math Namespace Reference

Classes
class	Coord
	Represents a position in 3D space with an associated time. More...
class	Matrix3
	A class representing a 3x3 matrix. More...
class	Path
	Represents a path with coordinates and allows for various interpolation methods. More...
class	PathException
	Exception class for handling path-related errors. More...
class	RotationCoord
	Represents a rotation in terms of azimuth, elevation, and time. More...
class	RotationPath
	Manages rotational paths with different interpolation techniques. More...
class	SVec3
	A class representing a vector in spherical coordinates. More...
class	Vec3
	A class representing a vector in rectangular coordinates. More...

Functions
Coord	operator* (const Coord &a, const Coord &b) noexcept
	Multiplies two Coord objects' positions and copies the time.
Coord	operator+ (const Coord &a, const Coord &b) noexcept
	Adds two Coord objects' positions and copies the time.
Coord	operator- (const Coord &a, const Coord &b) noexcept
	Subtracts two Coord objects' positions and copies the time.
Coord	operator/ (const Coord &a, const Coord &b) noexcept
	Divides two Coord objects' positions and copies the time.
Coord	operator+ (const Coord &a, const RealType b) noexcept
	Adds a scalar to a Coord's position while copying the time.
Coord	operator* (const Coord &a, const RealType b) noexcept
	Multiplies a Coord's position by a scalar while copying the time.
Coord	operator/ (const RealType a, const Coord &b) noexcept
	Divides a scalar by a Coord's position and copies the time.
Coord	operator/ (const Coord &b, const RealType a) noexcept
	Divides a Coord's position by a scalar while copying the time.
RotationCoord	operator* (const RotationCoord &a, const RotationCoord &b) noexcept
	Multiplies two RotationCoord objects' components and copies the time.
RotationCoord	operator+ (const RotationCoord &a, const RotationCoord &b) noexcept
	Adds two RotationCoord objects' components and copies the time.
RotationCoord	operator- (const RotationCoord &a, const RotationCoord &b) noexcept
	Subtracts two RotationCoord objects' components and copies the time.
RotationCoord	operator/ (const RotationCoord &a, const RotationCoord &b) noexcept
	Divides two RotationCoord objects' components and copies the time.
RotationCoord	operator+ (const RotationCoord &a, const RealType b) noexcept
	Adds a scalar to a RotationCoord's components while copying the time.
RotationCoord	operator* (const RotationCoord &a, const RealType b) noexcept
	Multiplies a RotationCoord's components by a scalar while copying the time.
RotationCoord	operator/ (const RealType a, const RotationCoord &b) noexcept
	Divides a scalar by a RotationCoord's components and copies the time.
RotationCoord	operator/ (const RotationCoord &b, const RealType a) noexcept
	Divides a RotationCoord's components by a scalar while copying the time.
SVec3	operator+ (const SVec3 &a, const SVec3 &b) noexcept
	Adds two SVec3 vectors.
SVec3	operator- (const SVec3 &a, const SVec3 &b) noexcept
	Subtracts two SVec3 vectors.
RealType	dotProduct (const Vec3 &a, const Vec3 &b) noexcept
	Computes the dot product of two Vec3 vectors.
Vec3	operator* (const Vec3 &a, const Vec3 &b) noexcept
	Multiplies two Vec3 vectors component-wise.
Vec3	operator+ (const Vec3 &a, const Vec3 &b) noexcept
	Adds two Vec3 vectors component-wise.
Vec3	operator- (const Vec3 &a, const Vec3 &b) noexcept
	Subtracts two Vec3 vectors component-wise.
Vec3	operator/ (const Vec3 &a, const Vec3 &b)
	Divides two Vec3 vectors component-wise.
Vec3	operator* (const Vec3 &a, const RealType b) noexcept
	Multiplies a Vec3 vector by a scalar value.
Vec3	operator/ (const Vec3 &a, const RealType b) noexcept
	Divides a Vec3 vector by a scalar value.
Vec3	operator/ (const RealType a, const Vec3 &b) noexcept
	Divides a scalar value by a Vec3 vector.
void	to_json (nlohmann::json &j, const Vec3 &v)
void	from_json (const nlohmann::json &j, Vec3 &v)
void	to_json (nlohmann::json &j, const Coord &c)
void	from_json (const nlohmann::json &j, Coord &c)
void	to_json (nlohmann::json &j, const RotationCoord &rc)
void	from_json (const nlohmann::json &j, RotationCoord &rc)
	NLOHMANN_JSON_SERIALIZE_ENUM (Path::InterpType, {{Path::InterpType::INTERP_STATIC, "static"}, {Path::InterpType::INTERP_LINEAR, "linear"}, {Path::InterpType::INTERP_CUBIC, "cubic"}}) void to_json(nlohmann
void	from_json (const nlohmann::json &j, Path &p)
	NLOHMANN_JSON_SERIALIZE_ENUM (RotationPath::InterpType, {{RotationPath::InterpType::INTERP_STATIC, "static"}, {RotationPath::InterpType::INTERP_CONSTANT, "constant"}, {RotationPath::InterpType::INTERP_LINEAR, "linear"}, {RotationPath::InterpType::INTERP_CUBIC, "cubic"}}) void to_json(nlohmann
void	from_json (const nlohmann::json &j, RotationPath &p)

Function Documentation

dotProduct()

RealType math::dotProduct ( const Vec3 &  a, const Vec3 &  b  )

noexcept

Computes the dot product of two Vec3 vectors.

Parameters

a	The first vector.
b	The second vector.

Returns

The dot product of the vectors.

Definition at line 214 of file geometry_ops.h.

{ return a.x * b.x + a.y * b.y + a.z * b.z; }

References a, and b.

from_json() [1/5]

void math::from_json	(	const nlohmann::json &	j,
		Coord &	c
	)

Definition at line 420 of file json_serializer.cpp.

    {
        j.at("time").get_to(c.t);
        j.at("x").get_to(c.pos.x);
        j.at("y").get_to(c.pos.y);
        j.at("altitude").get_to(c.pos.z);
    }

References c, and max.

from_json() [2/5]

void math::from_json	(	const nlohmann::json &	j,
		Path &	p
	)

Definition at line 455 of file json_serializer.cpp.

    {
        p.setInterp(j.at("interpolation").get<Path::InterpType>());
        for (const auto waypoints = j.at("positionwaypoints").get<std::vector<Coord>>(); const auto& wp : waypoints)
        {
            p.addCoord(wp);
        }
        p.finalize();
    }

References max.

from_json() [3/5]

void math::from_json	(	const nlohmann::json &	j,
		RotationCoord &	rc
	)

Definition at line 436 of file json_serializer.cpp.

    {
        j.at("time").get_to(rc.t);
        const auto external = serial::rotation_angle_utils::external_rotation_to_internal(
            j.at("azimuth").get<RealType>(), j.at("elevation").get<RealType>(), rc.t, params::rotationAngleUnit());
        rc.azimuth = external.azimuth;
        rc.elevation = external.elevation;
    }

References serial::rotation_angle_utils::external_rotation_to_internal(), max, and params::rotationAngleUnit().

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from_json() [4/5]

void math::from_json	(	const nlohmann::json &	j,
		RotationPath &	p
	)

Definition at line 498 of file json_serializer.cpp.

    {
        p.setInterp(j.at("interpolation").get<RotationPath::InterpType>());
        for (const auto waypoints = j.at("rotationwaypoints").get<std::vector<RotationCoord>>();
             const auto& wp : waypoints)
        {
            p.addCoord(wp);
        }
        p.finalize();
    }

References max.

from_json() [5/5]

void math::from_json	(	const nlohmann::json &	j,
		Vec3 &	v
	)

Definition at line 408 of file json_serializer.cpp.

    {
        j.at("x").get_to(v.x);
        j.at("y").get_to(v.y);
        j.at("z").get_to(v.z);
    }

References max, math::Vec3::x, math::Vec3::y, and math::Vec3::z.

NLOHMANN_JSON_SERIALIZE_ENUM() [1/2]

math::NLOHMANN_JSON_SERIALIZE_ENUM	(	Path::InterpType	,
		{{Path::InterpType::INTERP_STATIC, "static"}, {Path::InterpType::INTERP_LINEAR, "linear"}, {Path::InterpType::INTERP_CUBIC, "cubic"}}
	)

Definition at line 445 of file json_serializer.cpp.

                                 {{Path::InterpType::INTERP_STATIC, "static"},
                                  {Path::InterpType::INTERP_LINEAR, "linear"},
                                  {Path::InterpType::INTERP_CUBIC, "cubic"}})
 
    void to_json(nlohmann::json& j, const Path& p) // NOLINT(*-use-internal-linkage)
    {
        j = {{"interpolation", p.getType()}, {"positionwaypoints", p.getCoords()}};
    }

References math::Path::INTERP_CUBIC, math::Path::INTERP_LINEAR, and math::Path::INTERP_STATIC.

NLOHMANN_JSON_SERIALIZE_ENUM() [2/2]

math::NLOHMANN_JSON_SERIALIZE_ENUM	(	RotationPath::InterpType	,
		{{RotationPath::InterpType::INTERP_STATIC, "static"}, {RotationPath::InterpType::INTERP_CONSTANT, "constant"}, {RotationPath::InterpType::INTERP_LINEAR, "linear"}, {RotationPath::InterpType::INTERP_CUBIC, "cubic"}}
	)

Definition at line 465 of file json_serializer.cpp.

                                 {{RotationPath::InterpType::INTERP_STATIC, "static"},
                                  {RotationPath::InterpType::INTERP_CONSTANT,
                                   "constant"}, // Not used in xml_parser or UI yet, but for completeness
                                  {RotationPath::InterpType::INTERP_LINEAR, "linear"},
                                  {RotationPath::InterpType::INTERP_CUBIC, "cubic"}})
 
    void to_json(nlohmann::json& j, const RotationPath& p) // NOLINT(*-use-internal-linkage)
    {
        j["interpolation"] = p.getType();
        // This logic exists to map the two different rotation definitions from the
        // XML schema (<fixedrotation> and <rotationpath>) into a unified JSON
        // structure that the frontend can more easily handle.
        if (p.getType() == RotationPath::InterpType::INTERP_CONSTANT)
        {
            // A constant-rate rotation path corresponds to the <fixedrotation> XML element.
            // The start and rate values are converted to compass degrees per second.
            // No normalization is applied to preserve negative start angles.
            const auto unit = params::rotationAngleUnit();
            j["startazimuth"] = serial::rotation_angle_utils::internal_azimuth_to_external(p.getStart().azimuth, unit);
            j["startelevation"] =
                serial::rotation_angle_utils::internal_elevation_to_external(p.getStart().elevation, unit);
            j["azimuthrate"] =
                serial::rotation_angle_utils::internal_azimuth_rate_to_external(p.getRate().azimuth, unit);
            j["elevationrate"] =
                serial::rotation_angle_utils::internal_elevation_rate_to_external(p.getRate().elevation, unit);
        }
        else
        {
            j["rotationwaypoints"] = p.getCoords();
        }
    }

References math::RotationPath::INTERP_CONSTANT, math::RotationPath::INTERP_CUBIC, math::RotationPath::INTERP_LINEAR, and math::RotationPath::INTERP_STATIC.

operator*() [1/6]

Coord math::operator* ( const Coord &  a, const Coord &  b  )

noexcept

Multiplies two Coord objects' positions and copies the time.

Definition at line 51 of file coord.h.

{ return {a.pos * b.pos, a.t}; }

References a, b, and math::Coord::pos.

operator*() [2/6]

Coord math::operator* ( const Coord &  a, const RealType  b  )

noexcept

Multiplies a Coord's position by a scalar while copying the time.

Definition at line 61 of file coord.h.

{ return {a.pos * b, a.t}; }

References a, b, and math::Coord::pos.

operator*() [3/6]

RotationCoord math::operator* ( const RotationCoord &  a, const RealType  b  )

noexcept

Multiplies a RotationCoord's components by a scalar while copying the time.

Definition at line 148 of file coord.h.

    {
        return {a.azimuth * b, a.elevation * b, a.t};
    }

References a, b, and math::Coord::t.

operator*() [4/6]

RotationCoord math::operator* ( const RotationCoord &  a, const RotationCoord &  b  )

noexcept

Multiplies two RotationCoord objects' components and copies the time.

Definition at line 118 of file coord.h.

    {
        return {a.azimuth * b.azimuth, a.elevation * b.elevation, a.t};
    }

References a, b, and math::Coord::t.

operator*() [5/6]

Vec3 math::operator* ( const Vec3 &  a, const RealType  b  )

noexcept

Multiplies a Vec3 vector by a scalar value.

Definition at line 236 of file geometry_ops.h.

{ return {a.x * b, a.y * b, a.z * b}; }

References a, and b.

operator*() [6/6]

Vec3 math::operator* ( const Vec3 &  a, const Vec3 &  b  )

noexcept

Multiplies two Vec3 vectors component-wise.

Definition at line 224 of file geometry_ops.h.

{ return {a.x * b.x, a.y * b.y, a.z * b.z}; }

References a, and b.

operator+() [1/6]

Coord math::operator+ ( const Coord &  a, const Coord &  b  )

noexcept

Adds two Coord objects' positions and copies the time.

Definition at line 53 of file coord.h.

{ return {a.pos + b.pos, a.t}; }

References a, b, and math::Coord::pos.

operator+() [2/6]

Coord math::operator+ ( const Coord &  a, const RealType  b  )

noexcept

Adds a scalar to a Coord's position while copying the time.

Definition at line 59 of file coord.h.

{ return {a.pos + b, a.t}; }

References a, b, and math::Coord::pos.

operator+() [3/6]

RotationCoord math::operator+ ( const RotationCoord &  a, const RealType  b  )

noexcept

Adds a scalar to a RotationCoord's components while copying the time.

Definition at line 142 of file coord.h.

    {
        return {a.azimuth + b, a.elevation + b, a.t};
    }

References a, b, and math::Coord::t.

operator+() [4/6]

RotationCoord math::operator+ ( const RotationCoord &  a, const RotationCoord &  b  )

noexcept

Adds two RotationCoord objects' components and copies the time.

Definition at line 124 of file coord.h.

    {
        return {a.azimuth + b.azimuth, a.elevation + b.elevation, a.t};
    }

References a, b, and math::Coord::t.

operator+() [5/6]

SVec3 math::operator+ ( const SVec3 &  a, const SVec3 &  b  )

noexcept

Adds two SVec3 vectors.

Definition at line 117 of file geometry_ops.cpp.

    {
        const RealType new_azimuth = wrapSignedAngle(a.azimuth + b.azimuth);
        const RealType new_elevation = std::fmod(a.elevation + b.elevation, PI);
 
        return {a.length + b.length, new_azimuth, new_elevation};
    }

References a, b, max, and PI.

operator+() [6/6]

Vec3 math::operator+ ( const Vec3 &  a, const Vec3 &  b  )

noexcept

Adds two Vec3 vectors component-wise.

Definition at line 227 of file geometry_ops.h.

{ return {a.x + b.x, a.y + b.y, a.z + b.z}; }

References a, and b.

operator-() [1/4]

Coord math::operator- ( const Coord &  a, const Coord &  b  )

noexcept

Subtracts two Coord objects' positions and copies the time.

Definition at line 55 of file coord.h.

{ return {a.pos - b.pos, a.t}; }

References a, b, and math::Coord::pos.

operator-() [2/4]

RotationCoord math::operator- ( const RotationCoord &  a, const RotationCoord &  b  )

noexcept

Subtracts two RotationCoord objects' components and copies the time.

Definition at line 130 of file coord.h.

    {
        return {a.azimuth - b.azimuth, a.elevation - b.elevation, a.t};
    }

References a, b, and math::Coord::t.

operator-() [3/4]

SVec3 math::operator- ( const SVec3 &  a, const SVec3 &  b  )

noexcept

Subtracts two SVec3 vectors.

Definition at line 125 of file geometry_ops.cpp.

    {
        const RealType new_azimuth = wrapSignedAngle(a.azimuth - b.azimuth);
 
        // Elevation difference is typically simpler and doesn't need wrapping
        // unless 180 degree elevation sweeps are expected.
        const RealType new_elevation = std::fmod(a.elevation - b.elevation, PI);
 
        return {a.length - b.length, new_azimuth, new_elevation};
    }

References a, b, max, and PI.

operator-() [4/4]

Vec3 math::operator- ( const Vec3 &  a, const Vec3 &  b  )

noexcept

Subtracts two Vec3 vectors component-wise.

Definition at line 230 of file geometry_ops.h.

{ return {a.x - b.x, a.y - b.y, a.z - b.z}; }

References a, and b.

operator/() [1/9]

Coord math::operator/ ( const Coord &  a, const Coord &  b  )

noexcept

Divides two Coord objects' positions and copies the time.

Definition at line 57 of file coord.h.

{ return {a.pos / b.pos, a.t}; }

References a, b, and math::Coord::pos.

operator/() [2/9]

Coord math::operator/ ( const Coord &  b, const RealType  a  )

noexcept

Divides a Coord's position by a scalar while copying the time.

Definition at line 65 of file coord.h.

{ return {b.pos / a, b.t}; }

References a, b, and math::Coord::pos.

operator/() [3/9]

Coord math::operator/ ( const RealType  a, const Coord &  b  )

noexcept

Divides a scalar by a Coord's position and copies the time.

Definition at line 63 of file coord.h.

{ return {a / b.pos, b.t}; }

References a, b, and math::Coord::pos.

operator/() [4/9]

RotationCoord math::operator/ ( const RealType  a, const RotationCoord &  b  )

noexcept

Divides a scalar by a RotationCoord's components and copies the time.

Definition at line 154 of file coord.h.

    {
        return {a / b.azimuth, a / b.elevation, b.t};
    }

References a, b, and math::Coord::t.

operator/() [5/9]

Vec3 math::operator/ ( const RealType  a, const Vec3 &  b  )

noexcept

Divides a scalar value by a Vec3 vector.

Definition at line 242 of file geometry_ops.h.

{ return {a / b.x, a / b.y, a / b.z}; }

References a, and b.

operator/() [6/9]

RotationCoord math::operator/ ( const RotationCoord &  a, const RotationCoord &  b  )

noexcept

Divides two RotationCoord objects' components and copies the time.

Definition at line 136 of file coord.h.

    {
        return {a.azimuth / b.azimuth, a.elevation / b.elevation, a.t};
    }

References a, b, and math::Coord::t.

operator/() [7/9]

RotationCoord math::operator/ ( const RotationCoord &  b, const RealType  a  )

noexcept

Divides a RotationCoord's components by a scalar while copying the time.

Definition at line 160 of file coord.h.

    {
        return {b.azimuth / a, b.elevation / a, b.t};
    }

References a, b, and math::Coord::t.

operator/() [8/9]

Vec3 math::operator/ ( const Vec3 &  a, const RealType  b  )

noexcept

Divides a Vec3 vector by a scalar value.

Definition at line 239 of file geometry_ops.h.

{ return {a.x / b, a.y / b, a.z / b}; }

References a, and b.

operator/() [9/9]

Vec3 math::operator/	(	const Vec3 &	a,
		const Vec3 &	b
	)

Divides two Vec3 vectors component-wise.

Definition at line 233 of file geometry_ops.h.

{ return {a.x / b.x, a.y / b.y, a.z / b.z}; }

References a, and b.

to_json() [1/3]

void math::to_json	(	nlohmann::json &	j,
		const Coord &	c
	)

Definition at line 415 of file json_serializer.cpp.

    {
        j = {{"time", c.t}, {"x", c.pos.x}, {"y", c.pos.y}, {"altitude", c.pos.z}};
    }

References c, max, and math::Vec3::x.

to_json() [2/3]

void math::to_json	(	nlohmann::json &	j,
		const RotationCoord &	rc
	)

Definition at line 428 of file json_serializer.cpp.

    {
        const auto unit = params::rotationAngleUnit();
        j = {{"time", rc.t},
             {"azimuth", serial::rotation_angle_utils::internal_azimuth_to_external(rc.azimuth, unit)},
             {"elevation", serial::rotation_angle_utils::internal_elevation_to_external(rc.elevation, unit)}};
    }

References serial::rotation_angle_utils::internal_azimuth_to_external(), serial::rotation_angle_utils::internal_elevation_to_external(), max, and params::rotationAngleUnit().

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to_json() [3/3]

void math::to_json	(	nlohmann::json &	j,
		const Vec3 &	v
	)

Definition at line 403 of file json_serializer.cpp.

    {
        j = {{"x", v.x}, {"y", v.y}, {"z", v.z}};
    } // NOLINT(*-use-internal-linkage)

References max, math::Vec3::x, math::Vec3::y, and math::Vec3::z.