diff options
| -rw-r--r-- | ChangeLog | 6 | ||||
| -rw-r--r-- | examples/cairotwisted.c | 288 |
2 files changed, 171 insertions, 123 deletions
@@ -1,3 +1,9 @@ +2007-11-30 Behdad Esfahbod <behdad@gnome.org> + + * examples/cairotwisted.c (two_points_distance), (curve_length), + (parametrize_path), (point_on_path), (draw_twisted), (main): + Document cairotwisted example. + 2007-11-29 Behdad Esfahbod <behdad@gnome.org> * example/cairo*.c: Add some documentation. diff --git a/examples/cairotwisted.c b/examples/cairotwisted.c index 47d1e3d9..5697e57a 100644 --- a/examples/cairotwisted.c +++ b/examples/cairotwisted.c @@ -13,114 +13,10 @@ #include <stdlib.h> #include <pango/pangocairo.h> -void fancy_cairo_stroke (cairo_t *cr); -void fancy_cairo_stroke_preserve (cairo_t *cr); - - -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); -} - -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; - 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 (¤t_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; - -static parametrization_t * -parametrize_path (cairo_path_t *path) -{ - int i; - cairo_path_data_t *data, current_point; - parametrization_t *parametrization; - - parametrization = 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: - current_point = data[1]; - break; - case CAIRO_PATH_LINE_TO: - parametrization[i] = two_points_distance (¤t_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 (¤t_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.x, - 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; - case CAIRO_PATH_CLOSE_PATH: - break; - default: - g_assert_not_reached (); - } - } - - return parametrization; -} +/* 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) { @@ -224,20 +120,145 @@ _fancy_cairo_stroke (cairo_t *cr, cairo_bool_t preserve) 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; + 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 (¤t_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. + */ +static parametrization_t * +parametrize_path (cairo_path_t *path) +{ + int i; + cairo_path_data_t *data, current_point; + parametrization_t *parametrization; + + parametrization = 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: + current_point = data[1]; + break; + case CAIRO_PATH_LINE_TO: + parametrization[i] = two_points_distance (¤t_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 (¤t_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.x, + 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; + case CAIRO_PATH_CLOSE_PATH: + 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) { @@ -262,26 +283,33 @@ transform_path (cairo_path_t *path, transform_point_func_t f, void *closure) } } + +/* 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. */ static void point_on_path (parametrized_path_t *param, double *x, double *y) { int i; - double ratio, oldy = *y, d = *x, dx, dy; + double ratio, the_y = *y, the_x = *x, dx, dy; cairo_path_data_t *data, current_point; cairo_path_t *path = param->path; parametrization_t *parametrization = param->parametrization; for (i=0; i + path->data[i].header.length < path->num_data && - (d > parametrization[i] || + (the_x > parametrization[i] || path->data[i].header.type == CAIRO_PATH_MOVE_TO); i += path->data[i].header.length) { - d -= parametrization[i]; + the_x -= parametrization[i]; data = &path->data[i]; switch (data->header.type) { case CAIRO_PATH_MOVE_TO: @@ -306,23 +334,31 @@ point_on_path (parametrized_path_t *param, case CAIRO_PATH_MOVE_TO: break; case CAIRO_PATH_LINE_TO: - ratio = d / parametrization[i]; + 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); - d = oldy; - ratio = d / parametrization[i]; - /*ratio = d / sqrt (dx * dx + dy * dy);*/ - + /*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: - ratio = d / parametrization[i]; + /* 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. + */ + + ratio = the_x / parametrization[i]; + /* Bezier polynomial */ *x = current_point.point.x * (1 - ratio) * (1 - ratio) * (1 - ratio) + 3 * data[1].point.x * (1 - ratio) * (1 - ratio) * ratio + 3 * data[2].point.x * (1 - ratio) * ratio * ratio @@ -332,6 +368,7 @@ point_on_path (parametrized_path_t *param, + 3 * data[2].point.y * (1 - ratio) * ratio * ratio + data[3].point.y * ratio * ratio * ratio; + /* Bezier gradient */ dx =-3 * current_point.point.x * (1 - ratio) * (1 - ratio) + 3 * data[1].point.x * (1 - 4 * ratio + 3 * ratio * ratio) + 3 * data[2].point.x * ( 2 * ratio - 3 * ratio * ratio) @@ -341,9 +378,7 @@ point_on_path (parametrized_path_t *param, + 3 * data[2].point.y * ( 2 * ratio - 3 * ratio * ratio) + 3 * data[3].point.y * ratio * ratio; - d = oldy; - ratio = d / sqrt (dx * dx + dy * dy); - + ratio = the_y / sqrt (dx * dx + dy * dy); *x += -dy * ratio; *y += dx * ratio; @@ -355,6 +390,7 @@ point_on_path (parametrized_path_t *param, } } +/* Projects the current path of cr onto the provided path. */ static void map_path_onto (cairo_t *cr, cairo_path_t *path) { @@ -427,8 +463,16 @@ draw_twisted (cairo_t *cr, cairo_save (cr); /* Decrease tolerance a bit, since it's going to be magnified */ - cairo_set_tolerance (cr, 0.1); - + 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_flat (cr); /*path = cairo_copy_path (cr);*/ @@ -505,8 +549,6 @@ int main (int argc, char **argv) 1000, 800); cr = cairo_create (surface); - /* cairo_scale (cr, 0.5, 0.5); */ - cairo_set_source_rgb (cr, 1.0, 1.0, 1.0); cairo_paint (cr); |