Functions to generate polyhedra using the spiral algorithm. More...

#include "rwmodel.h"

Functions
Bmodel *	model_poly_spiral (Bstring &seq, int valence, int requirements)
	Generates a polyhedron using the spiral algorithm. More...

int	model_polyhedron_check (Bmodel *model, int valence)
	Checks a polyhedron for accuracy and completeness. More...

Bmodel *	model_poly_gen_sequence (Bstring &seq, int valence, int enantiomorph, int requirements, int nm)
	Generates a polyhedron using a given sequence. More...

Bmodel *	model_poly_gen_sequence (Bstring &seq, int valence, int enantiomorph, int requirements, int nm, vector< double > &table)
	Generates a polyhedron using a given sequence. More...

Bmodel *	model_poly_gen_permutations (int vertices, int valence, int enantiomorph)
	All polyhedra are generated for a given number of vertices. More...

Bmodel *	model_poly_gen_cone (int tip, int body, int base, int valence, int enantiomorph, int requirements)
	A cone tip with 5 pentagons and a base with 7 pentagons are use to generate polyhedra. More...

Bmodel *	model_poly_gen_lozenge (int ttop, int tbody, int valence, int enantiomorph, int requirements)
	Two icosahedral tips are set up and polyhedra generated by rotating the 2 tips. More...

Bmodel *	model_poly_gen_coffin (int ttop, int tbody, int tbase, int valence, int enantiomorph, int requirements)
	An icosahedral tip and a 6-fold base is set up and polyhedra generated by rotating the tip and base. More...

Bmodel *	model_poly_gen_coffin_loose (int ttop, int tbody, int tbase, int valence, int enantiomorph, int requirements)
	An icosahedral tip and a 6-fold base is set up and polyhedra generated by permuting the tip and base. More...

Bmodel *	model_poly_gen_coffin_jiggle (int ttop, int tbody, int tbase, int valence, int enantiomorph, int requirements)
	An icosahedral tip and a 6-fold base is set up and polyhedra generated by moving pentagons around. More...

Bmodel *	model_poly_gen_3part (Bstring stip, Bstring sbody, Bstring sbase, int valence, int enantiomorph, int requirements)
	Generates several polyhedra by permuting the first and last parts of a three-part sequence. More...

Bmodel *	model_poly_gen_move_pentagons (Bstring &seq, int valence, int enantiomorph, int requirements)
	Generates many polyhedrons using a given sequence and moving pentagons around. More...

Detailed Description

Functions to generate polyhedra using the spiral algorithm.

Author: Bernard Heymann

Date: Created: 20071127; Modified: 20210124

Function Documentation

◆ model_poly_gen_3part()

Bmodel * model_poly_gen_3part	(	Bstring	stip,
		Bstring	sbody,
		Bstring	sbase,
		int	valence,
		int	enantiomorph,
		int	requirements
	)

Generates several polyhedra by permuting the first and last parts of a three-part sequence.

Parameters

stip	tip sequence (permuted).
sbody	body sequence (all hexagons).
sbase	base/end sequence (permuted).
valence	vertex valence.
enantiomorph	flag to generate enantiomorphs.
requirements	polyhedron requirements.

Returns

Bmodel* new model, NULL if generation failed.

A recursive algorithm is used to generate several models by shifting the
positions of pentagons in a sequence.

◆ model_poly_gen_coffin()

Bmodel * model_poly_gen_coffin	(	int	ttop,
		int	tbody,
		int	tbase,
		int	valence,
		int	enantiomorph,
		int	requirements
	)

An icosahedral tip and a 6-fold base is set up and polyhedra generated by rotating the tip and base.

Parameters

ttop	number of polygons between pentagons in the tip.
tbody	number of body rings.
tbase	number of polygons between pentagons in the base
valence	vertex valence.
enantiomorph	flag to generate enantiomorphs.
requirements	polyhedron requirements.

Returns: Bmodel* new model, NULL if generation failed.

◆ model_poly_gen_coffin_jiggle()

Bmodel * model_poly_gen_coffin_jiggle	(	int	ttop,
		int	tbody,
		int	tbase,
		int	valence,
		int	enantiomorph,
		int	requirements
	)

An icosahedral tip and a 6-fold base is set up and polyhedra generated by moving pentagons around.

Parameters

ttop	number of polygons between pentagons in the tip.
tbody	number of body rings.
tbase	number of polygons between pentagons in the base
valence	vertex valence.
enantiomorph	flag to generate enantiomorphs.
requirements	polyhedron requirements.

Returns: Bmodel* new model, NULL if generation failed.

◆ model_poly_gen_coffin_loose()

Bmodel * model_poly_gen_coffin_loose	(	int	ttop,
		int	tbody,
		int	tbase,
		int	valence,
		int	enantiomorph,
		int	requirements
	)

An icosahedral tip and a 6-fold base is set up and polyhedra generated by permuting the tip and base.

Parameters

ttop	number of polygons between pentagons in the tip.
tbody	number of body rings.
tbase	number of polygons between pentagons in the base
valence	vertex valence.
enantiomorph	flag to generate enantiomorphs.
requirements	polyhedron requirements.

Returns: Bmodel* new model, NULL if generation failed.

◆ model_poly_gen_cone()

Bmodel * model_poly_gen_cone	(	int	tip,
		int	body,
		int	base,
		int	valence,
		int	enantiomorph,
		int	requirements
	)

A cone tip with 5 pentagons and a base with 7 pentagons are use to generate polyhedra.

Parameters

tip	number of vertices in the tip.
body	number of vertices in the body.
base	number of vertices in the base.
valence	vertex valence.
enantiomorph	flag to generate enantiomorphs.
requirements	polyhedron requirements.

Returns: Bmodel* new model, NULL if generation failed.

◆ model_poly_gen_lozenge()

Bmodel * model_poly_gen_lozenge	(	int	ttop,
		int	tbody,
		int	valence,
		int	enantiomorph,
		int	requirements
	)

Two icosahedral tips are set up and polyhedra generated by rotating the 2 tips.

Parameters

ttop	number of polygons between pentagons in the tip.
tbody	number of body rings.
valence	vertex valence.
enantiomorph	flag to generate enantiomorphs.
requirements	polyhedron requirements.

Returns: Bmodel* new model, NULL if generation failed.

◆ model_poly_gen_move_pentagons()

Bmodel * model_poly_gen_move_pentagons	(	Bstring &	seq,
		int	valence,
		int	enantiomorph,
		int	requirements
	)

Generates many polyhedrons using a given sequence and moving pentagons around.

Parameters

&seq	polygon sequence.
valence	vertex valence.
enantiomorph	flag to generate enantiomorphs.
requirements	polyhedron requirements.

Returns

Bmodel* new model, NULL if generation failed.

A recursive algorithm is used to generate several models by shifting the
positions of pentagons in a sequence.

◆ model_poly_gen_permutations()

Bmodel * model_poly_gen_permutations	(	int	vertices,
		int	valence,
		int	enantiomorph
	)

All polyhedra are generated for a given number of vertices.

Parameters

vertices	number of vertices.
valence	vertex valence.
enantiomorph	flag to generate enantiomorphs.

Returns: Bmodel* new model, NULL if generation failed.

◆ model_poly_gen_sequence() [1/2]

Bmodel * model_poly_gen_sequence	(	Bstring &	seq,
		int	valence,
		int	enantiomorph,
		int	requirements,
		int	nm
	)

Generates a polyhedron using a given sequence.

Parameters

&seq	polygon sequence.
valence	vertex valence.
enantiomorph	flag to generate enantiomorphs.
requirements	polyhedron requirements.
nm	current number of models (before creating this one).

Returns

Bmodel* new model, NULL if generation failed.

A single model is generated based on the sequence.

◆ model_poly_gen_sequence() [2/2]

Bmodel * model_poly_gen_sequence	(	Bstring &	seq,
		int	valence,
		int	enantiomorph,
		int	requirements,
		int	nm,
		vector< double > &	table
	)

Generates a polyhedron using a given sequence.

Parameters

&seq	polygon sequence.
valence	vertex valence.
enantiomorph	flag to generate enantiomorphs.
requirements	polyhedron requirements.
nm	current number of models (before creating this one).
&table	table for sets of eigenvalues.

Returns

Bmodel* new model, NULL if generation failed.

A single model is generated based on the sequence.
A table is used to keep track of sets of eigenvalues of previous models
to avoid generating redundant models.

◆ model_poly_spiral()

Bmodel * model_poly_spiral	(	Bstring &	seq,
		int	valence,
		int	requirements
	)

Generates a polyhedron using the spiral algorithm.

Parameters

&seq	polygon sequence.
valence	vertex valence.
requirements	polyhedron requirements.

Returns

Bmodel* new model, NULL if generation failed.

Polygons are added based on the given sequence.
The success of the algorithm is checked using the indicated requirements:
    0       only a polyhedron consistency check is done
    1       the exact number of vertices must be obtained
    2       only a polyhedron with isolated pentagons is accepted
The generation fails when an incorrect number of vertices are added
or some of the vertices have incorrect valency.

◆ model_polyhedron_check()

int model_polyhedron_check	(	Bmodel *	model,
		int	valence
	)

Checks a polyhedron for accuracy and completeness.

Parameters

*model	model structure.
valence	vertex valence.

Returns

int number of failed conditions.

Every component must have the required number of links = valence.
Every component must have the required number of polygons = valence.
The polyhedron must adhere to Euler's formula:
    components + polygons - links = 2