/* Basic definitions. */
/* Last edited on 2007-12-26 15:18:43 by stolfi */

#ifndef basis_H
#define basis_H

/* Copyright © 2007 by the State University of Campinas (UNICAMP). */
/* See the copyright, authorship, and warranty notice at end of file. */
/* Last edited on 2007-04-16 17:30:29 by stolfi */

#include <stdint.h>
#include <interval.h>
#include <bool.h>

#include <stdio.h>

/* Created apr/2007 by Jorge Stolfi, UNICAMP */

typedef int32_t basis_index_t;  
  /* Identifies one element of a basis. */

/* BASIS OBJECT */

typedef struct basis_t basis_t;
  /* A {basis_t} object {bas} describes a family of functions defined
    on some domain {dom} supplied externally. 
    
    The elements of the basis are identified by indices in the range
    {0..num-1} where {num = bas->size(bas)}. The support interval of
    an element with index {ix} is {bas->supp(bas, ix)}, and its value
    at a point {t} of the domain is {bas->eval(bas,ix,t)}.
    
    A concrete instance of a {basis_t} is any {struct} that has a
    {basis_t} as the first field. The string {bas->type} should
    identify the concrete instance type. */

#define basis_TYPE "basis."
  /* The required prefix of {b->type} for any concrete instance
    {b} of {basis_t}. */

/* METHODS OF A BASIS OBJECT */

typedef char *basis_name_fn_t(basis_t *bas);
  /* A succint string that identifies the basis, suitable for file
    names and such. */

typedef int32_t basis_size_fn_t(basis_t *bas);
  /* Returns the number of elements in the basis {bas}. */

typedef void basis_show_fn_t(basis_t *bas, FILE *wr);
  /* Prints a description of {bas} to file {wr}. */

typedef interval_t basis_supp_fn_t(basis_t *bas, basis_index_t ix);
  /* An interval {r} such that the element with index {ix} of
    basis {bas} is zero for {t < r.end[0]} or {t > r.end[1]}. */

typedef double basis_eval_fn_t(basis_t *bas, basis_index_t ix, double t[]);
  /* Evaluates the element with index {ix} of basis {bas} at the
    argument {t[]}. */

struct basis_def_t {
    basis_size_fn_t *size; /* Returns the number of elements in the family. */
    basis_supp_fn_t *supp; /* Returns the support interval. */
    basis_eval_fn_t *eval; /* Evaluates a member of the family. */
    basis_name_fn_t *name; /* Returns the family's name. */
    basis_show_fn_t *show; /* Prints a description of the basis. */
    char *type;            /* Concrete type. */
  };

/* USEFUL TYPES */

typedef int8_t basis_degree_t;
  /* Degree of a polynomial or spline, max order of a trig series, etc.. */
  
typedef int8_t basis_cont_t;
  /* Continuity order of a spline. Value {-1} means discontinuous.. */

#endif