Class SpatialVector

• Defined in File SpatialVector.h

Class Documentation

class SpatialVector

Represents a 6D spatial vector, split into angular (w) and linear (v) components.

See Spatial notation section for more discussion on spatial notation.

Public Functions

SpatialVector()

Construct initialized to zero.

SpatialVector(const Vec6 &sv)

Construct using a 6 vector. The first 3 components will be put into w and the last 3 components will be put into v.

Parameters:

sv – 6-element vector representing the entire spatial vector.

SpatialVector(const Vec3 &w, const Vec3 &v)

Construct using two 3-element vectors. The first will become w and the second will become v.

Parameters:

• w – Angular portion of the spatial vector.

• v – Linear portion of the spatial vector.

SpatialVector(const SpatialVector &other)

Copy constructor.

Parameters:

other – The SpatialVector to copy from.

SpatialVector &operator=(const SpatialVector &other)

Copy assignment operator.

Parameters:

other – The SpatialVector to assign from.

Returns:

Reference to this object.

SpatialVector(SpatialVector &&other) noexcept

Move constructor.

Parameters:

other – The SpatialVector to move from.

SpatialVector &operator=(SpatialVector &&other) noexcept

Move assignment operator.

Parameters:

other – The SpatialVector to move from.

Returns:

Reference to this object.

inline std::string typeString() const

Return object type as a string.

Returns:

String “SpatialVector”.

std::string dumpString(const std::string &prefix = "", unsigned int precision = 10, bool exponential = false) const

Dump the object as a formatted string.

Parameters:

• prefix – Optional prefix for each line.

• precision – Number of digits to use for floating point values.

• exponential – Use exponential formatting.

Returns:

Formatted string representation.

void dump(const std::string &prefix = "", unsigned int precision = 10, bool exponential = false) const

Write dumpString to std::cout.

Parameters:

• prefix – Optional prefix for each line.

• precision – Number of digits to use for floating point values.

• exponential – Use exponential formatting.

bool isZero(double prec = MATH_EPSILON) const

Return true if the spatial vector is zero.

Parameters:

prec – Tolerance to use when comparing with zero.

Returns:

True if both angular and linear components are zero.

void setZero()

Zero out the spatial vector’s values.

void uninitialize()

Mark the spatial vector as uninitialized.

bool isInitialized() const

Check if the spatial vector is initialized.

Returns:

True if both angular and linear components are initialized.

bool operator==(const SpatialVector &other) const

Equality operator.

Parameters:

other – Another SpatialVector to compare with.

Returns:

True if both components are equal.

double operator*(const SpatialVector &other) const

Dot product with another spatial vector.

Parameters:

other – The SpatialVector to compute the dot product with.

Returns:

Dot product result.

SpatialVector operator*(double scale) const

Scalar multiplication.

Parameters:

scale – Scalar value to multiply by.

Returns:

Scaled SpatialVector.

SpatialVector operator+(const SpatialVector &other) const

Component-wise addition.

Parameters:

other – The SpatialVector to add to this one.

Returns:

Resulting SpatialVector sum.

SpatialVector &operator+=(const SpatialVector &other)

In-place component-wise addition.

Parameters:

other – The SpatialVector to add to this one in-place.

Returns:

Reference to this object.

SpatialVector operator-() const

Negation operator.

Returns:

Negated SpatialVector.

SpatialVector operator-(const SpatialVector &other) const

Subtract another SpatialVector.

Parameters:

other – The SpatialVector to subtract from this one.

Returns:

Resulting SpatialVector.

SpatialVector operator-=(const SpatialVector &other)

In-place subtraction.

Parameters:

other – The SpatialVector to subtract from this one.

Returns:

Reference to this object.

SpatialVector operator+(const Vec6 &vec) const

Add a Vec6 to this spatial vector.

Parameters:

vec – The 6D vector to add to this SpatialVector.

Returns:

Resulting SpatialVector.

SpatialVector operator-(const Vec6 &vec) const

Subtract a Vec6 from this spatial vector.

Parameters:

vec – The 6D vector to subtract from this SpatialVector.

Returns:

Resulting SpatialVector.

bool isApprox(const SpatialVector &other, double prec = MATH_EPSILON) const

Check if another spatial vector is approximately equal within precision.

Parameters:

• other – The SpatialVector to compare to this one.

• prec – Precision tolerance.

Returns:

True if approximately equal.

const Vec3 &getw() const

Get the angular portion of the spatial vector.

Returns:

Const reference to angular vector.

void setw(const Vec3 &w)

Set the angular portion of the spatial vector.

Parameters:

w – New angular vector.

const Vec3 &getv() const

Get the linear portion of the spatial vector.

Returns:

Const reference to linear vector.

void setv(const Vec3 &v)

Set the linear portion of the spatial vector.

Parameters:

v – New linear vector.

Vec6 toVector6() const

Convert to a 6-vector by combining the w and v parts as [w;v].

Returns:

Combined 6D vector.

SpatialVector cross(const SpatialVector &other)

Compute 6-D cross product with another spatial vector.

\[\begin{split} A \times B = \tilde A B = \begin{bmatrix} \tilde A_w & \tilde A_v \\ 0 & \tilde A_w \end{bmatrix} \begin{bmatrix} B_w \\ B_v \end{bmatrix} \end{split}\]

Parameters:

other – The SpatialVector to compute the cross product with.

Returns:

Resulting SpatialVector.

Mat66 tilde() const

Compute 6-D cross product with another spatial vector.

\[\begin{split} \tilde A = \begin{bmatrix} \tilde A_w & 0 \\ \tilde A_v & \tilde A_w \end{bmatrix} \begin{bmatrix} B_w \\ B_v \end{bmatrix} \end{split}\]

Returns:

Resulting SpatialVector.

SpatialVector barprod(const SpatialVector &other)

Compute the bar product with another spatial vector.

\[\begin{split} \bar A B = - {\tilde A}^* B = \begin{bmatrix} \tilde A_w & \tilde A_v \\ 0 & \tilde A_w \end{bmatrix} \begin{bmatrix} B_w \\ B_v \end{bmatrix} \end{split}\]

Parameters:

other – The SpatialVector to compute the bar product with.

Returns:

Resulting SpatialVector.

SpatialVector multiplyFromLeft(const Mat66 &mat) const

Multiply from the vector from left with a matrix, i.e v * mat.

Parameters:

mat – Matrix to multiply.

Returns:

Resulting SpatialVector.