NAME

       exspline - Constructing smooth movement paths from spline curves. Allegro game programming library.

SYNOPSIS

       #include <allegro.h>

       Example exspline

DESCRIPTION

       This  program  demonstrates  the  use of spline curves to create smooth paths connecting a number of node
       points. This can be useful for constructing realistic motion and animations.

       The technique is to connect the series of guide points p1..p(n) with spline  curves  from  p1-p2,  p2-p3,
       etc.  Each spline must pass though both of its guide points, so they must be used as the first and fourth
       of the spline control points. The fun bit is coming up with sensible values  for  the  second  and  third
       spline control points, such that the spline segments will have equal gradients where they meet. I came up
       with the following solution:

       For each guide point p(n), calculate the desired tangent to the curve at that point. I took  this  to  be
       the  vector p(n-1) -> p(n+1), which can easily be calculated with the inverse tangent function, and gives
       decent looking results. One implication of this is that two dummy guide points are needed at each end  of
       the curve, which are used in the tangent calculations but not connected to the set of splines.

       Having  got  these  tangents, it becomes fairly easy to calculate the spline control points. For a spline
       between guide points p(a) and p(b), the second control point should lie along the positive  tangent  from
       p(a),  and  the  third  control  point  should lie along the negative tangent from p(b). How far they are
       placed along these tangents controls the shape of the curve: I found that applying a 'curviness'  scaling
       factor to the distance between p(a) and p(b) works well.

       One  thing  to note about splines is that the generated points are not all equidistant. Instead they tend
       to bunch up nearer to the ends of the spline, which means you will need to apply some fudges  to  get  an
       object  to  move  at  a constant speed. On the other hand, in situations where the curve has a noticeable
       change of direction at each guide point, the effect can be quite nice because it makes  the  object  slow
       down for the curve.

SEE ALSO

       END_OF_MAIN(3alleg4), SCREEN_W(3alleg4), acquire_screen(3alleg4), alert(3alleg4), allegro_error(3alleg4),
       allegro_init(3alleg4),     allegro_message(3alleg4),      calc_spline(3alleg4),      circlefill(3alleg4),
       clear_keybuf(3alleg4),      clear_to_color(3alleg4),     desktop_palette(3alleg4),     fixatan2(3alleg4),
       fixcos(3alleg4), fixed(3alleg4),  fixmul(3alleg4),  fixsin(3alleg4),  fixsqrt(3alleg4),  fixtof(3alleg4),
       fixtoi(3alleg4),   font(3alleg4),   ftofix(3alleg4),  install_keyboard(3alleg4),  install_mouse(3alleg4),
       install_timer(3alleg4),    itofix(3alleg4),     key(3alleg4),     keypressed(3alleg4),     line(3alleg4),
       makecol(3alleg4),    mouse_b(3alleg4),    mouse_x(3alleg4),   mouse_y(3alleg4),   palette_color(3alleg4),
       poll_mouse(3alleg4), readkey(3alleg4), release_screen(3alleg4),  screen(3alleg4),  set_gfx_mode(3alleg4),
       set_palette(3alleg4),       show_mouse(3alleg4),       spline(3alleg4),       textout_centre_ex(3alleg4),
       textprintf_centre_ex(3alleg4), textprintf_ex(3alleg4), vsync(3alleg4), xor_mode(3alleg4)