Data Structures
struct	htm_v3
	Cartesian coordinates for a point in R3. More...
struct	htm_sc
	Spherical coordinates (in degrees) for a point in S2. More...
Functions
HTM_INLINE enum htm_errcode	htm_v3_init (struct htm_v3 *out, double x, double y, double z)
	Stores the given cartesian coordinates in `out`.
HTM_INLINE enum htm_errcode	htm_sc_init (struct htm_sc *out, double lon_deg, double lat_deg)
	Stores the given spherical coordinates in `out`; coordinates are assumed to be in degrees.
HTM_INLINE void	htm_v3_add (struct htm_v3 out, const struct htm_v3 v1, const struct htm_v3 *v2)
	Stores the vector sum `v1 + v2` in `out`.
HTM_INLINE void	htm_v3_sub (struct htm_v3 out, const struct htm_v3 v1, const struct htm_v3 *v2)
	Stores the vector difference `v1 - v2` in `out`.
HTM_INLINE void	htm_v3_neg (struct htm_v3 out, const struct htm_v3 v)
	Stores the vector `v * -1` in `out`.
HTM_INLINE void	htm_v3_mul (struct htm_v3 out, const struct htm_v3 v, double s)
	Stores the vector-scalar product `v * s` in `out`.
HTM_INLINE void	htm_v3_div (struct htm_v3 out, const struct htm_v3 v, double s)
	Stores the vector-scalar quotient `v / s` in `out`.
HTM_INLINE double	htm_v3_dot (const struct htm_v3 v1, const struct htm_v3 v2)
	Returns the dot product of the 3-vectors `v1` and `v2`.
HTM_INLINE void	htm_v3_cwise_mul (struct htm_v3 out, const struct htm_v3 v1, const struct htm_v3 *v2)
	Stores the component-wise product of the 3-vectors `v1` and `v2` in `out`.
HTM_INLINE double	htm_v3_norm2 (const struct htm_v3 *v)
	Returns the squared norm of the 3-vector `v`, which must not be NULL.
HTM_INLINE double	htm_v3_norm (const struct htm_v3 *v)
	Returns the norm of the 3-vector `v`, which must not be NULL.
HTM_INLINE void	htm_v3_normalize (struct htm_v3 out, const struct htm_v3 v)
	Stores a normalized copy of `v` in `out`.
HTM_INLINE void	htm_v3_rcross (struct htm_v3 out, const struct htm_v3 v1, const struct htm_v3 *v2)
	Stores twice the vector cross product of `v1` and `v2` in `out`.
HTM_INLINE void	htm_v3_cross (struct htm_v3 out, const struct htm_v3 v1, const struct htm_v3 *v2)
	Stores the vector cross product of `v1` and `v2` in `out`.
enum htm_errcode	htm_v3_ne (struct htm_v3 north, struct htm_v3 east, const struct htm_v3 *v)
	Computes the N,E basis unit vectors at a position `v` on the unit sphere.
enum htm_errcode	htm_v3_tanrot (double angle, const struct htm_v3 v1, const struct htm_v3 *v2, double r)
	Computes the angle by which the normal of the plane defined by the origin, `v1` and `v2` should be rotated about the axis `v1 - v2`, such that the resulting plane is tangent to two small circles of radius `r` centered at `v1` and `v2`.
enum htm_errcode	htm_v3_rot (struct htm_v3 out, const struct htm_v3 v, const struct htm_v3 *k, double angle_deg)
	Rotates vector `v` around the axis `k` by the specified number of degrees.
enum htm_errcode	htm_v3_centroid (struct htm_v3 cen, const struct htm_v3 points, size_t n)
	Computes the normalized sum of the given list of vectors.
enum htm_errcode	htm_sc_tov3 (struct htm_v3 out, const struct htm_sc p)
	Converts the spherical coordinate pair `p` to a unit 3-vector and stores the results in `out`.
enum htm_errcode	htm_v3_tosc (struct htm_sc out, const struct htm_v3 v)
	Converts the 3-vector `v` to spherical coordinates and stores the results in `out`.

Function Documentation

HTM_INLINE enum htm_errcode htm_sc_init	(	struct htm_sc *	out,
		double	lon_deg,
		double	lat_deg
	)

Stores the given spherical coordinates in out; coordinates are assumed to be in degrees.

Returns:

HTM_ENANINF if any input coordinate is non-finite.
HTM_ELAT if lat is not in the [-90, 90] degree range.
HTM_ENULLPTR if out is NULL.
HTM_OK on success.

Definition at line 71 of file geometry.h.

References HTM_ELAT, HTM_ENANINF, HTM_ENULLPTR, HTM_ISSPECIAL, HTM_OK, htm_sc::lat, and htm_sc::lon.

enum htm_errcode htm_sc_tov3	(	struct htm_v3 *	out,
		const struct htm_sc *	p
	)

Converts the spherical coordinate pair p to a unit 3-vector and stores the results in out.

Returns:

HTM_ENULLPTR if out or p is NULL.
HTM_OK on success.

Definition at line 136 of file geometry.c.

References HTM_ENULLPTR, HTM_OK, HTM_RAD_PER_DEG, htm_sc::lat, htm_sc::lon, htm_v3::x, htm_v3::y, and htm_v3::z.

HTM_INLINE void htm_v3_add	(	struct htm_v3 *	out,
		const struct htm_v3 *	v1,
		const struct htm_v3 *	v2
	)

Stores the vector sum v1 + v2 in out.

Arguments must not be NULL pointers, but may alias.

Definition at line 90 of file geometry.h.

References htm_v3::x, htm_v3::y, and htm_v3::z.

Referenced by htm_s2cpoly_hull(), htm_s2cpoly_init(), htm_s2cpoly_pad(), htm_s2ellipse_init(), htm_s2ellipse_init2(), htm_tri_init(), and htm_v3_rot().

enum htm_errcode htm_v3_centroid	(	struct htm_v3 *	cen,
		const struct htm_v3 *	points,
		size_t	n
	)

Computes the normalized sum of the given list of vectors.

Returns:

HTM_ENULLPTR if cen or points is NULL.
HTM_ELEN if n == 0.
HTM_OK on success.

Definition at line 115 of file geometry.c.

References HTM_ELEN, HTM_ENULLPTR, HTM_OK, htm_v3_normalize(), htm_v3::x, htm_v3::y, and htm_v3::z.

Referenced by htm_s2cpoly_hull(), and htm_v3_convex().

HTM_INLINE void htm_v3_cross	(	struct htm_v3 *	out,
		const struct htm_v3 *	v1,
		const struct htm_v3 *	v2
	)

Stores the vector cross product of v1 and v2 in out.

Arguments must not be NULL pointers, but may alias.

Definition at line 221 of file geometry.h.

References htm_v3::x, htm_v3::y, and htm_v3::z.

Referenced by htm_v3_angsep(), and htm_v3_edgedist2().

HTM_INLINE void htm_v3_cwise_mul	(	struct htm_v3 *	out,
		const struct htm_v3 *	v1,
		const struct htm_v3 *	v2
	)

Stores the component-wise product of the 3-vectors v1 and v2 in out.

Arguments must not be NULL pointers, but may alias.

Definition at line 157 of file geometry.h.

References htm_v3::x, htm_v3::y, and htm_v3::z.

Referenced by htm_s2ellipse_init().

HTM_INLINE void htm_v3_div	(	struct htm_v3 *	out,
		const struct htm_v3 *	v,
		double	s
	)

Stores the vector-scalar quotient v / s in out.

Arguments must not be NULL pointers, but may alias.

Definition at line 136 of file geometry.h.

References htm_v3::x, htm_v3::y, and htm_v3::z.

Referenced by htm_s2cpoly_hull(), and htm_v3_convex().

HTM_INLINE double htm_v3_dot	(	const struct htm_v3 *	v1,
		const struct htm_v3 *	v2
	)

Returns the dot product of the 3-vectors v1 and v2.

Arguments must not be NULL pointers, but may alias.

Definition at line 148 of file geometry.h.

References htm_v3::x, htm_v3::y, and htm_v3::z.

Referenced by htm_s2cpoly_area(), htm_s2cpoly_cv3(), htm_s2cpoly_hull(), htm_s2cpoly_init(), htm_s2cpoly_pad(), htm_v3_angsep(), htm_v3_convex(), htm_v3_edgedist2(), htm_v3_id(), and htm_v3_rot().

HTM_INLINE enum htm_errcode htm_v3_init	(	struct htm_v3 *	out,
		double	x,
		double	y,
		double	z
	)

Stores the given cartesian coordinates in out.

Returns:

HTM_ENANINF if x, y, or z is non-finite.
HTM_ENULLPTR if out is NULL.
HTM_OK on success.

Definition at line 45 of file geometry.h.

References HTM_ENANINF, HTM_ENULLPTR, HTM_ISSPECIAL, HTM_OK, htm_v3::x, htm_v3::y, and htm_v3::z.

HTM_INLINE void htm_v3_mul	(	struct htm_v3 *	out,
		const struct htm_v3 *	v,
		double	s
	)

Stores the vector-scalar product v * s in out.

Arguments must not be NULL pointers, but may alias.

Definition at line 124 of file geometry.h.

References htm_v3::x, htm_v3::y, and htm_v3::z.

Referenced by htm_s2ellipse_init2(), and htm_v3_rot().

enum htm_errcode htm_v3_ne	(	struct htm_v3 *	north,
		struct htm_v3 *	east,
		const struct htm_v3 *	v
	)

Computes the N,E basis unit vectors at a position v on the unit sphere.

Returns:

HTM_ENULLPTR if any argument is NULL.
HTM_EZERONORM if v has a norm of 0.
HTM_OK on success.

Definition at line 24 of file geometry.c.

References HTM_ENULLPTR, HTM_EZERONORM, HTM_OK, htm_v3_norm2(), htm_v3_normalize(), htm_v3_rcross(), htm_v3::x, htm_v3::y, and htm_v3::z.

Referenced by htm_s2cpoly_box(), htm_s2cpoly_ngon(), and htm_s2ellipse_init2().

HTM_INLINE void htm_v3_neg	(	struct htm_v3 *	out,
		const struct htm_v3 *	v
	)

Stores the vector v * -1 in out.

Arguments must not be NULL pointers, but may alias.

Definition at line 114 of file geometry.h.

References htm_v3::x, htm_v3::y, and htm_v3::z.

Referenced by htm_s2cpoly_init(), and htm_s2cpoly_pad().

HTM_INLINE double htm_v3_norm2 ( const struct htm_v3 * v )

Returns the squared norm of the 3-vector v, which must not be NULL.

Equivalent to htm_v3_dot(v, v).

Definition at line 169 of file geometry.h.

References htm_v3::x, htm_v3::y, and htm_v3::z.

Referenced by htm_s2cpoly_box(), htm_s2cpoly_hull(), htm_s2cpoly_ngon(), htm_v3_convex(), htm_v3_edgedist2(), htm_v3_ne(), and htm_v3_norm().

HTM_INLINE void htm_v3_normalize	(	struct htm_v3 *	out,
		const struct htm_v3 *	v
	)

Stores a normalized copy of v in out.

Arguments must not be NULL pointers, but may alias.

Definition at line 184 of file geometry.h.

References htm_v3_norm(), htm_v3::x, htm_v3::y, and htm_v3::z.

Referenced by htm_s2cpoly_box(), htm_s2cpoly_line(), htm_s2cpoly_ngon(), htm_s2cpoly_pad(), htm_s2ellipse_init(), htm_tri_init(), htm_v3_centroid(), and htm_v3_ne().

HTM_INLINE void htm_v3_rcross	(	struct htm_v3 *	out,
		const struct htm_v3 *	v1,
		const struct htm_v3 *	v2
	)

Stores twice the vector cross product of v1 and v2 in out.

Arguments must not be NULL pointers, but may alias.

This is equivalent to the cross product of v2 + v1 and v2 - v1, and is more robust than htm_v3_cross() for nearly identical input unit vectors. This is because when v1 and v2 are nearly identical, the evaluation of v2 - v1 is exact and, for unit v1 and v2, v1 + v2 is perpendicular to v2 - v1.

Definition at line 203 of file geometry.h.

References htm_v3::x, htm_v3::y, and htm_v3::z.

Referenced by htm_s2cpoly_area(), htm_s2cpoly_box(), htm_s2cpoly_hull(), htm_s2cpoly_init(), htm_s2cpoly_line(), htm_s2cpoly_pad(), htm_v3_convex(), htm_v3_id(), htm_v3_ne(), and htm_v3_rot().

enum htm_errcode htm_v3_rot	(	struct htm_v3 *	out,
		const struct htm_v3 *	v,
		const struct htm_v3 *	k,
		double	angle_deg
	)

Rotates vector v around the axis k by the specified number of degrees.

Returns:

HTM_ENULLPTR if out, v or k is NULL.
HTM_EZERONORM if k has a norm of 0.
HTM_OK on success.

Definition at line 85 of file geometry.c.

References HTM_ENULLPTR, HTM_EZERONORM, HTM_OK, HTM_RAD_PER_DEG, htm_v3_add(), htm_v3_dot(), htm_v3_mul(), htm_v3_norm(), and htm_v3_rcross().

Referenced by htm_s2cpoly_box(), htm_s2cpoly_line(), and htm_s2cpoly_pad().

HTM_INLINE void htm_v3_sub	(	struct htm_v3 *	out,
		const struct htm_v3 *	v1,
		const struct htm_v3 *	v2
	)

Stores the vector difference v1 - v2 in out.

Arguments must not be NULL pointers, but may alias.

Definition at line 102 of file geometry.h.

References htm_v3::x, htm_v3::y, and htm_v3::z.

Referenced by htm_s2cpoly_line(), htm_s2cpoly_pad(), and htm_s2ellipse_init2().

enum htm_errcode htm_v3_tanrot	(	double *	angle,
		const struct htm_v3 *	v1,
		const struct htm_v3 *	v2,
		double	r
	)

Computes the angle by which the normal of the plane defined by the origin, v1 and v2 should be rotated about the axis v1 - v2, such that the resulting plane is tangent to two small circles of radius r centered at v1 and v2.

Note that v1 and v2 must be unit vectors!

Returns:

HTM_ENULLPTR if angle, v1 or v2 is NULL.
HTM_EDEGEN if v1 is too close to v2.
HTM_EANG if r is negative or too large.
HTM_OK on success.

Definition at line 54 of file geometry.c.

References HTM_DEG_PER_RAD, HTM_EANG, HTM_EDEGEN, HTM_ENULLPTR, HTM_OK, HTM_RAD_PER_DEG, and htm_v3_angsep().

Referenced by htm_s2cpoly_line(), and htm_s2cpoly_pad().

enum htm_errcode htm_v3_tosc	(	struct htm_sc *	out,
		const struct htm_v3 *	v
	)

Converts the 3-vector v to spherical coordinates and stores the results in out.

The vector v is not required to have unit norm.

Returns:

HTM_ENULLPTR if out or v is NULL.
HTM_OK on success.

Definition at line 152 of file geometry.c.

References htm_clamp(), HTM_DEG_PER_RAD, HTM_ENULLPTR, HTM_OK, htm_sc::lat, htm_sc::lon, htm_v3::x, htm_v3::y, and htm_v3::z.

Data Structures

Functions

Function Documentation