trapezoid.c

// Variant of https://github.com/GNOME/pango/blob/main/examples/cairotwisted.c to shape text a bit trapezoidal

/* Example code to show how to use pangocairo to render text
 * projected on a path.
 *
 *
 * Written by Behdad Esfahbod, 2006..2007
 *
 * Permission to use, copy, modify, distribute, and sell this example
 * for any purpose is hereby granted without fee.
 * It is provided "as is" without express or implied warranty.
 */

#include <math.h>
#include <stdlib.h>
#include <pango/pangocairo.h>

void fancy_cairo_stroke (cairo_t *cr);
void fancy_cairo_stroke_preserve (cairo_t *cr);

/* A fancy cairo_stroke[_preserve]() that draws points and control
 * points, and connects them together.
 */
static void
_fancy_cairo_stroke (cairo_t *cr, cairo_bool_t preserve)
{
  int i;
  double line_width;
  cairo_path_t *path;
  cairo_path_data_t *data;
  const double dash[] = {10, 10};

  cairo_save (cr);
  cairo_set_source_rgb (cr, 1.0, 0.0, 0.0);

  line_width = cairo_get_line_width (cr);
  path = cairo_copy_path (cr);
  cairo_new_path (cr);

  cairo_save (cr);
  cairo_set_line_width (cr, line_width / 3);
  cairo_set_dash (cr, dash, G_N_ELEMENTS (dash), 0);
  for (i=0; i < path->num_data; i += path->data[i].header.length) {
    data = &path->data[i];
    switch (data->header.type) {
    case CAIRO_PATH_MOVE_TO:
    case CAIRO_PATH_LINE_TO:
	cairo_move_to (cr, data[1].point.x, data[1].point.y);
	break;
    case CAIRO_PATH_CURVE_TO:
	cairo_line_to (cr, data[1].point.x, data[1].point.y);
	cairo_move_to (cr, data[2].point.x, data[2].point.y);
	cairo_line_to (cr, data[3].point.x, data[3].point.y);
	break;
    case CAIRO_PATH_CLOSE_PATH:
	break;
    default:
	g_assert_not_reached ();
    }
  }
  cairo_stroke (cr);
  cairo_restore (cr);

  cairo_save (cr);
  cairo_set_line_width (cr, line_width * 4);
  cairo_set_line_cap (cr, CAIRO_LINE_CAP_ROUND);
  for (i=0; i < path->num_data; i += path->data[i].header.length) {
    data = &path->data[i];
    switch (data->header.type) {
    case CAIRO_PATH_MOVE_TO:
	cairo_move_to (cr, data[1].point.x, data[1].point.y);
	break;
    case CAIRO_PATH_LINE_TO:
	cairo_rel_line_to (cr, 0, 0);
	cairo_move_to (cr, data[1].point.x, data[1].point.y);
	break;
    case CAIRO_PATH_CURVE_TO:
	cairo_rel_line_to (cr, 0, 0);
	cairo_move_to (cr, data[1].point.x, data[1].point.y);
	cairo_rel_line_to (cr, 0, 0);
	cairo_move_to (cr, data[2].point.x, data[2].point.y);
	cairo_rel_line_to (cr, 0, 0);
	cairo_move_to (cr, data[3].point.x, data[3].point.y);
	break;
    case CAIRO_PATH_CLOSE_PATH:
	cairo_rel_line_to (cr, 0, 0);
	break;
    default:
	g_assert_not_reached ();
    }
  }
  cairo_rel_line_to (cr, 0, 0);
  cairo_stroke (cr);
  cairo_restore (cr);

  for (i=0; i < path->num_data; i += path->data[i].header.length) {
    data = &path->data[i];
    switch (data->header.type) {
    case CAIRO_PATH_MOVE_TO:
	cairo_move_to (cr, data[1].point.x, data[1].point.y);
	break;
    case CAIRO_PATH_LINE_TO:
	cairo_line_to (cr, data[1].point.x, data[1].point.y);
	break;
    case CAIRO_PATH_CURVE_TO:
	cairo_curve_to (cr, data[1].point.x, data[1].point.y,
			    data[2].point.x, data[2].point.y,
			    data[3].point.x, data[3].point.y);
	break;
    case CAIRO_PATH_CLOSE_PATH:
	cairo_close_path (cr);
	break;
    default:
	g_assert_not_reached ();
    }
  }
  cairo_stroke (cr);

  if (preserve)
    cairo_append_path (cr, path);

  cairo_path_destroy (path);

  cairo_restore (cr);
}

/* A fancy cairo_stroke() that draws points and control points, and
 * connects them together.
 */
void
fancy_cairo_stroke (cairo_t *cr)
{
  _fancy_cairo_stroke (cr, FALSE);
}

/* A fancy cairo_stroke_preserve() that draws points and control
 * points, and connects them together.
 */
void
fancy_cairo_stroke_preserve (cairo_t *cr)
{
  _fancy_cairo_stroke (cr, TRUE);
}


/* Returns Euclidean distance between two points */
static double
two_points_distance (cairo_path_data_t *a, cairo_path_data_t *b)
{
  double dx, dy;

  dx = b->point.x - a->point.x;
  dy = b->point.y - a->point.y;

  return sqrt (dx * dx + dy * dy);
}

/* Returns length of a Bezier curve.
 * Seems like computing that analytically is not easy.  The
 * code just flattens the curve using cairo and adds the length
 * of segments.
 */
static double
curve_length (double x0, double y0,
	      double x1, double y1,
	      double x2, double y2,
	      double x3, double y3)
{
  cairo_surface_t *surface;
  cairo_t *cr;
  cairo_path_t *path;
  cairo_path_data_t *data, current_point = {{0,},};
  int i;
  double length;

  surface = cairo_image_surface_create (CAIRO_FORMAT_A8, 0, 0);
  cr = cairo_create (surface);
  cairo_surface_destroy (surface);

  cairo_move_to (cr, x0, y0);
  cairo_curve_to (cr, x1, y1, x2, y2, x3, y3);

  length = 0;
  path = cairo_copy_path_flat (cr);
  for (i=0; i < path->num_data; i += path->data[i].header.length) {
    data = &path->data[i];
    switch (data->header.type) {

    case CAIRO_PATH_MOVE_TO:
	current_point = data[1];
	break;

    case CAIRO_PATH_LINE_TO:
	length += two_points_distance (&current_point, &data[1]);
	current_point = data[1];
	break;

    default:
    case CAIRO_PATH_CURVE_TO:
    case CAIRO_PATH_CLOSE_PATH:
	g_assert_not_reached ();
    }
  }
  cairo_path_destroy (path);

  cairo_destroy (cr);

  return length;
}


typedef double parametrization_t;

/* Compute parametrization info.  That is, for each part of the 
 * cairo path, tags it with its length.
 *
 * Free returned value with g_free().
 */
static parametrization_t *
parametrize_path (cairo_path_t *path)
{
  int i;
  cairo_path_data_t *data, last_move_to = {{0,},}, current_point = {{0,},};
  parametrization_t *parametrization;

  parametrization = g_malloc (path->num_data * sizeof (parametrization[0]));

  for (i=0; i < path->num_data; i += path->data[i].header.length) {
    data = &path->data[i];
    parametrization[i] = 0.0;
    switch (data->header.type) {
    case CAIRO_PATH_MOVE_TO:
	last_move_to = data[1];
	current_point = data[1];
	break;
    case CAIRO_PATH_CLOSE_PATH:
	/* Make it look like it's a line_to to last_move_to */
	data = (&last_move_to) - 1;
        G_GNUC_FALLTHROUGH;
    case CAIRO_PATH_LINE_TO:
	parametrization[i] = two_points_distance (&current_point, &data[1]);
	current_point = data[1];
	break;
    case CAIRO_PATH_CURVE_TO:
	/* naive curve-length, treating bezier as three line segments:
	parametrization[i] = two_points_distance (&current_point, &data[1])
			   + two_points_distance (&data[1], &data[2])
			   + two_points_distance (&data[2], &data[3]);
	*/
	parametrization[i] = curve_length (current_point.point.x, current_point.point.y,
					   data[1].point.x, data[1].point.y,
					   data[2].point.x, data[2].point.y,
					   data[3].point.x, data[3].point.y);

	current_point = data[3];
	break;
    default:
	g_assert_not_reached ();
    }
  }

  return parametrization;
}


typedef void (*transform_point_func_t) (void *closure, double *x, double *y);

/* Project a path using a function.  Each point of the path (including
 * Bezier control points) is passed to the function for transformation.
 */
static void
transform_path (cairo_path_t *path, transform_point_func_t f, void *closure)
{
  int i;
  cairo_path_data_t *data;

  for (i=0; i < path->num_data; i += path->data[i].header.length) {
    data = &path->data[i];
    switch (data->header.type) {
    case CAIRO_PATH_CURVE_TO:
      f (closure, &data[3].point.x, &data[3].point.y);
      f (closure, &data[2].point.x, &data[2].point.y);
      G_GNUC_FALLTHROUGH;
    case CAIRO_PATH_MOVE_TO:
    case CAIRO_PATH_LINE_TO:
      f (closure, &data[1].point.x, &data[1].point.y);
      break;
    case CAIRO_PATH_CLOSE_PATH:
      break;
    default:
	g_assert_not_reached ();
    }
  }
}


/* Simple struct to hold a path and its parametrization */
typedef struct {
  cairo_path_t *path;
  parametrization_t *parametrization;
} parametrized_path_t;


/* Project a point X,Y onto a parameterized path.  The final point is
 * where you get if you walk on the path forward from the beginning for X
 * units, then stop there and walk another Y units perpendicular to the
 * path at that point.  In more detail:
 *
 * There's three pieces of math involved:
 *
 *   - The parametric form of the Line equation
 *     http://en.wikipedia.org/wiki/Line
 *
 *   - The parametric form of the Cubic Bézier curve equation
 *     http://en.wikipedia.org/wiki/B%C3%A9zier_curve
 *
 *   - The Gradient (aka multi-dimensional derivative) of the above
 *     http://en.wikipedia.org/wiki/Gradient
 *
 * The parametric forms are used to answer the question of "where will I be
 * if I walk a distance of X on this path".  The Gradient is used to answer
 * the question of "where will I be if then I stop, rotate left for 90
 * degrees and walk straight for a distance of Y".
 */
static void
point_on_path (parametrized_path_t *param,
	       double *x, double *y)
{
  int i;
  double ratio, the_y = *y, the_x = *x, dx, dy;
  cairo_path_data_t *data, last_move_to = {{0,},}, current_point = {{0,},};
  cairo_path_t *path = param->path;
  parametrization_t *parametrization = param->parametrization;

  for (i=0; i + path->data[i].header.length < path->num_data &&
	    (the_x > parametrization[i] ||
	     path->data[i].header.type == CAIRO_PATH_MOVE_TO);
       i += path->data[i].header.length) {
    the_x -= parametrization[i];
    data = &path->data[i];
    switch (data->header.type) {
    case CAIRO_PATH_MOVE_TO:
	current_point = data[1];
        last_move_to = data[1];
	break;
    case CAIRO_PATH_LINE_TO:
	current_point = data[1];
	break;
    case CAIRO_PATH_CURVE_TO:
	current_point = data[3];
	break;
    case CAIRO_PATH_CLOSE_PATH:
	break;
    default:
	g_assert_not_reached ();
    }
  }
  data = &path->data[i];

  switch (data->header.type) {

  case CAIRO_PATH_MOVE_TO:
      break;
  case CAIRO_PATH_CLOSE_PATH:
      /* Make it look like it's a line_to to last_move_to */
      data = (&last_move_to) - 1;
      G_GNUC_FALLTHROUGH;
  case CAIRO_PATH_LINE_TO:
      {
	ratio = the_x / parametrization[i];
	/* Line polynomial */
	*x = current_point.point.x * (1 - ratio) + data[1].point.x * ratio;
	*y = current_point.point.y * (1 - ratio) + data[1].point.y * ratio;

	/* Line gradient */
	dx = -(current_point.point.x - data[1].point.x);
	dy = -(current_point.point.y - data[1].point.y);

	/*optimization for: ratio = the_y / sqrt (dx * dx + dy * dy);*/
	ratio = the_y / parametrization[i];
	*x += -dy * ratio;
	*y +=  dx * ratio;
      }
      break;
  case CAIRO_PATH_CURVE_TO:
      {
	/* FIXME the formulas here are not exactly what we want, because the
	 * Bezier parametrization is not uniform.  But I don't know how to do
	 * better.  The caller can do slightly better though, by flattening the
	 * Bezier and avoiding this branch completely.  That has its own cost
	 * though, as large y values magnify the flattening error drastically.
	 */

        double ratio_1_0, ratio_0_1;
	double ratio_2_0, ratio_0_2;
	double ratio_3_0, ratio_2_1, ratio_1_2, ratio_0_3;
	double _1__4ratio_1_0_3ratio_2_0, _2ratio_1_0_3ratio_2_0;

	ratio = the_x / parametrization[i];

	ratio_1_0 = ratio;
	ratio_0_1 = 1 - ratio;

	ratio_2_0 = ratio_1_0 * ratio_1_0; /*      ratio  *      ratio  */
	ratio_0_2 = ratio_0_1 * ratio_0_1; /* (1 - ratio) * (1 - ratio) */

	ratio_3_0 = ratio_2_0 * ratio_1_0; /*      ratio  *      ratio  *      ratio  */
	ratio_2_1 = ratio_2_0 * ratio_0_1; /*      ratio  *      ratio  * (1 - ratio) */
	ratio_1_2 = ratio_1_0 * ratio_0_2; /*      ratio  * (1 - ratio) * (1 - ratio) */
	ratio_0_3 = ratio_0_1 * ratio_0_2; /* (1 - ratio) * (1 - ratio) * (1 - ratio) */

	_1__4ratio_1_0_3ratio_2_0 = 1 - 4 * ratio_1_0 + 3 * ratio_2_0;
	_2ratio_1_0_3ratio_2_0    =     2 * ratio_1_0 - 3 * ratio_2_0;

	/* Bezier polynomial */
	*x = current_point.point.x * ratio_0_3
	   + 3 *   data[1].point.x * ratio_1_2
	   + 3 *   data[2].point.x * ratio_2_1
	   +       data[3].point.x * ratio_3_0;
	*y = current_point.point.y * ratio_0_3
	   + 3 *   data[1].point.y * ratio_1_2
	   + 3 *   data[2].point.y * ratio_2_1
	   +       data[3].point.y * ratio_3_0;

	/* Bezier gradient */
	dx =-3 * current_point.point.x * ratio_0_2
	   + 3 *       data[1].point.x * _1__4ratio_1_0_3ratio_2_0
	   + 3 *       data[2].point.x * _2ratio_1_0_3ratio_2_0
	   + 3 *       data[3].point.x * ratio_2_0;
	dy =-3 * current_point.point.y * ratio_0_2
	   + 3 *       data[1].point.y * _1__4ratio_1_0_3ratio_2_0
	   + 3 *       data[2].point.y * _2ratio_1_0_3ratio_2_0
	   + 3 *       data[3].point.y * ratio_2_0;

	ratio = the_y / sqrt (dx * dx + dy * dy);
	*x += -dy * ratio;
	*y +=  dx * ratio;
      }
      break;
  default:
      g_assert_not_reached ();
  }
}

static void
point_on_trapezoid (void *,
	       double *x, double *y)
{
  double distance_from_neutral = *y - 200;
  double distance_from_center = *x - 100;
  *x += -10 * distance_from_center / distance_from_neutral;
}

/* Projects the current path of cr onto the provided path. */
static void
map_path_onto (cairo_t *cr)
{
  cairo_path_t *current_path;

  current_path = cairo_copy_path (cr);
  cairo_new_path (cr);

  transform_path (current_path,
		  (transform_point_func_t) point_on_trapezoid, NULL);

  cairo_append_path (cr, current_path);

  cairo_path_destroy (current_path);
}


typedef void (*draw_path_func_t) (cairo_t *cr);

static void
draw_text (cairo_t *cr,
	   double x,
	   double y,
	   const char *font,
	   const char *text)
{
  PangoLayout *layout;
  PangoLayoutLine *line;
  PangoFontDescription *desc;
  cairo_font_options_t *font_options;

  font_options = cairo_font_options_create ();

  cairo_font_options_set_hint_style (font_options, CAIRO_HINT_STYLE_NONE);
  cairo_font_options_set_hint_metrics (font_options, CAIRO_HINT_METRICS_OFF);

  cairo_set_font_options (cr, font_options);
  cairo_font_options_destroy (font_options);

  layout = pango_cairo_create_layout (cr);

  desc = pango_font_description_from_string (font);
  pango_layout_set_font_description (layout, desc);
  pango_font_description_free (desc);

  pango_layout_set_text (layout, text, -1);

  /* Use pango_layout_get_line() instead of pango_layout_get_line_readonly()
   * for older versions of pango
   */
  line = pango_layout_get_line_readonly (layout, 0);

  cairo_move_to (cr, x, y);
  pango_cairo_layout_line_path (cr, line);

  g_object_unref (layout);
}

static void
draw_twisted (cairo_t *cr,
	      double x,
	      double y,
	      const char *font,
	      const char *text)
{
  cairo_save (cr);

  /* Decrease tolerance a bit, since it's going to be magnified */
  cairo_set_tolerance (cr, 0.01);

  /* Using cairo_copy_path() here shows our deficiency in handling
   * Bezier curves, specially around sharper curves.
   *
   * Using cairo_copy_path_flat() on the other hand, magnifies the
   * flattening error with large off-path values.  We decreased
   * tolerance for that reason.  Increase tolerance to see that
   * artifact.
   */
/*path = cairo_copy_path (cr);*/

  cairo_new_path (cr);

  draw_text (cr, x, y, font, text);
  map_path_onto (cr);

  cairo_fill_preserve (cr);

  cairo_save (cr);
  cairo_set_source_rgb (cr, 0.1, 0.1, 0.1);
  cairo_stroke (cr);
  cairo_restore (cr);

  cairo_restore (cr);
}

static void
draw_dream (cairo_t *cr)
{
  draw_twisted (cr,
		0, 100,
		"Serif 72",
		"It was a dream... Oh Just a dream...");
}

static void
draw_wow (cairo_t *cr)
{
  cairo_move_to (cr, 400, 780);

  cairo_rel_curve_to (cr, 50, -50, 150, -50, 200, 0);

  cairo_scale (cr, 1.0, 2.0);
  cairo_set_line_width (cr, 2.0);
  cairo_set_source_rgba (cr, 0.3, 1.0, 0.3, 1.0);

  fancy_cairo_stroke_preserve (cr);

  draw_twisted (cr,
		-20, -150,
		"Serif 60",
		"WOW!");
}

int main (int argc, char **argv)
{
  cairo_t *cr;
  char *filename;
  cairo_status_t status;
  cairo_surface_t *surface;

  if (argc != 2)
    {
      g_printerr ("Usage: cairotwisted OUTPUT_FILENAME\n");
      return 1;
    }

  filename = argv[1];

  surface = cairo_image_surface_create (CAIRO_FORMAT_ARGB32,
					1000, 800);
  cr = cairo_create (surface);

  cairo_set_source_rgb (cr, 1.0, 1.0, 1.0);
  cairo_paint (cr);

  draw_dream (cr);
  //draw_wow (cr);

  cairo_destroy (cr);

  status = cairo_surface_write_to_png (surface, filename);
  cairo_surface_destroy (surface);

  if (status != CAIRO_STATUS_SUCCESS)
    {
      g_printerr ("Could not save png to '%s'\n", filename);
      return 1;
    }

  return 0;
}