static int
_cairo_pen_vertices_needed (double tolerance,
double radius,
cairo_matrix_t *matrix)
{
/*
* the pen is a circle that gets transformed to an ellipse by matrix.
* compute major axis length for a pen with the specified radius.
* we don't need the minor axis length.
*/
double major_axis = _cairo_matrix_transformed_circle_major_axis(matrix, radius);
/*
* compute number of vertices needed
*/
int num_vertices;
/* Where tolerance / M is > 1, we use 4 points */
if (tolerance >= major_axis) {
num_vertices = 4;
} else {
double delta = acos (1 - tolerance / major_axis);
num_vertices = ceil (M_PI / delta);
/* number of vertices must be even */
if (num_vertices % 2)
num_vertices++;
}
return num_vertices;
}
int
_cairo_pen_vertices_needed (double tolerance,
double radius,
const cairo_matrix_t *matrix)
{
/*
* the pen is a circle that gets transformed to an ellipse by matrix.
* compute major axis length for a pen with the specified radius.
* we don't need the minor axis length.
*/
double major_axis = _cairo_matrix_transformed_circle_major_axis (matrix,
radius);
int num_vertices;
if (tolerance >= 4*major_axis) { /* XXX relaxed from 2*major for inkscape */
num_vertices = 1;
} else if (tolerance >= major_axis) {
num_vertices = 4;
} else {
num_vertices = ceil (2*M_PI / acos (1 - tolerance / major_axis));
/* number of vertices must be even */
if (num_vertices % 2)
num_vertices++;
/* And we must always have at least 4 vertices. */
if (num_vertices < 4)
num_vertices = 4;
}
return num_vertices;
}
/*
* Verifies if _cairo_stroke_style_dash_approximate should be used to generate
* an approximation of the dash pattern in the specified style, when used for
* stroking a path with the given CTM and tolerance.
* Always %FALSE for non-dashed styles.
*/
cairo_bool_t
_cairo_stroke_style_dash_can_approximate (const cairo_stroke_style_t *style,
const cairo_matrix_t *ctm,
double tolerance)
{
double period;
if (! style->num_dashes)
return FALSE;
period = _cairo_stroke_style_dash_period (style);
return _cairo_matrix_transformed_circle_major_axis (ctm, period) < tolerance;
}
static int
_arc_segments_needed (double angle,
double radius,
cairo_matrix_t *ctm,
double tolerance)
{
double major_axis, max_angle;
/* the error is amplified by at most the length of the
* major axis of the circle; see cairo-pen.c for a more detailed analysis
* of this. */
major_axis = _cairo_matrix_transformed_circle_major_axis (ctm, radius);
max_angle = _arc_max_angle_for_tolerance_normalized (tolerance / major_axis);
return ceil (fabs (angle) / max_angle);
}
/*
* Create a 2-dashes approximation of a dashed style, by making the "on" and "off"
* parts respect the original ratio.
*/
void
_cairo_stroke_style_dash_approximate (const cairo_stroke_style_t *style,
const cairo_matrix_t *ctm,
double tolerance,
double *dash_offset,
double *dashes,
unsigned int *num_dashes)
{
double coverage, scale, offset;
cairo_bool_t on = TRUE;
unsigned int i = 0;
coverage = _cairo_stroke_style_dash_stroked (style) / _cairo_stroke_style_dash_period (style);
coverage = MIN (coverage, 1.0);
scale = tolerance / _cairo_matrix_transformed_circle_major_axis (ctm, 1.0);
/* We stop searching for a starting point as soon as the
* offset reaches zero. Otherwise when an initial dash
* segment shrinks to zero it will be skipped over. */
offset = style->dash_offset;
while (offset > 0.0 && offset >= style->dash[i]) {
offset -= style->dash[i];
on = !on;
if (++i == style->num_dashes)
i = 0;
}
*num_dashes = 2;
/*
* We want to create a new dash pattern with the same relative coverage,
* but composed of just 2 elements with total length equal to scale.
* Based on the formula in _cairo_stroke_style_dash_stroked:
* scale * coverage = dashes[0] + cap_scale * MIN (dashes[1], line_width)
* = MIN (dashes[0] + cap_scale * (scale - dashes[0]),
* dashes[0] + cap_scale * line_width) =
* = MIN (dashes[0] * (1 - cap_scale) + cap_scale * scale,
* dashes[0] + cap_scale * line_width)
*
* Solving both cases we get:
* dashes[0] = scale * (coverage - cap_scale) / (1 - cap_scale)
* when scale - dashes[0] <= line_width
* dashes[0] = scale * coverage - cap_scale * line_width
* when scale - dashes[0] > line_width.
*
* Comparing the two cases we get:
* second > first
* second > scale * (coverage - cap_scale) / (1 - cap_scale)
* second - cap_scale * second - scale * coverage + scale * cap_scale > 0
* (scale * coverage - cap_scale * line_width) - cap_scale * second - scale * coverage + scale * cap_scale > 0
* - line_width - second + scale > 0
* scale - second > line_width
* which is the condition for the second solution to be the valid one.
* So when second > first, the second solution is the correct one (i.e.
* the solution is always MAX (first, second).
*/
printf("cairostroke-style.c part 2 clear");
switch (style->line_cap) {
default:
ASSERT_NOT_REACHED;
dashes[0] = 0.0;
break;
//TODO DONE add LINE_CAP_TRIANGULAR
case CAIRO_LINE_CAP_BUTT:
/* Simplified formula (substituting 0 for cap_scale): */
dashes[0] = scale * coverage;
break;
case CAIRO_LINE_CAP_ROUND:
dashes[0] = MAX(scale * (coverage - ROUND_MINSQ_APPROXIMATION) / (1.0 - ROUND_MINSQ_APPROXIMATION),
scale * coverage - ROUND_MINSQ_APPROXIMATION * style->line_width);
break;
case CAIRO_LINE_CAP_TRIANGULAR:
dashes[0] = MAX(scale * (coverage - 0.5) / (1.0 - 0.5),
scale * coverage - 0.5 * style->line_width);
break;
case CAIRO_LINE_CAP_SQUARE:
/*
* Special attention is needed to handle the case cap_scale == 1 (since the first solution
* is either indeterminate or -inf in this case). Since dash lengths are always >=0, using
* 0 as first solution always leads to the correct solution.
*/
dashes[0] = MAX(0.0, scale * coverage - style->line_width);
break;
}
dashes[1] = scale - dashes[0];
*dash_offset = on ? 0.0 : dashes[0];
}
