeT > () const noexcept

operator VectorBundle< Valtype, ValtypeT > () const noexcept

Frame & Init () noexcept

Initializes the Frame structure to position (or zero) and the vectors to standard right-handed orthogonal unit vector system.

Frame & Init (const Position< Valtype > &pos) noexcept

Initializes the Frame structure to position (or zero) and the vectors to standard right-handed orthogonal unit vector system.

LookAt

Rotate the Frame so that a reference vector points along dir.

Returns: A reference to this object. Frame& Invert();

Parameters

dir	Direction to point to.
reference	The vector formulated in the frame reference, that is supposed to point in the direction of dir
up	Direction to bring B to by a final rotation.

Frame & LookAt (const Vector< ValtypeT > &reference, const Vector< ValtypeT > &dir) noexcept

Frame & LookTAt (const Vector< ValtypeT > &dir) noexcept

Frame & LookTAt (const Vector< ValtypeT > &dir, const Vector< ValtypeT > &up) noexcept

Frame & LookNAt (const Vector< ValtypeT > &dir) noexcept

Frame & LookBAt (const Vector< ValtypeT > &dir) noexcept

AircraftPrincipalAxes

Calculate the vectors as orthonormal vectors from Yaw, Pitch and Roll.

The angles used in aviation refer to a right handed coordinate system and rotate Yaw, Pitch and Roll in the order of Z, Y, and X following a right handed orientation rule. Note that in order to keep the Pitch positive on upward rotation, aeroplanes are typically oriented with the Z-axis down in the frame.

Parameters

yaw	The Yaw angle (rotation around Z).
pitch	The Pitch angle (rotation around rotated Y).
roll	The Roll angle (rotation around rotated X).
epsilon	If T is epsilon-close to Ez, the yaw will be zero and Pitch +- pi/2.

Returns: Yaw, Pitch, Roll in a Position struct.

Frame & AircraftPrincipalAxes (ValtypeT yaw, ValtypeT pitch, ValtypeT roll)

Frame & AircraftPrincipalAxes (const Position< ValtypeT > &angles)

Position< ValtypeT > AircraftPrincipalAxes (ValtypeT epsilon=std::numeric_limits< ValtypeT >::epsilon()) const

Transformations to parent frame.

Transformation to the coordinate system in wich this Frame is formulated.

The coordinates are understood to be formulated relative to this Frame and get calculated to be formulated to the base Frame.

template<typename Valtype2>

Position< Valtype2 > & ToParent (Position< Valtype2 > &p) const noexcept

template<typename Valtype2>

Vector< Valtype2 > & ToParent (Vector< Valtype2 > &v) const noexcept

template<typename Valtype2>

Vector< Valtype2 > & NormalToParent (Vector< Valtype2 > &normal) const noexcept

template<typename Valtype2, typename ValtypeT2>

VectorBundle< Valtype2, ValtypeT2 > & ToParent (VectorBundle< Valtype2, ValtypeT2 > &v) const noexcept

template<typename Valtype2, typename ValtypeT2>

VectorBundle2< Valtype2, ValtypeT2 > & ToParent (VectorBundle2< Valtype2, ValtypeT2 > &v) const noexcept

template<typename Valtype2, typename ValtypeT2>

Frame< Valtype2, ValtypeT2 > & ToParent (Frame< Valtype2, ValtypeT2 > &frame) const noexcept

template<typename Valtype2>

Box< Valtype2 > & ToParent (Box< Valtype2 > &box) const noexcept

template<typename Valtype2>

Sphere< Valtype2 > & ToParent (Sphere< Valtype2 > &sphere) const noexcept

Transformations from parent frame.

Transformation from the coordinate system in wich this Frame is formulated.

The coordinates are understood to be formulated relative to the parent Frame and get calculated to be formulated relative to this Frame.

template<typename Valtype2>

Position< Valtype2 > & FromParent (Position< Valtype2 > &p) const noexcept

template<typename Valtype2>

Vector< Valtype2 > & FromParent (Vector< Valtype2 > &v) const noexcept

template<typename Valtype2, typename ValtypeT2>

VectorBundle< Valtype2, ValtypeT2 > & FromParent (VectorBundle< Valtype2, ValtypeT2 > &b) const noexcept

template<typename Valtype2, typename ValtypeT2>

VectorBundle2< Valtype2, ValtypeT2 > & FromParent (VectorBundle2< Valtype2, ValtypeT2 > &b) const noexcept

template<typename Valtype2, typename ValtypeT2>

Frame< Valtype2, ValtypeT2 > & FromParent (Frame< Valtype2, ValtypeT2 > &frame) const noexcept

Public Attributes
Position< Valtype >	P
	Point in 3D space.
Vector< ValtypeT >	T
	Tangential axis or x-axis.
Vector< ValtypeT >	N
	Normal axis or y-axis.
Vector< ValtypeT >	B
	Binormal axis or z-axis.

Detailed Description

template<typename Valtype, typename ValtypeT = Valtype>
struct spat::Frame< Valtype, ValtypeT >

A Frame ("TNBFrame") describes a location in 3d space and an orientation using a right handed coordinate cross of vectors.

These axes normaly are used right handed. If tan points in the direction of the thump of the right hand and the index finger points along the nor vector, then bin points along the middle finger.

Member Function Documentation

◆ Equals()

template<typename Valtype, typename ValtypeT>

bool spat::Frame< Valtype, ValtypeT >::Equals	(	const Frame< Valtype, ValtypeT > &	frame,
		Valtype	epsilon_length = std::numeric_limits<Valtype>::epsilon(),
		ValtypeT	epsilon_lengthT = std::numeric_limits<ValtypeT>::epsilon() ) const

inlineconstexprnoexcept

Comparison within some ranges.

The area within two positions regarded as equal is a sphere with radius epsilon_length; the absolute difference of two vectors will at most be epsilon_lengthT. If the two vectors are both unit vectors, the actual difference between them will be sin(a) with a being the rotational angle. This makes a small enough epsilon_lengthT a limit in rotational angle.

Parameters

frame	Frame to compare with.
epsilon_length	epsilon distance <= which two positions are regarded as equal.
epsilon_lengthT	epsilon for the Vectors of the Frames.

◆ Init() [1/2]

template<typename Valtype, typename ValtypeT>

Frame< Valtype, ValtypeT > & spat::Frame< Valtype, ValtypeT >::Init ( const VectorBundle2< Valtype, ValtypeT > & vb2 )

inlinenoexcept

Initializes the Frame structure.

Parameters

vb2	VectorBundle2 object giving the P,T,N part; B gets computed.

◆ Init() [2/2]

template<typename Valtype, typename ValtypeT>

Frame< Valtype, ValtypeT > & spat::Frame< Valtype, ValtypeT >::Init	(	const VectorBundle< Valtype, ValtypeT > &	vb,
		const Vector< ValtypeT > &	up )

inlinenoexcept

Initializes the Frame structure to vb and calculates nor as to be orthogonal to up.

Parameters

vb	Values for pos and tan.
up	Vector pointing in up direction.

◆ IsOrthoNormal()

template<typename Valtype, typename ValtypeT>

bool spat::Frame< Valtype, ValtypeT >::IsOrthoNormal	(	ValtypeT	epsilon_length = 2*std::numeric_limits<ValtypeT>::epsilon(),
		ValtypeT	epsilon_angle = 2*std::numeric_limits<ValtypeT>::epsilon() ) const

inlinenoexcept

Parameters

epsilon_length	Margin for deviation.
epsilon_angle	Margin for deviation.

Returns: true if the Frame forms an orthonormal frameset.

◆ Rotate() [1/2]

template<typename Valtype, typename ValtypeT = Valtype>

template<typename Valtype2>

Frame & spat::Frame< Valtype, ValtypeT >::Rotate ( const VectorBundle< Valtype, Valtype2 > & axis )

noexcept

Rotates the frame by axis (length of axis.T make angle in radiants).

Template Parameters

Valtype2 template parameter of axis.T

Parameters

axis	rotation axis

◆ Rotate() [2/2]

template<typename Valtype, typename ValtypeT = Valtype>

template<typename Valtype2>

Frame & spat::Frame< Valtype, ValtypeT >::Rotate	(	const VectorBundle< Valtype, Valtype2 > &	axis,
		Valtype2	angle )

noexcept

Rotates the frame by axis and angle in radiants.

Template Parameters

Valtype2 template parameter of axis.T and angle

Parameters

axis	rotation axis
angle	rotation angle in radiants

◆ RotateBin()

template<typename Valtype, typename ValtypeT>

Frame< Valtype, ValtypeT > & spat::Frame< Valtype, ValtypeT >::RotateBin ( ValtypeT angle )

inlinenoexcept

Rotates the vectors around the bin vector (-yaw).

Parameters

angle rotation angle in radiants

◆ RotateNor()

template<typename Valtype, typename ValtypeT>

Frame< Valtype, ValtypeT > & spat::Frame< Valtype, ValtypeT >::RotateNor ( ValtypeT angle )

inlinenoexcept

Rotates the vectors around the nor vector (-pitch).

Parameters

angle rotation angle in radiants

◆ RotateTan()

template<typename Valtype, typename ValtypeT>

Frame< Valtype, ValtypeT > & spat::Frame< Valtype, ValtypeT >::RotateTan ( ValtypeT angle )

inlinenoexcept

Rotates the vectors around the tan vector (roll).

Parameters

angle rotation angle in radiants

◆ TransportBin()

template<typename Valtype, typename ValtypeT>

Frame< Valtype, ValtypeT > & spat::Frame< Valtype, ValtypeT >::TransportBin ( Valtype d )

inlinenoexcept

Moves the Frame by d in direction B.

Parameters

d	Distance to move along B.

◆ TransportBy()

template<typename Valtype, typename ValtypeT>

Frame< Valtype, ValtypeT > & spat::Frame< Valtype, ValtypeT >::TransportBy ( const Vector< Valtype > & v )

inlinenoexcept

Moves the Frame by v.

Parameters

v	Vector formulated in parent Frame, giving the distance to move P

◆ TransportNor()

template<typename Valtype, typename ValtypeT>

Frame< Valtype, ValtypeT > & spat::Frame< Valtype, ValtypeT >::TransportNor ( Valtype d )

inlinenoexcept

Moves the Frame by d in direction N.

Parameters

d	Distance to move along N.

◆ TransportTan()

template<typename Valtype, typename ValtypeT>

Frame< Valtype, ValtypeT > & spat::Frame< Valtype, ValtypeT >::TransportTan ( Valtype d )

inlinenoexcept

Moves the Frame by d in direction T.

Parameters

d	Distance to move along T.

◆ TransportTo() [1/2]

template<typename Valtype, typename ValtypeT>

Frame< Valtype, ValtypeT > & spat::Frame< Valtype, ValtypeT >::TransportTo ( const Position< Valtype > & p )

inlinenoexcept

Transport this Frame to p.

Parameters

p	a point in space formulated with respect to this Frame.

◆ TransportTo() [2/2]

template<typename Valtype, typename ValtypeT>

Frame< Valtype, ValtypeT > & spat::Frame< Valtype, ValtypeT >::TransportTo ( Valtype d )

inlinenoexcept

Moves the Frame by d in direction T.

Parameters

d	Distance to move along T.

The documentation for this struct was generated from the following file:

C:/Trend/Development/Trax3/Code/spat/Frame.h

Public Member Functions

Public Attributes

Detailed Description

Member Function Documentation

◆ Equals()

◆ Init() [1/2]

◆ Init() [2/2]

◆ IsOrthoNormal()

◆ Rotate() [1/2]

◆ Rotate() [2/2]

◆ RotateBin()

◆ RotateNor()

◆ RotateTan()

◆ TransportBin()

◆ TransportBy()

◆ TransportNor()

◆ TransportTan()

◆ TransportTo() [1/2]

◆ TransportTo() [2/2]