/* draws a straight line in red,
   waits a second,
   rotates that line, and
   draw the result in blue 

   near the middle of main (note main is not the last function here)   
     const double line[4] = { 0, 150, 150, 1 };
   defines the line to be rotated, it is at a slant of 45 degrees
   but only to the y and z axes. We can't see in z, so it appears vertical
   if you change it to
     const double line[4] = { 150, 150, 0, 1 };
   it is not slanting in x and y, so you will see a slant before and after rotation
   so long as the 4th number is always 1, you can use anything for the x, y, and z
   coordinates, but if the numbers are too big it will go off the edge of the window

   if you change BOTH draw_to calls in main into draw_slowly_to, the line doesn't
   just appear fully formed, you see it being drawn */


#include "library.h"

const int winsize = 500;
const int halfwinsize = winsize / 2;

double matvecmul(const double m[4][4], const double v[4], const int i, const int p)
{ if (p == 4)
    return 0.0;
  return m[i][p] * v[p] + matvecmul(m, v, i, p + 1); }

double matvecmul(const double m[4][4], const double v[4], const int i)
{ return matvecmul(m, v, i, 0); }

const double pi = acos(-1.0);

double degrees(const double x)
{ return x * pi / 180.0; }

void move_to(const double p[4])
{ move_to(halfwinsize + p[0], halfwinsize - p[1]); }

void draw_to(const double p[4])
{ draw_to(halfwinsize + p[0], halfwinsize - p[1]); }

void draw_slowly_to(const double x1, const double y1, const int numsteps);
void draw_slowly_to(const double p[4]);

void main()
{ make_window(winsize, winsize);
  set_pen_width(3);
  const double rotz[4][4] = { { cos(degrees(30)), sin(degrees(30)), 0, 0 },
                              { -sin(degrees(30)), cos(degrees(30)), 0, 0 },
                              { 0, 0, 1, 0 },
                              { 0, 0, 0, 1 } };
  const double centre[4] = { 0, 0, 0, 1 };
  const double line[4] = { 0, 150, 150, 1 };
  set_pen_color(color::red);
  move_to(centre);
  draw_to(line);       // change to draw_slowly_to here and below
  wait(1);
  const double rotated[4] = { matvecmul(rotz, line, 0),
                              matvecmul(rotz, line, 1),
                              matvecmul(rotz, line, 2),
                              matvecmul(rotz, line, 3) };
  set_pen_color(color::blue);
  move_to(centre);
  draw_to(rotated); }



void draw_slowly_to(const double x1, const double y1, const int numsteps)
{ if (numsteps == 0)
    return;
  const double x0 = get_x_position() - halfwinsize,
               y0 = halfwinsize - get_y_position();
  const double xrange = x1 - x0,
               yrange = y1 - y0;
  const double xstep = xrange / numsteps,
               ystep = yrange / numsteps;
  const double newx = x0 + xstep,
               newy = y0 + ystep;
  draw_to(halfwinsize + newx, halfwinsize - newy);
  wait(0.01);
  draw_slowly_to(x1, y1, numsteps - 1); }

void draw_slowly_to(const double p[4])
{ draw_slowly_to(p[0], p[1], 100); }