#include <AP_GeodesicGrid.h>

Inheritance diagram for AP_GeodesicGrid:

Collaboration diagram for AP_GeodesicGrid:

Classes
struct	neighbor_umbrella

Static Public Member Functions
static int	section (const Vector3f &v, bool inclusive=false)

Static Public Attributes
static const int	NUM_SUBTRIANGLES = 4

Static Private Member Functions
static int	_neighbor_umbrella_component (int umbrella_index, int component_idx)

static int	_from_neighbor_umbrella (int umbrella_index, const Vector3f &v, const Vector3f &u, bool inclusive)

static int	_triangle_index (const Vector3f &v, bool inclusive)

static int	_subtriangle_index (const unsigned int triangle_index, const Vector3f &v, bool inclusive)

Static Private Attributes
static const Matrix3f	_inverses [10]

static const Matrix3f	_mid_inverses [10]

static const struct AP_GeodesicGrid::neighbor_umbrella	_neighbor_umbrellas [3]

Friends
class	GeodesicGridTest

Detailed Description

AP_GeodesicGrid is a class for working on geodesic sections.

For quick information regarding geodesic grids, see: https://en.wikipedia.org/wiki/Geodesic_grid

The grid is formed by a tessellation of an icosahedron by a factor of 2, i.e., each triangular face of the icosahedron is divided into 4 by splitting each edge into 2 line segments and projecting the vertices to the icosahedron's circumscribed sphere. That will give a total of 80 triangular faces, which are called sections in this context.

A section index is given by the icosahedron's triangle it belongs to and by its index in that triangle. Let i in [0,20) be the icosahedron's triangle index and j in [0,4) be the sub-triangle's (which is the section) index inside the greater triangle. Then the section index is given by s = 4 * i + j .

The icosahedron's triangles are defined by the tuple (T_0, T_1, ..., T_19), where T_i is the i-th triangle. Each triangle is represented with a tuple of the form (a, b, c), where a, b and c are the triangle vertices in the space.

Given the definitions above and the golden ration as g, the triangles must be defined in the following order:

(
    ((-g, 1, 0), (-1, 0,-g), (-g,-1, 0)),
    ((-1, 0,-g), (-g,-1, 0), ( 0,-g,-1)),
    ((-g,-1, 0), ( 0,-g,-1), ( 0,-g, 1)),
    ((-1, 0,-g), ( 0,-g,-1), ( 1, 0,-g)),
    (( 0,-g,-1), ( 0,-g, 1), ( g,-1, 0)),
    (( 0,-g,-1), ( 1, 0,-g), ( g,-1, 0)),
    (( g,-1, 0), ( 1, 0,-g), ( g, 1, 0)),
    (( 1, 0,-g), ( g, 1, 0), ( 0, g,-1)),
    (( 1, 0,-g), ( 0, g,-1), (-1, 0,-g)),
    (( 0, g,-1), (-g, 1, 0), (-1, 0,-g)),
    -T_0,
    -T_1,
    -T_2,
    -T_3,
    -T_4,
    -T_5,
    -T_6,
    -T_7,
    -T_8,
    -T_9,
)

Where for a given T_i = (a, b, c), -T_i = (-a, -b, -c). We call -T_i the opposite triangle of T_i in this specification. For any i in [0,20), T_j is the opposite of T_i iff j = (i + 10) % 20.

Let an icosahedron triangle T be defined as T = (a, b, c). The "middle triangle" M is defined as the triangle formed by the points that bisect the edges of T. M is defined by:

M = (m_a, m_b, m_c) = ((a + b) / 2, (b + c) / 2, (c + a) / 2)

Let elements of the tuple (W_0, W_1, W_2, W_3) comprise the sub-triangles of T, so that W_j is the j-th sub-triangle of T. The sub-triangles are defined as the following:

W_0 = M W_1 = (a, m_a, m_c) W_2 = (m_a, b, m_b) W_3 = (m_c, m_b, c)

Definition at line 110 of file AP_GeodesicGrid.cpp.

Member Function Documentation

◆ _from_neighbor_umbrella()

int AP_GeodesicGrid::_from_neighbor_umbrella	(	int	umbrella_index,
		const Vector3f &	v,
		const Vector3f &	u,
		bool	inclusive
	)

staticprivate

Find the icosahedron triangle index of the component of _neighbor_umbrellas[umbrella_index] that is crossed by v.

Parameters

umbrella_index[in]	The umbrella index. Must be in [0,6).
v[in]	The vector to be tested.
u[in]	The vector `u` must be `v` expressed with respect to the base formed by the umbrella's 0-th, 1-th and 3-th vertices, in that order.
inclusive[in]	This parameter follows the same rules defined in #section() const.

Returns: The index of the icosahedron triangle. The value -1 is returned if v is the null vector or the triangle isn't found, which might happen when inclusive is false.

Definition at line 210 of file AP_GeodesicGrid.cpp.

Referenced by _triangle_index().

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◆ _neighbor_umbrella_component()

int AP_GeodesicGrid::_neighbor_umbrella_component	(	int	umbrella_index,
		int	component_idx
	)

staticprivate

Get the component_index-th component of the umbrella_index-th neighbor umbrella.

Parameters

umbrella_index[in]	The neighbor umbrella's index.
component_index[in]	The component's index.

Returns: The icosahedron triangle's index of the component.

Definition at line 202 of file AP_GeodesicGrid.cpp.

Referenced by _from_neighbor_umbrella().

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◆ _subtriangle_index()

int AP_GeodesicGrid::_subtriangle_index	(	const unsigned int	triangle_index,
		const Vector3f &	v,
		bool	inclusive
	)

staticprivate

Find which sub-triangle of the icosahedron's triangle pointed by triangle_index is crossed by v.

The vector v must belong to the super-section formed by the triangle pointed by triangle_index, otherwise the result is undefined.

Parameters

triangle_index[in]	The icosahedron's triangle index, it must be in the interval [0,20). Passing invalid values is undefined behavior.
v[in]	The vector to be verified.
inclusive[in]	This parameter follow the same rules defined in #section() const.

Returns: The index of the sub-triangle. The value -1 is returned if the triangle isn't found, which might happen when inclusive is false.

Definition at line 440 of file AP_GeodesicGrid.cpp.

Referenced by section(), and GeodesicGridTest::test_triangles_indexes().

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◆ _triangle_index()

int AP_GeodesicGrid::_triangle_index	(	const Vector3f &	v,
		bool	inclusive
	)

staticprivate

Find which icosahedron's triangle is crossed by v.

Parameters

v[in]	The vector to be verified.
inclusive[in]	This parameter follow the same rules defined in #section() const.

Returns: The index of the triangle. The value -1 is returned if the triangle isn't found, which might happen when inclusive is false.

Definition at line 307 of file AP_GeodesicGrid.cpp.

Referenced by section(), and GeodesicGridTest::test_triangles_indexes().

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◆ section()

int AP_GeodesicGrid::section	(	const Vector3f &	v,
		bool	inclusive = `false`
	)

static

Find which section is crossed by v.

Parameters

v[in]	The vector to be verified.
inclusive[in]	If true, then if `v` crosses one of the edges of one of the sections, then that section is returned. If `inclusive` is false, then `v` is considered to cross no section. Note that, if `inclusive` is true, then `v` can belong to more than one section and only the first one found is returned. The order in which the triangles are checked is unspecified. The default value for `inclusive` is false.

Returns: The index of the section. The value -1 is returned if v is the null vector or the section isn't found, which might happen when inclusive is false.

Definition at line 187 of file AP_GeodesicGrid.cpp.

Referenced by BM_GeodesicGridSections(), TEST_P(), and CompassCalibrator::update_completion_mask().

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Friends And Related Function Documentation

◆ GeodesicGridTest

friend class GeodesicGridTest

friend

Definition at line 89 of file AP_GeodesicGrid.h.

Member Data Documentation

◆ _inverses

const Matrix3f AP_GeodesicGrid::_inverses

staticprivate

The inverses of the change-of-basis matrices for the icosahedron triangles.

The i-th matrix is the inverse of the change-of-basis matrix from natural basis to the basis formed by T_i's vectors.

Definition at line 171 of file AP_GeodesicGrid.h.

Referenced by _from_neighbor_umbrella(), and _triangle_index().

◆ _mid_inverses

const Matrix3f AP_GeodesicGrid::_mid_inverses

staticprivate

The inverses of the change-of-basis matrices for the middle triangles.

The i-th matrix is the inverse of the change-of-basis matrix from natural basis to the basis formed by T_i's middle triangle's vectors.

Definition at line 179 of file AP_GeodesicGrid.h.

Referenced by _subtriangle_index().

◆ _neighbor_umbrellas

const struct AP_GeodesicGrid::neighbor_umbrella AP_GeodesicGrid::_neighbor_umbrellas[3]

staticprivate

Referenced by _from_neighbor_umbrella(), and _neighbor_umbrella_component().

◆ NUM_SUBTRIANGLES

const int AP_GeodesicGrid::NUM_SUBTRIANGLES = 4

static

Number of sub-triangles for an icosahedron triangle.

Definition at line 107 of file AP_GeodesicGrid.h.

Referenced by GeodesicGridTest::test_triangles_indexes().

The documentation for this class was generated from the following files:

libraries/AP_Math/AP_GeodesicGrid.cpp
libraries/AP_Math/AP_GeodesicGrid.h

Classes

Static Public Member Functions

Static Public Attributes

Static Private Member Functions

Static Private Attributes

Friends

Detailed Description

Member Function Documentation

◆ _from_neighbor_umbrella()

◆ _neighbor_umbrella_component()

◆ _subtriangle_index()

◆ _triangle_index()

◆ section()

Friends And Related Function Documentation

◆ GeodesicGridTest

Member Data Documentation

◆ _inverses

◆ _mid_inverses

◆ _neighbor_umbrellas

◆ NUM_SUBTRIANGLES