YAC: src/core/geometry.h File Reference

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#include "config.h"
#include <math.h>
#include <float.h>
#include "basic_grid.h"
#include "grid_cell.h"
#include "utils_core.h"

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Data Structures
struct	sin_cos_angle

struct	bounding_circle

struct	yac_circle

Macros
#define	YAC_RAD (0.01745329251994329576923690768489)

#define	yac_angle_tol (1e-9)

#define	yac_sq_angle_tol (1e-9 * 1e-9)

#define	yac_cos_angle_tol (0.9999999999999999995)

#define	yac_angle_low_tol (1e-11)

#define	yac_cos_angle_low_tol (1.0)

Enumerations
enum	yac_circle_type { GREAT_CIRCLE = YAC_GREAT_CIRCLE_EDGE , LAT_CIRCLE = YAC_LAT_CIRCLE_EDGE , LON_CIRCLE = YAC_LON_CIRCLE_EDGE , POINT }

Functions
int	yac_point_in_cell (double point_coords[3], struct yac_grid_cell cell)

int	yac_point_in_cell2 (double point_coords[3], struct yac_grid_cell cell, struct bounding_circle bnd_circle)

static double	get_angle (double a_lon, double b_lon)

static double	get_angle_deg (double a_lon, double b_lon)

int	yac_intersect_vec (enum yac_edge_type edge_type_a, double const a[3], double const b[3], enum yac_edge_type edge_type_b, double const c[3], double const d[3], double p[3], double q[3])

void	yac_get_cell_bounding_circle (struct yac_grid_cell cell, struct bounding_circle *bnd_circle)

int	yac_extents_overlap (struct bounding_circle extent_a, struct bounding_circle extent_b)

static double	sq_len_diff_vec (double const a[3], double const b[3])
	computes square of the lenght of the vector ab

static double	compute_sq_crd (struct sin_cos_angle angle)

static int	yac_point_in_bounding_circle_vec (double point_vector[3], struct bounding_circle *bnd_circle)

static double	clamp_abs_one (double val)

static void	compute_sin_cos (double angle, double sin_value, double cos_value)

static void	LLtoXYZ (double lon, double lat, double p_out[])

static void	LLtoXYZ_deg (double lon, double lat, double p_out[])

static void	XYZtoLL (double const p_in[], double lon, double lat)

static double	det2_kahan (double a, double b, double c, double d)

static void	crossproduct_kahan (double const a[], double const b[], double cross[])

static void	crossproduct_d (const double a[], const double b[], double cross[])

static double	get_vector_angle (double const a[3], double const b[3])

static struct sin_cos_angle	sin_cos_angle_new (double sin, double cos)

static struct sin_cos_angle	get_vector_angle_2 (double const a[3], double const b[3])

static int	compare_angles (struct sin_cos_angle a, struct sin_cos_angle b)

static double	sin_cos_angle_to_dble (struct sin_cos_angle angle)

static struct sin_cos_angle	sum_angles_no_check (struct sin_cos_angle a, struct sin_cos_angle b)

static int	sum_angles (struct sin_cos_angle a, struct sin_cos_angle b, struct sin_cos_angle *restrict sum)

static struct sin_cos_angle	sub_angles_no_check (struct sin_cos_angle a, struct sin_cos_angle b)

static int	sub_angles (struct sin_cos_angle a, struct sin_cos_angle b, struct sin_cos_angle *restrict sub)

static double	compute_angle (struct sin_cos_angle angle)
	return angles in the range of [0;2PI[

static struct sin_cos_angle	half_angle (struct sin_cos_angle angle)

static struct sin_cos_angle	quarter_angle (struct sin_cos_angle angle)

static int	points_are_identically (double const a, double const b)

static int	compare_coords (double const a, double const b)

static void	normalise_vector (double v[])

static void	rotate_vector2 (double axis[], struct sin_cos_angle angle, double v_in[], double v_out[])

static void	rotate_vector (double axis[], double angle, double v_in[], double v_out[])

void	yac_triangulate_cell (struct yac_grid_cell cell, size_t start_corner, struct yac_grid_cell *triangles)

void	yac_triangulate_cell_indices (size_t const corner_indices, size_t num_corners, size_t start_corner, size_t(triangle_indices)[3])

void	yac_compute_bnd_triangle (double *vertices, size_t num_vertices, double triangle[][3], size_t num_tests)

int	yac_circle_intersect (struct yac_circle a, struct yac_circle b, double p[3], double q[3])

int	yac_point_on_edge (double p[3], double const a[3], double const b[3], enum yac_circle_type circle_type)

Variables
static const struct sin_cos_angle	SIN_COS_ZERO = {0.0, 1.0}

static const struct sin_cos_angle	SIN_COS_TOL = {yac_angle_tol, yac_cos_angle_tol}

static const struct sin_cos_angle	SIN_COS_LOW_TOL = {yac_angle_low_tol, yac_cos_angle_low_tol}

static const struct sin_cos_angle	SIN_COS_M_PI_2 = {1.0, 0.0}

static const struct sin_cos_angle	SIN_COS_M_PI = {0.0, -1.0}

static const struct sin_cos_angle	SIN_COS_7_M_PI_4 = {-0.707106781186547524401, +0.707106781186547524401}

Macro Definition Documentation

◆ yac_angle_low_tol

#define yac_angle_low_tol (1e-11)

Definition at line 29 of file geometry.h.

◆ yac_angle_tol

#define yac_angle_tol (1e-9)

Definition at line 26 of file geometry.h.

◆ yac_cos_angle_low_tol

#define yac_cos_angle_low_tol (1.0)

Definition at line 30 of file geometry.h.

◆ yac_cos_angle_tol

#define yac_cos_angle_tol (0.9999999999999999995)

Definition at line 28 of file geometry.h.

◆ YAC_RAD

#define YAC_RAD (0.01745329251994329576923690768489)

Definition at line 22 of file geometry.h.

◆ yac_sq_angle_tol

#define yac_sq_angle_tol (1e-9 * 1e-9)

Definition at line 27 of file geometry.h.

Enumeration Type Documentation

◆ yac_circle_type

enum yac_circle_type

Enumerator
GREAT_CIRCLE
LAT_CIRCLE
LON_CIRCLE
POINT

Definition at line 59 of file geometry.h.

Function Documentation

◆ clamp_abs_one()

static double clamp_abs_one ( double val )

inlinestatic

Definition at line 208 of file geometry.h.

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◆ compare_angles()

static int compare_angles	(	struct sin_cos_angle	a,
		struct sin_cos_angle	b )

inlinestatic

Definition at line 389 of file geometry.h.

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◆ compare_coords()

static int compare_coords	(	double const *	a,
		double const *	b )

inlinestatic

compares two 3d coordinates (vectors need to have a length of 1.0)

Parameters

[in]	a	coordinates of point a
[in]	b	coordinates of point b

Returns: 0 if points are identical, otherwise -1 or 1 depending on their relation

Definition at line 623 of file geometry.h.

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◆ compute_angle()

static double compute_angle ( struct sin_cos_angle angle )

inlinestatic

return angles in the range of [0;2PI[

Definition at line 533 of file geometry.h.

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◆ compute_sin_cos()

static void compute_sin_cos	(	double	angle,
		double *	sin_value,
		double *	cos_value )

inlinestatic

compute the sine and cosine of a provided angle in RAD (avoids values close to zero and ensures that the result is in the range [-1,1])

Parameters

[in]	angle	angle in the range of [-PI;PI]
[out]	sin_value
[out]	cos_value

Definition at line 220 of file geometry.h.

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◆ compute_sq_crd()

static double compute_sq_crd ( struct sin_cos_angle angle )

inlinestatic

Definition at line 185 of file geometry.h.

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◆ crossproduct_d()

static void crossproduct_d	(	const double	a[],
		const double	b[],
		double	cross[] )

inlinestatic

for small angles <= 1e-?8? the crossproduct is inaccurate
use crossproduct_kahan for these cases

Definition at line 312 of file geometry.h.

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◆ crossproduct_kahan()

static void crossproduct_kahan	(	double const	a[],
		double const	b[],
		double	cross[] )

inlinestatic

Definition at line 297 of file geometry.h.

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◆ det2_kahan()

static double det2_kahan	(	double	a,
		double	b,
		double	c,
		double	d )

inlinestatic

Definition at line 290 of file geometry.h.

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◆ get_angle()

static double get_angle	(	double	a_lon,
		double	b_lon )

inlinestatic

computes the angle between two longitude coordinates (in rad)
takes into account that longitude have a period of 2 pi

Parameters

[in]	a_lon
[in]	b_lon

Returns: angle between both coordinates (in rad)

Definition at line 110 of file geometry.h.

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◆ get_angle_deg()

static double get_angle_deg	(	double	a_lon,
		double	b_lon )

inlinestatic

computes the angle between two longitude coordinates (in deg)
takes into account that longitude have a period of 360

Parameters

[in]	a_lon
[in]	b_lon

Returns: angle between both coordinates (in rad)

Definition at line 126 of file geometry.h.

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◆ get_vector_angle()

static double get_vector_angle	(	double const	a[3],
		double const	b[3] )

inlinestatic

computes the great circle distance in rad for two points given in xyz coordinates taken from http://johnblackburne.blogspot.de/2012/05/angle-between-two-3d-vectors.html

Parameters

[in]	a	point coordinates of point a
[in]	b	point coordinates of point b

Returns: great circle distance in rad between both points

Definition at line 329 of file geometry.h.

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◆ get_vector_angle_2()

static struct sin_cos_angle get_vector_angle_2	(	double const	a[3],
		double const	b[3] )

inlinestatic

Definition at line 376 of file geometry.h.

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◆ half_angle()

static struct sin_cos_angle half_angle ( struct sin_cos_angle angle )

inlinestatic

computes angle / 2 The basic idea is to imagin angle being a vector v with (cos(x); sin(x)) and w being a vector with (1.0; 0.0). The normalised sum of v and w gives us v_h with (cos(x/2); sin(x/2)). For quadrants 2, 3, and 4 we have to apply some little tricks for higher accuracy.

Definition at line 561 of file geometry.h.

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◆ LLtoXYZ()

static void LLtoXYZ	(	double	lon,
		double	lat,
		double	p_out[] )

inlinestatic

converts lon-lat coordinates into xyz ones

Further information: http://en.wikipedia.org/wiki/List_of_common_coordinate_transformations

Parameters

[in]	lon	longitude coordinates in radian
[in]	lat	latitude coordinates in radian
[out]	p_out	xyz coordinates

Definition at line 249 of file geometry.h.

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◆ LLtoXYZ_deg()

static void LLtoXYZ_deg	(	double	lon,
		double	lat,
		double	p_out[] )

inlinestatic

converts lon-lat coordinates into xyz ones

Parameters

[in]	lon	longitude coordinates in deg
[in]	lat	latitude coordinates in deg
[out]	p_out	xyz coordinates

Definition at line 269 of file geometry.h.

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◆ normalise_vector()

static void normalise_vector ( double v[] )

inlinestatic

normalises a vector

Definition at line 650 of file geometry.h.

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◆ points_are_identically()

static int points_are_identically	(	double const *	a,
		double const *	b )

inlinestatic

determines whether two given points are (nearly) identically

Parameters

[in]	a	point coordinates of point a
[in]	b	point coordinates of point b

Returns: true if both points are (nearly) identically

Definition at line 609 of file geometry.h.

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◆ quarter_angle()

static struct sin_cos_angle quarter_angle ( struct sin_cos_angle angle )

inlinestatic

computes angle / 4 I derived it based on half_angle

Definition at line 578 of file geometry.h.

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◆ rotate_vector()

static void rotate_vector	(	double	axis[],
		double	angle,
		double	v_in[],
		double	v_out[] )

inlinestatic

rotate vector v_in around the given axis by a given angle

Parameters

[in]	axis	axis around which v_in is to rotated
[in]	angle	rotation angle
[in]	v_in	vector to be rotated
[out]	v_out	rotated vector

Definition at line 693 of file geometry.h.

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◆ rotate_vector2()

static void rotate_vector2	(	double	axis[],
		struct sin_cos_angle	angle,
		double	v_in[],
		double	v_out[] )

inlinestatic

rotate vector v_in around the given axis by a given angle

Parameters

[in]	axis	axis around which v_in is to rotated
[in]	angle	rotation angle
[in]	v_in	vector to be rotated
[out]	v_out	rotated vector

Definition at line 665 of file geometry.h.

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◆ sin_cos_angle_new()

static struct sin_cos_angle sin_cos_angle_new	(	double	sin,
		double	cos )

inlinestatic

Definition at line 366 of file geometry.h.

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◆ sin_cos_angle_to_dble()

static double sin_cos_angle_to_dble ( struct sin_cos_angle angle )

inlinestatic

this routine converts a struct sin_cos_angle into a double, which allows to easily compare angles 0: 0 <= angle < PI/4 => ret = 0 * M_SQRT1_2 + sin(angle) 1: PI/4 <= angle < 3*PI/4 => ret = 2 * M_SQRT1_2 - cos(angle) 2: 3*PI/4 <= angle < 5*PI/4 => ret = 4 * M_SQRT1_2 - sin(angle) 3: 5*PI/4 <= angle < 7*PI/4 => ret = 6 * M_SQRT1_2 + cos(angle) 4: 7*PI/4 <= angle < 2*PI => ret = 8 * M_SQRT1_2 + sin(angle)

Definition at line 466 of file geometry.h.

◆ sq_len_diff_vec()

static double sq_len_diff_vec	(	double const	a[3],
		double const	b[3] )

inlinestatic

computes square of the lenght of the vector ab

Definition at line 180 of file geometry.h.

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◆ sub_angles()

static int sub_angles	(	struct sin_cos_angle	a,
		struct sin_cos_angle	b,
		struct sin_cos_angle *restrict	sub )

inlinestatic

computes (a-b), if (a-b) <= 0, the result is (a-b+2*PI) a and be have to be in the range [0;2*PI[

Returns: 1 if (a-b) < 0

Definition at line 519 of file geometry.h.

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◆ sub_angles_no_check()

static struct sin_cos_angle sub_angles_no_check	(	struct sin_cos_angle	a,
		struct sin_cos_angle	b )

inlinestatic

computes (a-b), if (a-b) < 0, the result is (a-b+2*PI) a and be have to be in the range [0;2*PI[

Definition at line 509 of file geometry.h.

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◆ sum_angles()

static int sum_angles	(	struct sin_cos_angle	a,
		struct sin_cos_angle	b,
		struct sin_cos_angle *restrict	sum )

inlinestatic

computes (a+b), if (a+b) >= 2*PI, the result is (a+b-2*PI) a and be have to be in the range [0;2*PI[

Returns: 1 if (a+b) is >= 2*PI

Definition at line 495 of file geometry.h.

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◆ sum_angles_no_check()

static struct sin_cos_angle sum_angles_no_check	(	struct sin_cos_angle	a,
		struct sin_cos_angle	b )

inlinestatic

computes (a+b), if (a+b) >= 2*PI, the result is (a+b-2*PI) a and be have to be in the range [0;2*PI[

Definition at line 485 of file geometry.h.

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◆ XYZtoLL()

static void XYZtoLL	(	double const	p_in[],
		double *	lon,
		double *	lat )

inlinestatic

converts lon-lat coordinates into xyz ones

Further information: http://en.wikipedia.org/wiki/List_of_common_coordinate_transformations

Parameters

[in]	p_in	xyz coordinates
[out]	lon	longitude coordinate in radian
[out]	lat	latitude coordinate in radian

Definition at line 283 of file geometry.h.

◆ yac_circle_intersect()

int yac_circle_intersect	(	struct yac_circle	a,
		struct yac_circle	b,
		double	p[3],
		double	q[3] )

Definition at line 266 of file intersection.c.

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◆ yac_compute_bnd_triangle()

void yac_compute_bnd_triangle	(	double *	vertices,
		size_t	num_vertices,
		double	triangle[][3],
		size_t	num_tests )

computes a spherical triangle that contains all given vertices, the algorithm tries to minimise the size of the triangle

Parameters

[in]	vertices	vertices that are supposed to be within the triangle
[in]	num_vertices	number of vertices in vertices
[out]	triangle	bounding triangle
[in]	num_tests	with increasing number of tests computation time and chance of smaller bounding triangle increases

Remarks: num_tests has to be > 0

Definition at line 99 of file bnd_triangle.c.

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◆ yac_extents_overlap()

int yac_extents_overlap	(	struct bounding_circle *	extent_a,
		struct bounding_circle *	extent_b )

checks whether two extents overlap

Parameters

[in]	extent_a	bounding circle
[in]	extent_b	bounding circle

Returns: 0 if the bounding circles do not overlap

Definition at line 533 of file bnd_circle.c.

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◆ yac_get_cell_bounding_circle()

void yac_get_cell_bounding_circle	(	struct yac_grid_cell	cell,
		struct bounding_circle *	bnd_circle )

gets the bounding circle for a grid cell

Parameters

[in]	cell	grid cell (coordinates have to be in radian)
[out]	bnd_circle	bounding circle of the grid cell

Definition at line 422 of file bnd_circle.c.

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◆ yac_intersect_vec()

int yac_intersect_vec	(	enum yac_edge_type	edge_type_a,
		double const	a[3],
		double const	b[3],
		enum yac_edge_type	edge_type_b,
		double const	c[3],
		double const	d[3],
		double	p[3],
		double	q[3] )

computes the intersection points of two edges

Parameters

[in]	edge_type_a	type of edge a
[in]	a	first point of edge a
[in]	b	second point of edge a
[in]	edge_type_b	type of edge b
[in]	c	first point of edge b
[in]	d	second point of edge b
[out]	p	first intersection point
[out]	q	second intersection point

Returns: 0 if the intersection points are neither on edge a or b
-1 if the two circles do not intersect
1st bit will be set if p is on edge a
2nd bit will be set if q is on edge a
3rd bit will be set if p is on edge b
4th bit will be set if q is on edge b
5th bit will be set if both circles are identically

Remarks: if -1 is returned neither p or q is set; if the two circles only have one intersection point, p and q will be identically, but only the p bits will be set

Definition at line 763 of file intersection.c.

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◆ yac_point_in_bounding_circle_vec()

static int yac_point_in_bounding_circle_vec	(	double	point_vector[3],
		struct bounding_circle *	bnd_circle )

inlinestatic

checks whether a point is within a bounding circle

Parameters

[in]	point_vector	point to be checked
[in]	bnd_circle	bounding circle

Returns: 0 if point is not within the bounding circle

Definition at line 197 of file geometry.h.

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◆ yac_point_in_cell()

int yac_point_in_cell	(	double	point_coords[3],
		struct yac_grid_cell	cell )

checks whether a given point is within a given cell

Parameters

[in]	point_coords
[in]	cell

Returns: 0 if the point is not in the cell

Definition at line 465 of file check_overlap.c.

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◆ yac_point_in_cell2()

int yac_point_in_cell2	(	double	point_coords[3],
		struct yac_grid_cell	cell,
		struct bounding_circle	bnd_circle )

checks whether a given point is within a given cell

Parameters

[in]	point_coords
[in]	cell
[in]	bnd_circle

Returns: 0 if the point is not in the cell

Definition at line 474 of file check_overlap.c.

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◆ yac_point_on_edge()

int yac_point_on_edge	(	double	p[3],
		double const	a[3],
		double const	b[3],
		enum yac_circle_type	circle_type )

Definition at line 860 of file intersection.c.

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◆ yac_triangulate_cell()

void yac_triangulate_cell	(	struct yac_grid_cell	cell,
		size_t	start_corner,
		struct yac_grid_cell *	triangles )

splits given cell into triangles

Parameters

[in]	cell	cell to be triangulated
[in]	start_corner	start algorithm at corner with this index (0 <= start_corner < n; with n being number of cell corners)
[out]	triangles	triangles that are the result of the triangulation

Remarks: the user needs to provide (n-2) initialised grid_cells for the argument triangles (n being the number of cell corners of the cell); this routine currently only works for convex grid cells; the algorithm ignores that actual edge types for cells with more than 3 corners and assumes them to be great circle edges

Definition at line 66 of file grid_cell.c.

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◆ yac_triangulate_cell_indices()

void yac_triangulate_cell_indices	(	size_t const *	corner_indices,
		size_t	num_corners,
		size_t	start_corner,
		size_t(*)	triangle_indices[3] )

splits given indices of a cell into triangles

Parameters

[in]	corner_indices	cell corner indices to be triangulated
[in]	num_corners	number of corners of the cell
[in]	start_corner	start algorithm at corner with this index (0 <= start_corner < n; with n being number of cell corners)
[out]	triangle_indices	triangle indices that are the result of the triangulation

Remarks: the user needs to provide provide an array of size 3*(num_corners-2) for the argument triangle_indices

Definition at line 144 of file grid_cell.c.

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Variable Documentation

◆ SIN_COS_7_M_PI_4

const struct sin_cos_angle SIN_COS_7_M_PI_4 = {-0.707106781186547524401, +0.707106781186547524401}

static

Definition at line 42 of file geometry.h.

◆ SIN_COS_LOW_TOL

const struct sin_cos_angle SIN_COS_LOW_TOL = {yac_angle_low_tol, yac_cos_angle_low_tol}

static

Definition at line 38 of file geometry.h.

◆ SIN_COS_M_PI

const struct sin_cos_angle SIN_COS_M_PI = {0.0, -1.0}

static

Definition at line 41 of file geometry.h.

◆ SIN_COS_M_PI_2

const struct sin_cos_angle SIN_COS_M_PI_2 = {1.0, 0.0}

static

Definition at line 40 of file geometry.h.

◆ SIN_COS_TOL

const struct sin_cos_angle SIN_COS_TOL = {yac_angle_tol, yac_cos_angle_tol}

static

Definition at line 37 of file geometry.h.

◆ SIN_COS_ZERO

const struct sin_cos_angle SIN_COS_ZERO = {0.0, 1.0}

static

Definition at line 36 of file geometry.h.

Data Structures

Macros

Enumerations

Functions

Variables

Macro Definition Documentation

◆ yac_angle_low_tol

◆ yac_angle_tol

◆ yac_cos_angle_low_tol

◆ yac_cos_angle_tol

◆ YAC_RAD

◆ yac_sq_angle_tol

Enumeration Type Documentation

◆ yac_circle_type

Function Documentation

◆ clamp_abs_one()

◆ compare_angles()

◆ compare_coords()

◆ compute_angle()

◆ compute_sin_cos()

◆ compute_sq_crd()

◆ crossproduct_d()

◆ crossproduct_kahan()

◆ det2_kahan()

◆ get_angle()

◆ get_angle_deg()

◆ get_vector_angle()

◆ get_vector_angle_2()

◆ half_angle()

◆ LLtoXYZ()

◆ LLtoXYZ_deg()

◆ normalise_vector()

◆ points_are_identically()

◆ quarter_angle()

◆ rotate_vector()

◆ rotate_vector2()

◆ sin_cos_angle_new()

◆ sin_cos_angle_to_dble()

◆ sq_len_diff_vec()

◆ sub_angles()

◆ sub_angles_no_check()

◆ sum_angles()

◆ sum_angles_no_check()

◆ XYZtoLL()

◆ yac_circle_intersect()

◆ yac_compute_bnd_triangle()

◆ yac_extents_overlap()

◆ yac_get_cell_bounding_circle()

◆ yac_intersect_vec()

◆ yac_point_in_bounding_circle_vec()

◆ yac_point_in_cell()

◆ yac_point_in_cell2()

◆ yac_point_on_edge()

◆ yac_triangulate_cell()

◆ yac_triangulate_cell_indices()

Variable Documentation

◆ SIN_COS_7_M_PI_4

◆ SIN_COS_LOW_TOL

◆ SIN_COS_M_PI

◆ SIN_COS_M_PI_2

◆ SIN_COS_TOL

◆ SIN_COS_ZERO