/* --------------------------------------------------------------------- 
//  Figure 6.33:  Linear interpolation.
//  Figure 6.26:  Instructions for linear interpolation.
// --------------------------------------------------------------------- 
//  Given two points in the form (x, f(x)), calculate the equation 
//  of a straight line through those points.  In a second program 
//  phase, read the x-coordinates of a series of points and use the 
//  linear equation to obtain an approximation for f(x) for each input
*/

#include "tools.h"
void instructions( void );

void main( void )
{
    double  x1, fx1;    /* The point with the smaller x-coordinate. */  
    double  x2, fx2;    /* The point with the larger x-coordinate. */  
    double  x, fx, slope;
 
    instructions();

    /* Phase I.------------------------------------------------------------- */ 
    do {
        printf( " Enter the smaller x value and f(x) for that value: " );
        scanf( "%lg%lg",  &x1, &fx1 );  
        printf( " Enter the larger x value and f(x) for that value: " );
        scanf( "%lg%lg",  &x2, &fx2 );
        if (x1 >= x2) puts( " Error: first x-value must be < second.\n" );  
    } while (x1 >= x2); 
    printf( "\n\t For p1=(%g, %g) and p2=(%g, %g)\n", x1, fx1, x2, fx2 ); 

    slope = (fx2 - fx1) / (x2 - x1) ;
    printf( "\n\t f_approx(x) = %g + %g * (x - %g)\n",  fx1, slope, x1 );

   /* Phase II.------------------------------------------------------------ */ 
    printf( "\n Enter x-values between %g and %g\n", x1, x2 );
    printf( "\t The value of f_approx(x) will be printed for each x. \n"
            "\t To quit, enter an x-value outside this range.\n" );

    scanf( "%lg", &x );
    while (x1 <= x && x <= x2) {
        fx = fx1 + slope * (x - x1);                       
        printf( "\t x=%g   f_approx(x)=%g\n", x, fx );  
        scanf( "%lg", &x );
    } 
    bye();  
}

   /* Phase II.------------------------------------------------------------ */ 
void instructions( void )
{   
    banner();
    puts( "\n\n Linear Interpolation\n"
          "    This program uses a straight line to approximate an unknown \n"
          "    function, f(x).  The user enters x and f(x) for two points. \n"
          "    The program calculates the formula for f_approx(x), the  \n"
          "    straight line through these two points. \n" );
}