Program Listing for File SpatialVector.h#
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/**
* @file
* @brief Contains the declarations for the SpatialVector class.
*/
#pragma once
#include "Karana/Math/Defs.h"
namespace Karana::Math {
/**
* @class SpatialVector
* @brief Represents a 6D spatial vector, split into angular (w) and linear (v) components.
*
* See \sref{spatial_notation_sec} section for more discussion on
* spatial notation.
*/
class SpatialVector {
// Constructors
public:
/**
* @brief Construct initialized to zero.
*/
SpatialVector();
/**
* @brief Construct using a 6 vector. The first 3 components will be put into w and
* the last 3 components will be put into v.
*
* @param sv 6-element vector representing the entire spatial vector.
*/
SpatialVector(const Vec6 &sv);
/**
* @brief Construct using two 3-element vectors. The first will become w and the
* second will become v.
*
* @param w Angular portion of the spatial vector.
* @param v Linear portion of the spatial vector.
*/
SpatialVector(const Vec3 &w, const Vec3 &v);
// Copy and move operations
public:
/**
* @brief Copy constructor.
*
* @param other The SpatialVector to copy from.
*/
SpatialVector(const SpatialVector &other);
/**
* @brief Copy assignment operator.
*
* @param other The SpatialVector to assign from.
* @return Reference to this object.
*/
SpatialVector &operator=(const SpatialVector &other);
/**
* @brief Move constructor.
*
* @param other The SpatialVector to move from.
*/
SpatialVector(SpatialVector &&other) noexcept;
/**
* @brief Move assignment operator.
*
* @param other The SpatialVector to move from.
* @return Reference to this object.
*/
SpatialVector &operator=(SpatialVector &&other) noexcept;
/**
* @brief Return object type as a string.
*
* @return String "SpatialVector".
*/
std::string_view typeString() const;
/**
* @brief Dump the object as a formatted string.
*
* @param prefix Optional prefix for each line.
* @param precision Number of digits to use for floating point values.
* @param format_type The format type to use.
* @return Formatted string representation.
*/
std::string dumpString(std::string_view prefix = "",
unsigned int precision = 10,
DumpFormatType format_type = DumpFormatType::DEFAULT_FLOAT) const;
/**
* @brief Write dumpString to std::cout.
*
* @param prefix Optional prefix for each line.
* @param precision Number of digits to use for floating point values.
* @param format_type The format type to use.
*/
void dump(std::string_view prefix = "",
unsigned int precision = 10,
DumpFormatType format_type = DumpFormatType::DEFAULT_FLOAT) const;
/**
* @brief Return true if the spatial vector is zero.
*
* @param prec Tolerance to use when comparing with zero.
* @return True if both angular and linear components are zero.
*/
bool isZero(double prec = MATH_EPSILON) const;
/**
* @brief Zero out the spatial vector's values.
*/
void setZero();
/**
* @brief Mark the spatial vector as not ready.
*/
void makeNotReady();
/**
* @brief Check if the spatial vector is initialized.
*
* @return True if both angular and linear components are initialized.
*/
bool isReady() const;
// Operators
public:
/**
* @brief Equality operator.
*
* @param other Another SpatialVector to compare with.
* @return True if both components are equal.
*/
bool operator==(const SpatialVector &other) const;
/**
* @brief Dot product with another spatial vector.
*
* @param other The SpatialVector to compute the dot product with.
* @return Dot product result.
*/
double operator*(const SpatialVector &other) const;
/**
* @brief Scalar multiplication.
*
* @param scale Scalar value to multiply by.
* @return Scaled SpatialVector.
*/
SpatialVector operator*(double scale) const;
/**
* @brief Component-wise addition.
*
* @param other The SpatialVector to add to this one.
* @return Resulting SpatialVector sum.
*/
SpatialVector operator+(const SpatialVector &other) const;
/**
* @brief In-place component-wise addition.
*
* @param other The SpatialVector to add to this one in-place.
* @return Reference to this object.
*/
SpatialVector &operator+=(const SpatialVector &other);
/**
* @brief Negation operator.
*
* @return Negated SpatialVector.
*/
SpatialVector operator-() const;
/**
* @brief Subtract another SpatialVector.
*
* @param other The SpatialVector to subtract from this one.
* @return Resulting SpatialVector.
*/
SpatialVector operator-(const SpatialVector &other) const;
/**
* @brief In-place subtraction.
*
* @param other The SpatialVector to subtract from this one.
* @return Reference to this object.
*/
SpatialVector operator-=(const SpatialVector &other);
/**
* @brief Add a Vec6 to this spatial vector.
*
* @param vec The 6D vector to add to this SpatialVector.
* @return Resulting SpatialVector.
*/
SpatialVector operator+(const Vec6 &vec) const;
/**
* @brief Subtract a Vec6 from this spatial vector.
*
* @param vec The 6D vector to subtract from this SpatialVector.
* @return Resulting SpatialVector.
*/
SpatialVector operator-(const Vec6 &vec) const;
// SpatialVector methods
public:
/**
* @brief Check if another spatial vector is approximately equal within precision.
*
* @param other The SpatialVector to compare to this one.
* @param prec Precision tolerance.
* @return True if approximately equal.
*/
bool isApprox(const SpatialVector &other, double prec = MATH_EPSILON) const;
/**
* @brief Get the angular portion of the spatial vector.
*
* @return Const reference to angular vector.
*/
const Vec3 &getw() const;
/**
* @brief Set the angular portion of the spatial vector.
*
* @param w New angular vector.
*/
void setw(const Vec3 &w);
/**
* @brief Get the linear portion of the spatial vector.
*
* @return Const reference to linear vector.
*/
const Vec3 &getv() const;
/**
* @brief Set the linear portion of the spatial vector.
*
* @param v New linear vector.
*/
void setv(const Vec3 &v);
/**
* @brief Convert to a 6-vector by combining the w and v parts as [w;v].
*
* @return Combined 6D vector.
*/
Vec6 toVector6() const;
/**
* @brief Compute 6-D cross product with another spatial vector.
*
* @f[
* 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}
* @f]
*
* @param other The SpatialVector to compute the cross product with.
* @return Resulting SpatialVector.
*/
SpatialVector cross(const SpatialVector &other);
/**
* @brief Compute 6-D cross product with another spatial vector.
*
* @f[
* \tilde A = \begin{bmatrix} \tilde A_w & 0 \\ \tilde A_v & \tilde A_w
* \end{bmatrix} \begin{bmatrix} B_w \\ B_v \end{bmatrix}
* @f]
*
* @return Resulting SpatialVector.
*/
Mat66 tilde() const;
/**
* @brief Compute the bar product with another spatial vector.
*
* \f[ \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} \f]
*
* @param other The SpatialVector to compute the bar product with.
* @return Resulting SpatialVector.
*/
SpatialVector barprod(const SpatialVector &other);
/**
* @brief Multiply from the vector from left with a matrix, i.e v * mat.
*
* @param mat Matrix to multiply.
* @return Resulting SpatialVector.
*/
SpatialVector multiplyFromLeft(const Mat66 &mat) const;
private:
/// Angular portion of the spatial vector
Vec3 _w;
/// Linear portion of the spatial vector
Vec3 _v;
};
} // namespace Karana::Math