/*  Written by W. Taylor, Math Dept, University of Colorado, Boulder, CO
    80309-0426, USA. wtaylor@euclid.colorado.edu. Last revised 6/3/89      */

#include <math.h>
#include <stdio.h>
#include "coords.h"

/* The units used in this file are such that if the picture is put on
an 8.5 x 8.5 window on a laser printer, then the units are inches. Printed
on other devices, the units may not be real inches. */

#define SIZE 6.4                  /*  width = height of picture, in inches  */

                                   /* The location of the upper left corner
                                      of the picture will be as follows:  */

#define H_OFFSET 1.2               /* inches from left edge of paper */
#define V_OFFSET 2                 /* inches from top edge of paper */

circle(p,R)
point p; double R;
{
#define CIRC_STEPS 100
point q,r;
int k;
q = p;
q.x_coord+=R;
for (k=1;k<=CIRC_STEPS;k++)
{
	r = q;
	q.x_coord = p.x_coord + R*cos((2*PI*k)/CIRC_STEPS);
	q.y_coord = p.y_coord + R*sin((2*PI*k)/CIRC_STEPS);
	segment(r,q);
}
}

begin_small_text() {printf("t");}

end_small_text() {printf("\n");}

begin_medium_text() {printf("x");}

end_medium_text() {printf("\n");}

begin_large_text() {printf("T");}

end_large_text() {printf("\n");}

set_clip_region()
{
point p, q;
p.x_coord = H_OFFSET;  p.y_coord = 8.5 - V_OFFSET - SIZE;
q.x_coord = H_OFFSET + SIZE;  q.y_coord = 8.5 - V_OFFSET;
printf("%%Here begins the designation of the clip region.\n");
printf("r %3.3f %3.3f %3.3f %3.3f\n", p.x_coord, p.y_coord,
					q.x_coord, q.y_coord);
printf("%%This concludes the designation of the clip region.\n");
}

draw_axes(left,right,bottom,top)
double left, right, bottom, top;
{
point p0, p1;
printf("%%Here we draw the coordinate axes, if they fit.\n");
set_pen(2);
if ( (left < 0.0) && (right > 0.0))
	{
	p0.x_coord = p1.x_coord = H_OFFSET + SIZE * (left/(left - right));
	p0.y_coord = 8.5 - V_OFFSET;
	p1.y_coord = 8.5 - V_OFFSET - SIZE;
	segment(p0,p1);
	}
if ( (bottom < 0.0) && (top > 0.0))
	{
	p0.y_coord = p1.y_coord = 8.5 - V_OFFSET
				- SIZE*(1.0-(bottom/(bottom - top)));
	p0.x_coord = H_OFFSET;
	p1.x_coord = H_OFFSET + SIZE;
	segment(p0,p1);
	}
printf("%%This ends the laying down of the axes.\n");
}

draw_frame()
{
point p,q,r,s;
p.x_coord = q.x_coord = H_OFFSET;
q.y_coord = r.y_coord = 8.5 - V_OFFSET;
r.x_coord = s.x_coord = H_OFFSET + SIZE;
s.y_coord = p.y_coord = 8.5 - V_OFFSET - SIZE;
printf("%%Here we begin drawing a frame.\n");
set_pen(12);
move_to(p); line_to(q); line_to(r); line_to(s); line_to(p);
printf("%%This concludes the drawing of a frame.\n");
}

print_path(start_t,stop_t,step,width,left,right,bottom,top,f)
double left, right, bottom, top, start_t, stop_t;
point (*f)();
int step, width;
{
int i,printing;
double t0, t1;
point lower_corner, p0, p1;
point lower_corner_inches;
point plus(), minus(), ttimes();

lower_corner.x_coord = left;
lower_corner.y_coord = bottom;

lower_corner_inches.x_coord = H_OFFSET;
lower_corner_inches.y_coord = 8.5 - V_OFFSET - SIZE;

printf("%%Here we begin printing a curve.\n");

set_pen(width);
printing = 0;
for (i=0; i<(step+1); i++)
	{
		t0 = t1;
		t1 = (start_t + (((double) i)/step)*(stop_t - start_t));
		p0 = p1;
		p1 = (*f)(t1);
		p1 = minus(p1,lower_corner);
		p1.x_coord = p1.x_coord/(right-left);
		p1.y_coord = p1.y_coord/(top-bottom);
		p1 = plus(lower_corner_inches,ttimes(SIZE,p1));
		if
		(
		p0.x_coord <= H_OFFSET + SIZE  &&
		p0.x_coord >= H_OFFSET         &&
		p1.x_coord <= H_OFFSET + SIZE  &&
		p1.x_coord >= H_OFFSET         &&
		p0.y_coord <= 8.5 - V_OFFSET   &&
		p0.y_coord >= 8.5 - V_OFFSET - SIZE   &&
		p1.y_coord <= 8.5 - V_OFFSET   &&
		p1.y_coord >= 8.5 - V_OFFSET - SIZE   
		)
		{
		if (printing) line_to(p1); else move_to(p1); 
		printing = 1;
		}
		else printing = 0;
	}
printf("%%Now we have finished printing a curve.\n");
}

print_path_param(start_t,stop_t,step,left,right,bottom,top,f,r)
double left, right, bottom, top, start_t, stop_t;
point (*f)();
int step, r;
{
int i,printing;
double t0, t1;
double test1, test2, test3, test4;
point lower_corner, p0, p1;
point lower_corner_inches;
point plus(), minus(), ttimes();

lower_corner.x_coord = left;
lower_corner.y_coord = bottom;

lower_corner_inches.x_coord = H_OFFSET;
lower_corner_inches.y_coord = 8.5 - SIZE - V_OFFSET;

printing=0;
for (i=0; i<(step+1); i++)
	{
		t0 = t1;
		t1 = (start_t + (((double) i)/step)*(stop_t - start_t));
		test3 = test1; test4 = test2;
		p0 = p1;
		p1 = (*f)(t1,r);
		p1 = minus(p1,lower_corner);
		p1.x_coord = p1.x_coord/(right-left);
		p1.y_coord = p1.y_coord/(top-bottom);
		p1 = plus(lower_corner_inches,ttimes(SIZE,p1));
		if
		(
		p0.x_coord <= H_OFFSET + SIZE  &&
		p0.x_coord >= H_OFFSET         &&
		p1.x_coord <= H_OFFSET + SIZE  &&
		p1.x_coord >= H_OFFSET         &&
		p0.y_coord <= 8.5 - V_OFFSET   &&
		p0.y_coord >= 8.5 - V_OFFSET - SIZE   &&
		p1.y_coord <= 8.5 - V_OFFSET   &&
		p1.y_coord >= 8.5 - V_OFFSET - SIZE   
		)
		{
		if (printing) line_to(p1); else move_to(p1); 
		printing = 1;
		}
		else printing = 0;
	}
}


move_to(p)
point p;
{
printf("m %3.3f %3.3f\n",p.x_coord,p.y_coord);
}

line_to(p)
point p;
{
printf("l %3.3f %3.3f\n",p.x_coord,p.y_coord);
}

set_pen(width)
int width;
{
printf("W %d  ---- sets the width to %d points.\n",width,width);
}

segment(p,q)
point p, q;
{
move_to(p); line_to(q);
}

point affine(p,q,r)
point p, q, r;
{
point z;
z.x_coord = p.x_coord - q.x_coord + r.x_coord;
z.y_coord = p.y_coord - q.y_coord + r.y_coord;
return (z);
}

point convex_comb(alpha,p,q)
double alpha;
point p, q;
{
point z;
z.x_coord = alpha*(p.x_coord) + (1.0 - alpha)*(q.x_coord);
z.y_coord = alpha*(p.y_coord) + (1.0 - alpha)*(q.y_coord);
return (z);
}
	
point plus(p,q)
point p, q;
{
point z;
z.x_coord = p.x_coord + q.x_coord;
z.y_coord = p.y_coord + q.y_coord;
return (z);
}

point minus(p,q)
point p, q;
{
point z;
z.x_coord = p.x_coord - q.x_coord;
z.y_coord = p.y_coord - q.y_coord;
return (z);
}

point ttimes(alpha,p)
double alpha;
point p;
{
point z;
z.x_coord = alpha*(p.x_coord);
z.y_coord = alpha*(p.y_coord);
return (z);
}

point_3 convex_comb_3(alpha,p,q)
double alpha;
point_3 p, q;
{
point_3 z;
z.coord_1 = alpha*(p.coord_1) + (1.0 - alpha)*(q.coord_1);
z.coord_2 = alpha*(p.coord_2) + (1.0 - alpha)*(q.coord_2);
z.coord_3 = alpha*(p.coord_3) + (1.0 - alpha)*(q.coord_3);
return (z);
}
	
point_3 plus_3(p,q)
point_3 p, q;
{
point_3 z;
z.coord_1 = p.coord_1 + q.coord_1;
z.coord_2 = p.coord_2 + q.coord_2;
z.coord_3 = p.coord_3 + q.coord_3;
return (z);
}

point_3 minus_3(p,q)
point_3 p, q;
{
point_3 z;
z.coord_1 = p.coord_1 - q.coord_1;
z.coord_2 = p.coord_2 - q.coord_2;
z.coord_3 = p.coord_3 - q.coord_3;
return (z);
}

point_3 ttimes_3(alpha,p)
double alpha;
point_3 p;
{
point_3 z;
z.coord_1 = alpha*(p.coord_1);
z.coord_2 = alpha*(p.coord_2);
z.coord_3 = alpha*(p.coord_3);
return (z);
}


label_x_axis(left,right)
double left, right;
{
point p;
p.x_coord = H_OFFSET - 0.2;
p.y_coord = 8.5 - V_OFFSET - SIZE - 0.22;
printf("%%Here we label the x-axis.\n");
	move_to(p);
		begin_medium_text();
			printf("%4.2f",left);
		end_medium_text();
	p.x_coord = p.x_coord + SIZE + 0.1;
	move_to(p);
		begin_medium_text();
			printf("%4.2f",right);
		end_medium_text();
printf("%%This finishes the job of labeling the x-axis.\n");
}

label_y_axis(top,bottom)
double top, bottom;
{
point p;
p.x_coord = H_OFFSET - 0.55;
p.y_coord = 8.5 - V_OFFSET - .07;
printf("%%Here we label the y-axis.\n");
	move_to(p);
		begin_medium_text();
			printf("%4.2f",top);
		end_medium_text();
p.y_coord = p.y_coord - SIZE + .1;
	move_to(p);
		begin_medium_text();
			printf("%4.2f",bottom);
		end_medium_text();
printf("%%This finishes the job of labeling the y-axis.\n");
}

window()
{
printf("w 0.0 0.0 8.5 8.5\n");  /* This allows us to use inches everywhere */
}

position_label()
{
printf("%%Moving to the label position\n");
printf("m 1.1  -0.7\n");
}

position_login_signature()
{
printf("%%Moving to the login signature position\n");
printf("m 5.5  -1.5\n");
}