DymaxIcosa Class Reference

Public Member Functions
void	InitIcosa ()
void	FindFaceUV (const DPoint2 &p, int &face, int &subface, DPoint3 &uvw)
void	FindFace (const DPoint3 &p, int &face, int &subface)
void	FindUV (const DPoint3 &p_in, int face, DPoint3 &uvw)
void	GeoToFacePoint (const DPoint2 &p, int &face, int &subface, DPoint3 &p_out)
void	FaceUVToGeo (int face, DPoint3 &uvw, double &lon, double &lat)
bool	GeoToDymax (const DPoint2 &geo, DPoint2 &dymax)
double	DihedralAngle ()
void	GetDymaxEdges (DLine2Array &polys)

Protected Member Functions
void	AddFlatTri (DLine2Array &polys, int a, int b, int c, int d=-1)

Protected Attributes
DPoint3	m_verts [12]
icoface	m_face [20]
DPoint2	m_flatverts [27]
double	m_edge_length

Detailed Description

This class contains a full description of an icosahedron in the Dymaxion orientation. It provides the ability to convert points to and from a simple Gnomonic projection based on the icosahedron. No attempt is made to implement the precise "Dymaxion Projection" which would require using arc lengths.

The basis for this decision is Robert Gray's notes which state: "Fuller's world map image is indistinguishable to the world map image created by the Gnomonic projection method indicates that it is the use of the icosahedron, and not the projection method, that seems to be the critical point."

Member Function Documentation

void DymaxIcosa::FaceUVToGeo	(	int	face,
		DPoint3 &	uvw,
		double &	lon,
		double &	lat
	)

Given information about a point in the referenced frame of an icosahedral face (tri, uvw), find the corresponding surface location in geographic coordinate (lon, lat)

void DymaxIcosa::FindFace	(	const DPoint3 &	p,
		int &	face,
		int &	subface
	)

Determine which part of which icosahedral face a point is on.

Parameters

p	A 3D point.
face	Will receive the face number, from 0 to 19.
subface	Will receive the subface number, from 0 to 5.

void DymaxIcosa::FindFaceUV	(	const DPoint2 &	p,
		int &	face,
		int &	subface,
		DPoint3 &	uvw
	)

Given a geographic coordinate (lon, lat), find the corresponding face, subface, and UVW coordinates on surface of the icosahedron.

void DymaxIcosa::FindUV	(	const DPoint3 &	p_in,
		int	face,
		DPoint3 &	uvw
	)

Given a point and a face number, determine the u,v,w coordinates of the point in the reference frame of the face triangle.

bool DymaxIcosa::GeoToDymax	(	const DPoint2 &	geo,
		DPoint2 &	dymax
	)

Given a geographic coordinate (lon, lat), find the corresponding dymaxion map coordinate, on the classic flattened dymaxion map. The output is unit-edge triangles, which means the whole output extents are x [0, 5.5] and y [0, 2.6].

void DymaxIcosa::GeoToFacePoint	(	const DPoint2 &	p,
		int &	face,
		int &	subface,
		DPoint3 &	p_out
	)

Given a geographic coordinate (lon, lat), find the corresponding point on the surface of the icosahedron.

void DymaxIcosa::InitIcosa

(

)

Initializes the object with the values of the icosahedron and precomputes information for the faces.