C interface to some transform-related math functions. More...

Collaboration diagram for Math:

Files
file	m_api.h
	C interface to math library.

file	m_base.cpp
	Base implementations for math library.

file	m_clock_offset.h
	Helpers to estimate offsets between clocks.

file	m_documentation.hpp
	Header with only documentation.

file	m_eigen_interop.hpp
	Interoperability helpers connecting internal math types and Eigen.

file	m_filter_fifo.c
	A fifo that also lets you dynamically filter.

file	m_filter_fifo.h
	A fifo that also lets you dynamically filter.

file	m_filter_one_euro.c
	The "One Euro Filter" for filtering interaction data.

file	m_filter_one_euro.h
	Header for a "One Euro Filter" implementation.

file	m_hash.cpp
	Hashing function.

file	m_imu_3dof.c
	A IMU fusion specially made for 3dof devices.

file	m_imu_3dof.h
	A IMU fusion specially made for 3dof devices.

file	m_imu_pre.c
	IMU pre filter struct.

file	m_imu_pre.h
	IMU pre filter struct.

file	m_lowpass_float.cpp
	Wrap float filters for C.

file	m_lowpass_float.h
	Low-pass IIR filter for floats - C wrapper.

file	m_lowpass_float.hpp
	Low-pass IIR filter.

file	m_lowpass_float_vector.hpp
	Low-pass IIR filter on vectors.

file	m_lowpass_integer.cpp
	Wrap integer filters for C.

file	m_lowpass_integer.h
	Low-pass IIR filter for integers - C wrapper.

file	m_lowpass_integer.hpp
	Low-pass IIR filter for integers.

file	m_mathinclude.h
	Wrapper header for <math.h> to ensure pi-related math constants are defined.

file	m_matrix_2x2.h
	C matrix_2x2 math library.

file	m_matrix_4x4_f64.h
	C matrix 4x4 f64 math library.

file	m_matrix_projection.cpp
	Matrix function for creating projection matrices.

file	m_optics.c
	Functions related to field-of-view.

file	m_permutation.c
	Code to generate permutation of indices.

file	m_permutation.h
	Code to generate permutation of indices.

file	m_predict.c
	Simple function to predict a new pose from a given pose.

file	m_predict.h
	Simple function to predict a new pose from a given pose.

file	m_quatexpmap.cpp
	Base implementations for math library.

file	m_rational.hpp
	A very simple rational number type.

file	m_relation_history.cpp
	Small utility for keeping track of the history of an xrt_space_relation, ie.

file	m_space.cpp
	Functions for manipulating a xrt_relation_chain struct.

file	m_space.h
	Functions for manipulating xrt_pose, xrt_space_relation and xrt_relation_chain structs.

file	m_vec2.h
	C vec2 math library.

file	m_vec3.h
	C vec3 math library.

Data Structures
struct	m_filter_one_euro_base
	Base data type for One Euro filter instances. More...

struct	m_filter_euro_f32
	One Euro filter for a single float measurement. More...

struct	m_filter_euro_vec2
	One Euro filter for a 2D float measurement. More...

struct	m_filter_euro_vec3
	One Euro filter for a 3D float measurement. More...

struct	m_filter_euro_quat
	One Euro filter for a unit quaternion (used as 3D rotation). More...

Macros
#define	MATH_GRAVITY_M_S2 (9.8066)
	Standard gravity acceleration constant. More...

#define	MIN(A, B) ((A) < (B) ? (A) : (B))
	Minimum of A and B. More...

#define	MAX(A, B) ((A) > (B) ? (A) : (B))
	Maximum of A and B. More...

#define	CLAMP(X, A, B) (MIN(MAX((X), (A)), (B)))
	X clamped to the range [A, B]. More...

Functions
size_t	math_hash_string (const char *str_c, size_t length)
	Generate a hash value from the given string, trailing zero not included. More...

void	math_matrix_3x3_identity (struct xrt_matrix_3x3 *mat)
	Initialize a 3x3 matrix to the identity matrix. More...

void	math_matrix_3x3_from_quat (const struct xrt_quat q, struct xrt_matrix_3x3 result_out)
	Initialize a 3x3 matrix from a quaternion. More...

void	math_matrix_3x3_f64_identity (struct xrt_matrix_3x3_f64 *mat)
	Initialize a double 3x3 matrix to the identity matrix. More...

void	math_matrix_3x3_transform_vec3 (const struct xrt_matrix_3x3 left, const struct xrt_vec3 right, struct xrt_vec3 *result_out)
	Transform a vec3 by a 3x3 matrix. More...

void	math_matrix_4x4_transform_vec3 (const struct xrt_matrix_4x4 left, const struct xrt_vec3 right, struct xrt_vec3 *result_out)
	Transform a vec3 by a 4x4 matrix, extending the vector with w = 1.0. More...

void	math_matrix_3x3_f64_transform_vec3_f64 (const struct xrt_matrix_3x3_f64 left, const struct xrt_vec3_f64 right, struct xrt_vec3_f64 *result_out)
	Transform a double vec3 by a 3x3 double matrix. More...

bool	math_compute_fovs (double w_total, double w_1, double horizfov_total, double h_total, double h_1, double vertfov_total, struct xrt_fov *fov)
	Perform the computations from "Computing Half-Fields-Of-View from Simpler Display Models", to get half-FOVs from things we can retrieve from other APIs. More...

void	m_predict_relation (const struct xrt_space_relation rel, double delta_s, struct xrt_space_relation out_rel)
	Using the given `xrt_space_relation` predicts a new `xrt_space_relation` `delta_s` into the future. More...

static bool	m_pose_is_identity (const struct xrt_pose *pose)

static void	m_space_relation_from_pose (const struct xrt_pose pose, bool set_tracked, struct xrt_space_relation out_relation)
	Create an xrt_space_relation from a pose. More...

static void	m_space_relation_ident (struct xrt_space_relation *out_relation)
	Create an xrt_space_relation with only orientation and position valid flags. More...

void	m_space_relation_invert (struct xrt_space_relation relation, struct xrt_space_relation out_relation)

void	m_space_relation_interpolate (struct xrt_space_relation a, struct xrt_space_relation b, float t, enum xrt_space_relation_flags flags, struct xrt_space_relation *out_relation)
	Linearly interpolate between two relations `a` and `b`. More...

bool	math_vec3_validate (const struct xrt_vec3 *vec3)
	Check if this vec3 is valid for math operations. More...

void	math_vec3_accum (const struct xrt_vec3 additional, struct xrt_vec3 inAndOut)
	Accumulate a vector by adding in-place. More...

void	math_vec3_subtract (const struct xrt_vec3 subtrahend, struct xrt_vec3 inAndOut)
	Subtract from a vector in-place. More...

void	math_vec3_scalar_mul (float scalar, struct xrt_vec3 *inAndOut)
	Multiply a vector in-place. More...

void	math_vec3_cross (const struct xrt_vec3 l, const struct xrt_vec3 r, struct xrt_vec3 *result)
	Cross product of a vector. More...

void	math_vec3_translation_from_isometry (const struct xrt_matrix_4x4 isometry, struct xrt_vec3 result)
	Get translation vector from isometry matrix (col-major). More...

void	math_vec3_normalize (struct xrt_vec3 *in)
	Normalize a vec3 in place. More...

void	math_vec3_f64_cross (const struct xrt_vec3_f64 l, const struct xrt_vec3_f64 r, struct xrt_vec3_f64 *result)
	Cross product of a vec3_f64. More...

void	math_vec3_f64_normalize (struct xrt_vec3_f64 *in)
	Normalize a vec3_f64 in place. More...

void	math_quat_from_angle_vector (float angle_rads, const struct xrt_vec3 vector, struct xrt_quat result)
	Create a rotation from an angle in radians and a unit vector. More...

void	math_quat_from_euler_angles (const struct xrt_vec3 angles, struct xrt_quat result)
	Create a rotation from euler angles to a quaternion. More...

void	math_quat_from_matrix_3x3 (const struct xrt_matrix_3x3 mat, struct xrt_quat result)
	Create a rotation from a 3x3 rotation (row major) matrix. More...

void	math_quat_from_plus_x_z (const struct xrt_vec3 plus_x, const struct xrt_vec3 plus_z, struct xrt_quat *result)
	Create a rotation from two vectors plus x and z, by creating a rotation matrix by crossing z and x to get the y axis. More...

bool	math_quat_validate (const struct xrt_quat *quat)
	Check if this quat can be used in transformation operations. More...

bool	math_quat_validate_within_1_percent (const struct xrt_quat *quat)
	Check if this quat is within 1% of unit length. More...

void	math_quat_invert (const struct xrt_quat quat, struct xrt_quat out_quat)
	Invert a quaternion. More...

float	math_quat_len (const struct xrt_quat *quat)
	The euclidean norm or length of a quaternion. More...

void	math_quat_normalize (struct xrt_quat *inout)
	Normalize a quaternion. More...

bool	math_quat_ensure_normalized (struct xrt_quat *inout)
	Normalizes a quaternion if it has accumulated float precision errors. More...

void	math_quat_rotate_vec3 (const struct xrt_quat left, const struct xrt_vec3 right, struct xrt_vec3 *result)
	Rotate a vector. More...

void	math_quat_rotate (const struct xrt_quat left, const struct xrt_quat right, struct xrt_quat *result)
	Rotate a quaternion (compose rotations). More...

void	math_quat_unrotate (const struct xrt_quat left, const struct xrt_quat right, struct xrt_quat *result)
	Inverse of math_quat_rotate. More...

void	math_quat_integrate_velocity (const struct xrt_quat quat, const struct xrt_vec3 ang_vel, float dt, struct xrt_quat *result)
	Integrate a local angular velocity vector (exponential map) and apply to a quaternion. More...

void	math_quat_finite_difference (const struct xrt_quat quat0, const struct xrt_quat quat1, float dt, struct xrt_vec3 *out_ang_vel)
	Compute a global angular velocity vector (exponential map format) by taking the finite difference of two quaternions. More...

void	math_quat_exp (const struct xrt_vec3 axis_angle, struct xrt_quat out_quat)
	Takes a rotation vector equal to half of a Rodrigues rotation vector and returns its corresponding unit quaternion. More...

void	math_quat_ln (const struct xrt_quat quat, struct xrt_vec3 out_axis_angle)
	Takes a unit quaternion and returns a rotation vector equal to half of its corresponding Rodrigues rotation vector. More...

void	math_quat_rotate_derivative (const struct xrt_quat quat, const struct xrt_vec3 deriv, struct xrt_vec3 *result)
	Used to rotate a derivative like a angular velocity. More...

void	math_quat_slerp (const struct xrt_quat left, const struct xrt_quat right, float t, struct xrt_quat *result)
	Slerp (spherical linear interpolation) between two quaternions. More...

void	math_quat_from_swing (const struct xrt_vec2 swing, struct xrt_quat result)
	Converts a 2D vector to a quaternion. More...

void	math_quat_from_swing_twist (const struct xrt_vec2 swing, const float twist, struct xrt_quat result)
	Converts a 2D vector and a float to a quaternion. More...

void	math_quat_to_swing_twist (const struct xrt_quat in, struct xrt_vec2 out_swing, float *out_twist)
	Converts a quaternion to XY-swing and Z-twist. More...

void	math_matrix_3x3_multiply (const struct xrt_matrix_3x3 left, const struct xrt_matrix_3x3 right, struct xrt_matrix_3x3 *result_out)
	Multiply Matrix3x3. More...

void	math_matrix_3x3_inverse (const struct xrt_matrix_3x3 in, struct xrt_matrix_3x3 result)
	Invert Matrix3x3. More...

void	math_matrix_3x3_transpose (const struct xrt_matrix_3x3 in, struct xrt_matrix_3x3 result)
	Transpose Matrix3x3. More...

void	math_matrix_3x3_f64_from_plus_x_z (const struct xrt_vec3_f64 plus_x, const struct xrt_vec3_f64 plus_z, struct xrt_matrix_3x3_f64 *result)
	Create a rotation from two vectors plus x and z, by creating a rotation matrix by crossing z and x to get the y axis. More...

void	math_matrix_3x3_rotation_from_isometry (const struct xrt_matrix_4x4 isometry, struct xrt_matrix_3x3 result)
	Get the rotation matrix from an isomertry matrix (col-major). More...

void	math_matrix_4x4_identity (struct xrt_matrix_4x4 *result)
	Initialize Matrix4x4 with identity. More...

void	math_matrix_4x4_multiply (const struct xrt_matrix_4x4 left, const struct xrt_matrix_4x4 right, struct xrt_matrix_4x4 *result)
	Multiply Matrix4x4. More...

void	math_matrix_4x4_inverse (const struct xrt_matrix_4x4 in, struct xrt_matrix_4x4 result)
	Invert Matrix4x4. More...

void	math_matrix_4x4_isometry_inverse (const struct xrt_matrix_4x4 in, struct xrt_matrix_4x4 result)
	Invert a homogeneous isometry 4x4 (col-major) matrix in SE(3). More...

void	math_matrix_4x4_transpose (const struct xrt_matrix_4x4 in, struct xrt_matrix_4x4 result)
	Transpose Matrix4x4. More...

void	math_matrix_4x4_view_from_pose (const struct xrt_pose pose, struct xrt_matrix_4x4 result)
	Compute view matrix from xrt_pose. More...

void	math_matrix_4x4_isometry_from_rt (const struct xrt_matrix_3x3 rotation, const struct xrt_vec3 translation, struct xrt_matrix_4x4 *result)
	Get an isometry matrix —in SE(3)— from a rotation matrix —SO(3)— and a translation vector. More...

void	math_matrix_4x4_isometry_from_pose (const struct xrt_pose pose, struct xrt_matrix_4x4 result)
	Get a col-major isometry matrix —in SE(3)— from a pose. More...

void	math_matrix_4x4_model (const struct xrt_pose pose, const struct xrt_vec3 size, struct xrt_matrix_4x4 *result)
	Compute quad layer model matrix from xrt_pose and xrt_vec2 size. More...

void	math_matrix_4x4_inverse_view_projection (const struct xrt_matrix_4x4 view, const struct xrt_matrix_4x4 projection, struct xrt_matrix_4x4 *result)
	Compute inverse view projection matrix, using only the starting 3x3 block of the view. More...

void	math_matrix_4x4_projection_vulkan_infinite_reverse (const struct xrt_fov fov, float near_plane, struct xrt_matrix_4x4 result)
	Compute a projection matrix with settings for Vulkan, it will also have it's far plane at infinite and the NDC depth will be reversed. More...

void	math_pose_identity (struct xrt_pose *pose)
	Somewhat laboriously make an xrt_pose identity. More...

bool	math_pose_validate (const struct xrt_pose *pose)
	Check if this pose can be used in transformation operations. More...

void	math_pose_invert (const struct xrt_pose pose, struct xrt_pose outPose)
	Invert pose. More...

void	math_pose_from_isometry (const struct xrt_matrix_4x4 transform, struct xrt_pose result)
	Converts a (col-major) isometry into a pose. More...

void	math_pose_interpolate (const struct xrt_pose a, const struct xrt_pose b, float t, struct xrt_pose *outPose)
	Interpolated pose between poses `a` and `b` by lerping position and slerping orientation by t. More...

void	math_pose_transform (const struct xrt_pose transform, const struct xrt_pose pose, struct xrt_pose *outPose)
	Apply a rigid-body transformation to a pose. More...

void	math_pose_transform_point (const struct xrt_pose transform, const struct xrt_vec3 point, struct xrt_vec3 *out_point)
	Apply a rigid-body transformation to a point. More...

void	m_mat4_f64_identity (struct xrt_matrix_4x4_f64 *result)
	Initialize Matrix4x4 F64 with identity. More...

void	m_mat4_f64_invert (const struct xrt_matrix_4x4_f64 matrix, struct xrt_matrix_4x4_f64 result)
	Invert a Matrix4x4 F64. More...

void	m_mat4_f64_multiply (const struct xrt_matrix_4x4_f64 left, const struct xrt_matrix_4x4_f64 right, struct xrt_matrix_4x4_f64 *result)
	Multiply Matrix4x4 F64. More...

void	m_mat4_f64_orientation (const struct xrt_quat quat, struct xrt_matrix_4x4_f64 result)
	Initialize Matrix4x4 F64 with a orientation. More...

void	m_mat4_f64_model (const struct xrt_pose pose, const struct xrt_vec3 size, struct xrt_matrix_4x4_f64 *result)
	Initialize Matrix4x4 F64 with a pose and size that can be used as a model matrix. More...

void	m_mat4_f64_view (const struct xrt_pose pose, const struct xrt_vec3 size, struct xrt_matrix_4x4_f64 *result)
	Initialize Matrix4x4 F64 with a pose that can be used as a view martix. More...

static struct xrt_space_relation *	xrt_relation_chain::m_relation_chain_reserve (struct xrt_relation_chain *xrc)
	Reserve a step in the chain and return a pointer to the relation. More...

static void	xrt_relation_chain::m_relation_chain_push_relation (struct xrt_relation_chain xrc, const struct xrt_space_relation relation)
	Append a new relation. More...

static void	xrt_relation_chain::m_relation_chain_push_inverted_relation (struct xrt_relation_chain xrc, const struct xrt_space_relation relation)
	Append the inverse of the provided relation. More...

static void	xrt_relation_chain::m_relation_chain_push_pose (struct xrt_relation_chain xrc, const struct xrt_pose pose)
	Append a new pose as a fully tracked relation. More...

static void	xrt_relation_chain::m_relation_chain_push_pose_if_not_identity (struct xrt_relation_chain xrc, const struct xrt_pose pose)
	Append a new pose as a relation without velocity, if it is not the identity pose. More...

static void	xrt_relation_chain::m_relation_chain_push_inverted_pose_if_not_identity (struct xrt_relation_chain xrc, const struct xrt_pose pose)
	Append the inverse of a pose as a relation without velocity, if it is not the identity pose. More...

void	xrt_relation_chain::m_relation_chain_resolve (const struct xrt_relation_chain xrc, struct xrt_space_relation out_relation)
	Compute the equivalent single relation from flattening a relation chain. More...

Detailed Description

C interface to some transform-related math functions.

Macro Definition Documentation

◆ CLAMP

#define CLAMP	(	X,
		A,
		B
	)	(MIN(MAX((X), (A)), (B)))

#include <auxiliary/math/m_api.h>

X clamped to the range [A, B].

◆ MATH_GRAVITY_M_S2

#define MATH_GRAVITY_M_S2 (9.8066)

#include <auxiliary/math/m_api.h>

Standard gravity acceleration constant.

◆ MAX

#define MAX	(	A,
		B
	)	((A) > (B) ? (A) : (B))

#include <auxiliary/math/m_api.h>

Maximum of A and B.

◆ MIN

#define MIN	(	A,
		B
	)	((A) < (B) ? (A) : (B))

#include <auxiliary/math/m_api.h>

Minimum of A and B.

Function Documentation

◆ m_mat4_f64_identity()

void m_mat4_f64_identity ( struct xrt_matrix_4x4_f64 * result )

◆ m_mat4_f64_invert()

void m_mat4_f64_invert	(	const struct xrt_matrix_4x4_f64 *	matrix,
		struct xrt_matrix_4x4_f64 *	result
	)

Referenced by render_calc_time_warp_matrix().

◆ m_mat4_f64_model()

void m_mat4_f64_model	(	const struct xrt_pose *	pose,
		const struct xrt_vec3 *	size,
		struct xrt_matrix_4x4_f64 *	result
	)

◆ m_mat4_f64_multiply()

void m_mat4_f64_multiply	(	const struct xrt_matrix_4x4_f64 *	left,
		const struct xrt_matrix_4x4_f64 *	right,
		struct xrt_matrix_4x4_f64 *	result
	)

Referenced by render_calc_time_warp_matrix().

◆ m_mat4_f64_orientation()

void m_mat4_f64_orientation	(	const struct xrt_quat *	quat,
		struct xrt_matrix_4x4_f64 *	result
	)

Referenced by render_calc_time_warp_matrix().

◆ m_mat4_f64_view()

void m_mat4_f64_view	(	const struct xrt_pose *	pose,
		const struct xrt_vec3 *	size,
		struct xrt_matrix_4x4_f64 *	result
	)

◆ m_predict_relation()

void m_predict_relation	(	const struct xrt_space_relation *	rel,
		double	delta_s,
		struct xrt_space_relation *	out_rel
	)

#include <auxiliary/math/m_predict.h>

Using the given xrt_space_relation predicts a new xrt_space_relation delta_s into the future.

Assumes that angular velocity is relative to the space the relation is in, not relative to relation::pose.

◆ m_relation_chain_push_inverted_pose_if_not_identity()

static void m_relation_chain_push_inverted_pose_if_not_identity	(	struct xrt_relation_chain *	xrc,
		const struct xrt_pose *	pose
	)

inline

Append the inverse of a pose as a relation without velocity, if it is not the identity pose.

Validity flags stay the same, only the pose is inverted.

Referenced by qwerty_controller::qwerty_follow_hmd().

◆ m_relation_chain_push_inverted_relation()

static void m_relation_chain_push_inverted_relation	(	struct xrt_relation_chain *	xrc,
		const struct xrt_space_relation *	relation
	)

inline

Append the inverse of the provided relation.

Validity flags stay the same, only the pose and velocities are inverted.

◆ m_relation_chain_push_pose()

static void m_relation_chain_push_pose	(	struct xrt_relation_chain *	xrc,
		const struct xrt_pose *	pose
	)

inline

Append a new pose as a fully tracked relation.

This follows OpenXR conventions where a space that is purely an offset to another space is fully tracked in that space. Conceptually, a pose is only considered not fully tracked when it is related to an xrt_space_relation that is not fully tracked.

References xrt_relation_chain::m_relation_chain_push_relation(), and m_space_relation_from_pose().

Referenced by qwerty_controller::qwerty_follow_hmd().

◆ m_relation_chain_push_pose_if_not_identity()

static void m_relation_chain_push_pose_if_not_identity	(	struct xrt_relation_chain *	xrc,
		const struct xrt_pose *	pose
	)

inline

Append a new pose as a relation without velocity, if it is not the identity pose.

Referenced by CDeviceDriver_Monado::GetPose().

◆ m_relation_chain_push_relation()

static void m_relation_chain_push_relation	(	struct xrt_relation_chain *	xrc,
		const struct xrt_space_relation *	relation
	)

inline

Append a new relation.

References xrt_relation_chain::XRT_RELATION_CHAIN_CAPACITY.

Referenced by CDeviceDriver_Monado::GetPose(), and xrt_relation_chain::m_relation_chain_push_pose().

◆ m_relation_chain_reserve()

static struct xrt_space_relation * m_relation_chain_reserve ( struct xrt_relation_chain * xrc )

inline

Reserve a step in the chain and return a pointer to the relation.

Note: The data pointed to by the returned pointer is not initialized: you must populate it before using m_relation_chain_resolve

References xrt_relation_chain::XRT_RELATION_CHAIN_CAPACITY.

◆ m_relation_chain_resolve()

void m_relation_chain_resolve	(	const struct xrt_relation_chain *	xrc,
		struct xrt_space_relation *	out_relation
	)

Compute the equivalent single relation from flattening a relation chain.

The input chain is not modified.

Referenced by qwerty_controller::qwerty_follow_hmd().

◆ m_space_relation_from_pose()

static void m_space_relation_from_pose	(	const struct xrt_pose *	pose,
		bool	set_tracked,
		struct xrt_space_relation *	out_relation
	)

inlinestatic

#include <auxiliary/math/m_space.h>

Create an xrt_space_relation from a pose.

If set_tracked is false, only orientation and position valid flags are set.

Referenced by xrt_relation_chain::m_relation_chain_push_pose().

◆ m_space_relation_ident()

static void m_space_relation_ident ( struct xrt_space_relation * out_relation )

inlinestatic

#include <auxiliary/math/m_space.h>

Create an xrt_space_relation with only orientation and position valid flags.

◆ m_space_relation_interpolate()

void m_space_relation_interpolate	(	struct xrt_space_relation *	a,
		struct xrt_space_relation *	b,
		float	t,
		enum xrt_space_relation_flags	flags,
		struct xrt_space_relation *	out_relation
	)

#include <auxiliary/math/m_space.h>

Linearly interpolate between two relations a and b.

Uses slerp for their orientations. Sets flags in out_relation.

◆ math_compute_fovs()

bool math_compute_fovs	(	double	w_total,
		double	w_1,
		double	horizfov_total,
		double	h_total,
		double	h_1,
		double	vertfov_total,
		struct xrt_fov *	fov
	)

#include <auxiliary/math/m_api.h>

Perform the computations from "Computing Half-Fields-Of-View from Simpler Display Models", to get half-FOVs from things we can retrieve from other APIs.

The origin is in the lower-left corner of the display, so w_1 is the width to the left of CoP, and h_1 is the height below CoP.

If vertfov_total is set to 0, it will be computed from h_total.

Distances are in arbitrary but consistent units. Angles are in radians.

In the diagram below, treating it like a FOV for horizontal, the top angle is horizfov_total, the length of the bottom is w_total, and the distance between the vertical line and the left corner is w_1. Vertical is similar - h_1 is above the center line. The triangle need not be symmetrical, despite how the diagram looks.

              horizfov_total
                      *
angle_left (neg) -> / |  \ <- angle_right
                   /  |   \
                  /   |    \
                 /    |     \
                -------------
                [ w_1 ]
                [ --- w  --- ]
 
-------     --- |\
                |   \
            h_1 |      \ angle_up
h_total     ___ |-------* vertfov_total
                |      / angle_down (neg)
                |    /
                |  /
-------         |/

Returns: true if successful.

References math_solve_triangle().

◆ math_hash_string()

size_t math_hash_string	(	const char *	str_c,
		size_t	length
	)

#include <auxiliary/math/m_api.h>

Generate a hash value from the given string, trailing zero not included.

Hashing function used is not specified so no guarantee of staying the same between different versions of the software, or even when the same version is compiled on different platforms/libc++ as it might use std::hash.

◆ math_matrix_3x3_f64_from_plus_x_z()

void math_matrix_3x3_f64_from_plus_x_z	(	const struct xrt_vec3_f64 *	plus_x,
		const struct xrt_vec3_f64 *	plus_z,
		struct xrt_matrix_3x3_f64 *	result
	)

Input vectors should be normalized.

◆ math_matrix_3x3_f64_identity()

void math_matrix_3x3_f64_identity ( struct xrt_matrix_3x3_f64 * mat )

#include <auxiliary/math/m_api.h>

Initialize a double 3x3 matrix to the identity matrix.

See also: xrt_matrix_3x3

References xrt::auxiliary::math::map_matrix_3x3_f64().

◆ math_matrix_3x3_f64_transform_vec3_f64()

void math_matrix_3x3_f64_transform_vec3_f64	(	const struct xrt_matrix_3x3_f64 *	left,
		const struct xrt_vec3_f64 *	right,
		struct xrt_vec3_f64 *	result_out
	)

#include <auxiliary/math/m_api.h>

Transform a double vec3 by a 3x3 double matrix.

See also: xrt_matrix_3x3

References xrt::auxiliary::math::map_vec3_f64().

◆ math_matrix_3x3_from_quat()

void math_matrix_3x3_from_quat	(	const struct xrt_quat *	q,
		struct xrt_matrix_3x3 *	result_out
	)

#include <auxiliary/math/m_api.h>

Initialize a 3x3 matrix from a quaternion.

See also: xrt_matrix_3x3

◆ math_matrix_3x3_identity()

void math_matrix_3x3_identity ( struct xrt_matrix_3x3 * mat )

#include <auxiliary/math/m_api.h>

Initialize a 3x3 matrix to the identity matrix.

See also: xrt_matrix_3x3

References xrt::auxiliary::math::map_matrix_3x3().

Referenced by wmr_hmd_config_init_defaults().

◆ math_matrix_3x3_inverse()

void math_matrix_3x3_inverse	(	const struct xrt_matrix_3x3 *	in,
		struct xrt_matrix_3x3 *	result
	)

◆ math_matrix_3x3_multiply()

void math_matrix_3x3_multiply	(	const struct xrt_matrix_3x3 *	left,
		const struct xrt_matrix_3x3 *	right,
		struct xrt_matrix_3x3 *	result_out
	)

◆ math_matrix_3x3_rotation_from_isometry()

void math_matrix_3x3_rotation_from_isometry	(	const struct xrt_matrix_4x4 *	isometry,
		struct xrt_matrix_3x3 *	result
	)

◆ math_matrix_3x3_transform_vec3()

void math_matrix_3x3_transform_vec3	(	const struct xrt_matrix_3x3 *	left,
		const struct xrt_vec3 *	right,
		struct xrt_vec3 *	result_out
	)

#include <auxiliary/math/m_api.h>

Transform a vec3 by a 3x3 matrix.

See also: xrt_matrix_3x3

References xrt::auxiliary::math::map_vec3().

◆ math_matrix_3x3_transpose()

void math_matrix_3x3_transpose	(	const struct xrt_matrix_3x3 *	in,
		struct xrt_matrix_3x3 *	result
	)

◆ math_matrix_4x4_identity()

void math_matrix_4x4_identity ( struct xrt_matrix_4x4 * result )

◆ math_matrix_4x4_inverse()

void math_matrix_4x4_inverse	(	const struct xrt_matrix_4x4 *	in,
		struct xrt_matrix_4x4 *	result
	)

◆ math_matrix_4x4_inverse_view_projection()

void math_matrix_4x4_inverse_view_projection	(	const struct xrt_matrix_4x4 *	view,
		const struct xrt_matrix_4x4 *	projection,
		struct xrt_matrix_4x4 *	result
	)

◆ math_matrix_4x4_isometry_from_pose()

void math_matrix_4x4_isometry_from_pose	(	const struct xrt_pose *	pose,
		struct xrt_matrix_4x4 *	result
	)

Referenced by wmr_hmd_fill_slam_cams_calibration().

◆ math_matrix_4x4_isometry_from_rt()

void math_matrix_4x4_isometry_from_rt	(	const struct xrt_matrix_3x3 *	rotation,
		const struct xrt_vec3 *	translation,
		struct xrt_matrix_4x4 *	result
	)

All col-major matrices.

◆ math_matrix_4x4_isometry_inverse()

void math_matrix_4x4_isometry_inverse	(	const struct xrt_matrix_4x4 *	in,
		struct xrt_matrix_4x4 *	result
	)

◆ math_matrix_4x4_model()

void math_matrix_4x4_model	(	const struct xrt_pose *	pose,
		const struct xrt_vec3 *	size,
		struct xrt_matrix_4x4 *	result
	)

◆ math_matrix_4x4_multiply()

void math_matrix_4x4_multiply	(	const struct xrt_matrix_4x4 *	left,
		const struct xrt_matrix_4x4 *	right,
		struct xrt_matrix_4x4 *	result
	)

◆ math_matrix_4x4_projection_vulkan_infinite_reverse()

void math_matrix_4x4_projection_vulkan_infinite_reverse	(	const struct xrt_fov *	fov,
		float	near_plane,
		struct xrt_matrix_4x4 *	result
	)

◆ math_matrix_4x4_transform_vec3()

void math_matrix_4x4_transform_vec3	(	const struct xrt_matrix_4x4 *	left,
		const struct xrt_vec3 *	right,
		struct xrt_vec3 *	result_out
	)

#include <auxiliary/math/m_api.h>

Transform a vec3 by a 4x4 matrix, extending the vector with w = 1.0.

See also: xrt_matrix_4x4

◆ math_matrix_4x4_transpose()

void math_matrix_4x4_transpose	(	const struct xrt_matrix_4x4 *	in,
		struct xrt_matrix_4x4 *	result
	)

◆ math_matrix_4x4_view_from_pose()

void math_matrix_4x4_view_from_pose	(	const struct xrt_pose *	pose,
		struct xrt_matrix_4x4 *	result
	)

Referenced by comp_render_cs_layer().

◆ math_pose_from_isometry()

void math_pose_from_isometry	(	const struct xrt_matrix_4x4 *	transform,
		struct xrt_pose *	result
	)

Referenced by rift_s_fill_slam_cameras_calibration().

◆ math_pose_identity()

void math_pose_identity ( struct xrt_pose * pose )

Referenced by wmr_hmd_config_init_defaults().

◆ math_pose_interpolate()

void math_pose_interpolate	(	const struct xrt_pose *	a,
		const struct xrt_pose *	b,
		float	t,
		struct xrt_pose *	outPose
	)

◆ math_pose_invert()

void math_pose_invert	(	const struct xrt_pose *	pose,
		struct xrt_pose *	outPose
	)

OK if input and output are the same addresses.

Referenced by multi_create_tracking_override(), precompute_sensor_transforms(), and rift_s_fill_slam_cameras_calibration().

◆ math_pose_transform()

void math_pose_transform	(	const struct xrt_pose *	transform,
		const struct xrt_pose *	pose,
		struct xrt_pose *	outPose
	)

OK if input and output are the same addresses.

Referenced by precompute_sensor_transforms().

◆ math_pose_transform_point()

void math_pose_transform_point	(	const struct xrt_pose *	transform,
		const struct xrt_vec3 *	point,
		struct xrt_vec3 *	out_point
	)

The input point and output may be the same pointer.

See also: xrt_vec3

◆ math_pose_validate()

bool math_pose_validate ( const struct xrt_pose * pose )

◆ math_quat_ensure_normalized()

bool math_quat_ensure_normalized ( struct xrt_quat * inout )

Returns true if the quaternion was already normalized or was normalized after being found within a small float precision tolerance. Returns false if the quaternion was not at all normalized.

◆ math_quat_exp()

void math_quat_exp	(	const struct xrt_vec3 *	axis_angle,
		struct xrt_quat *	out_quat
	)

Useful for head tracking and pose-prediction.

See also: xrt_vec3

◆ math_quat_finite_difference()

void math_quat_finite_difference	(	const struct xrt_quat *	quat0,
		const struct xrt_quat *	quat1,
		float	dt,
		struct xrt_vec3 *	out_ang_vel
	)

quat1 is the orientation dt time after the orientation was quat0

out_ang_vel and dt share the same units of time, and out_ang_vel is be in radians per unit of time.

See also: xrt_vec3

◆ math_quat_from_angle_vector()

void math_quat_from_angle_vector	(	float	angle_rads,
		const struct xrt_vec3 *	vector,
		struct xrt_quat *	result
	)

See also: xrt_vec3

Referenced by svr_hmd_get_view_poses().

◆ math_quat_from_euler_angles()

void math_quat_from_euler_angles	(	const struct xrt_vec3 *	angles,
		struct xrt_quat *	result
	)

◆ math_quat_from_matrix_3x3()

void math_quat_from_matrix_3x3	(	const struct xrt_matrix_3x3 *	mat,
		struct xrt_quat *	result
	)

See also: xrt_matrix_3x3

◆ math_quat_from_plus_x_z()

void math_quat_from_plus_x_z	(	const struct xrt_vec3 *	plus_x,
		const struct xrt_vec3 *	plus_z,
		struct xrt_quat *	result
	)

Input vectors should be normalized.

See also: xrt_vec3

◆ math_quat_from_swing()

void math_quat_from_swing	(	const struct xrt_vec2 *	swing,
		struct xrt_quat *	result
	)

◆ math_quat_from_swing_twist()

void math_quat_from_swing_twist	(	const struct xrt_vec2 *	swing,
		const float	twist,
		struct xrt_quat *	result
	)

◆ math_quat_integrate_velocity()

void math_quat_integrate_velocity	(	const struct xrt_quat *	quat,
		const struct xrt_vec3 *	ang_vel,
		float	dt,
		struct xrt_quat *	result
	)

ang_vel and dt should share the same units of time, and the ang_vel vector should be in radians per unit of time.

See also: xrt_vec3

◆ math_quat_invert()

void math_quat_invert	(	const struct xrt_quat *	quat,
		struct xrt_quat *	out_quat
	)

◆ math_quat_len()

float math_quat_len ( const struct xrt_quat * quat )

Same as if it were a vec4.

◆ math_quat_ln()

void math_quat_ln	(	const struct xrt_quat *	quat,
		struct xrt_vec3 *	out_axis_angle
	)

Useful for head tracking and pose-prediction.

See also: xrt_vec3

Referenced by m_filter_euro_quat::m_filter_euro_quat_run().

◆ math_quat_normalize()

void math_quat_normalize ( struct xrt_quat * inout )

Referenced by hydra_device_parse_controller().

◆ math_quat_rotate()

void math_quat_rotate	(	const struct xrt_quat *	left,
		const struct xrt_quat *	right,
		struct xrt_quat *	result
	)

Referenced by precompute_sensor_transforms(), and rift_s_tracker_correct_pose_from_basalt().

◆ math_quat_rotate_derivative()

void math_quat_rotate_derivative	(	const struct xrt_quat *	quat,
		const struct xrt_vec3 *	deriv,
		struct xrt_vec3 *	result
	)

See also: xrt_vec3

Referenced by psmv_get_fusion_pose(), pssense_get_fusion_pose(), and rift_s_controller_get_fusion_pose().

◆ math_quat_rotate_vec3()

void math_quat_rotate_vec3	(	const struct xrt_quat *	left,
		const struct xrt_vec3 *	right,
		struct xrt_vec3 *	result
	)

See also: xrt_vec3

Referenced by rift_s_tracker_correct_pose_from_basalt().

◆ math_quat_slerp()

void math_quat_slerp	(	const struct xrt_quat *	left,
		const struct xrt_quat *	right,
		float	t,
		struct xrt_quat *	result
	)

◆ math_quat_to_swing_twist()

void math_quat_to_swing_twist	(	const struct xrt_quat *	in,
		struct xrt_vec2 *	out_swing,
		float *	out_twist
	)

References xrt::auxiliary::math::map_quat().

◆ math_quat_unrotate()

void math_quat_unrotate	(	const struct xrt_quat *	left,
		const struct xrt_quat *	right,
		struct xrt_quat *	result
	)

Removes left rotation from right.

Referenced by m_filter_euro_quat::m_filter_euro_quat_run().

◆ math_quat_validate()

bool math_quat_validate ( const struct xrt_quat * quat )

◆ math_quat_validate_within_1_percent()

bool math_quat_validate_within_1_percent ( const struct xrt_quat * quat )

◆ math_vec3_accum()

void math_vec3_accum	(	const struct xrt_vec3 *	additional,
		struct xrt_vec3 *	inAndOut
	)

Logically, *inAndOut += *additional OK if the two arguments are the same addresses.

◆ math_vec3_cross()

void math_vec3_cross	(	const struct xrt_vec3 *	l,
		const struct xrt_vec3 *	r,
		struct xrt_vec3 *	result
	)

◆ math_vec3_f64_cross()

void math_vec3_f64_cross	(	const struct xrt_vec3_f64 *	l,
		const struct xrt_vec3_f64 *	r,
		struct xrt_vec3_f64 *	result
	)

◆ math_vec3_f64_normalize()

void math_vec3_f64_normalize ( struct xrt_vec3_f64 * in )

◆ math_vec3_normalize()

void math_vec3_normalize ( struct xrt_vec3 * in )

References xrt::auxiliary::math::map_vec3().

◆ math_vec3_scalar_mul()

void math_vec3_scalar_mul	(	float	scalar,
		struct xrt_vec3 *	inAndOut
	)

Logically, *inAndOut *= scalar

◆ math_vec3_subtract()

void math_vec3_subtract	(	const struct xrt_vec3 *	subtrahend,
		struct xrt_vec3 *	inAndOut
	)

Logically, *inAndOut -= *subtrahend OK if the two arguments are the same addresses.

◆ math_vec3_translation_from_isometry()

void math_vec3_translation_from_isometry	(	const struct xrt_matrix_4x4 *	isometry,
		struct xrt_vec3 *	result
	)

◆ math_vec3_validate()

bool math_vec3_validate ( const struct xrt_vec3 * vec3 )

Files

Data Structures

Macros

Functions

Detailed Description

Macro Definition Documentation

◆ CLAMP

◆ MATH_GRAVITY_M_S2

◆ MAX

◆ MIN

Function Documentation

◆ m_mat4_f64_identity()

◆ m_mat4_f64_invert()

◆ m_mat4_f64_model()

◆ m_mat4_f64_multiply()

◆ m_mat4_f64_orientation()

◆ m_mat4_f64_view()

◆ m_predict_relation()

◆ m_relation_chain_push_inverted_pose_if_not_identity()

◆ m_relation_chain_push_inverted_relation()

◆ m_relation_chain_push_pose()

◆ m_relation_chain_push_pose_if_not_identity()

◆ m_relation_chain_push_relation()

◆ m_relation_chain_reserve()

◆ m_relation_chain_resolve()

◆ m_space_relation_from_pose()

◆ m_space_relation_ident()

◆ m_space_relation_interpolate()

◆ math_compute_fovs()

◆ math_hash_string()

◆ math_matrix_3x3_f64_from_plus_x_z()

◆ math_matrix_3x3_f64_identity()

◆ math_matrix_3x3_f64_transform_vec3_f64()

◆ math_matrix_3x3_from_quat()

◆ math_matrix_3x3_identity()

◆ math_matrix_3x3_inverse()

◆ math_matrix_3x3_multiply()

◆ math_matrix_3x3_rotation_from_isometry()

◆ math_matrix_3x3_transform_vec3()

◆ math_matrix_3x3_transpose()

◆ math_matrix_4x4_identity()

◆ math_matrix_4x4_inverse()

◆ math_matrix_4x4_inverse_view_projection()

◆ math_matrix_4x4_isometry_from_pose()

◆ math_matrix_4x4_isometry_from_rt()

◆ math_matrix_4x4_isometry_inverse()

◆ math_matrix_4x4_model()

◆ math_matrix_4x4_multiply()

◆ math_matrix_4x4_projection_vulkan_infinite_reverse()

◆ math_matrix_4x4_transform_vec3()

◆ math_matrix_4x4_transpose()

◆ math_matrix_4x4_view_from_pose()

◆ math_pose_from_isometry()

◆ math_pose_identity()

◆ math_pose_interpolate()

◆ math_pose_invert()

◆ math_pose_transform()

◆ math_pose_transform_point()

◆ math_pose_validate()

◆ math_quat_ensure_normalized()

◆ math_quat_exp()

◆ math_quat_finite_difference()

◆ math_quat_from_angle_vector()

◆ math_quat_from_euler_angles()

◆ math_quat_from_matrix_3x3()

◆ math_quat_from_plus_x_z()

◆ math_quat_from_swing()

◆ math_quat_from_swing_twist()

◆ math_quat_integrate_velocity()

◆ math_quat_invert()

◆ math_quat_len()

◆ math_quat_ln()

◆ math_quat_normalize()

◆ math_quat_rotate()

◆ math_quat_rotate_derivative()

◆ math_quat_rotate_vec3()

◆ math_quat_slerp()

◆ math_quat_to_swing_twist()

◆ math_quat_unrotate()

◆ math_quat_validate()