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Rescale CTM used for PS/PDF stroking to reduce rounding error

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The PS/PDF CTM is transformed to the user space CTM when emitting
paths to be stroked to ensure the correct pen shape used. However this
can result in rounding errors.

For example the device space point (1.234, 3.142) when transformed to
a user space CTM of [100 0 0 100 0 0] will be emitted as
(0.012, 0.031).

Fix this by rescaling the user space CTM so that the path coordinates
emitted to the PDF file stay within the range the maximizes the
precision. The line width and dashing is also rescaled to be the same
size in the rescaled CTM.
This commit is contained in:
Adrian Johnson 2008-03-18 22:25:18 +10:30
parent 7f4b967c02
commit 4d9e5b51aa
1 changed files with 63 additions and 7 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

70
src/cairo-pdf-operators.c
View file

@ -480,7 +480,8 @@ _cairo_pdf_line_join (cairo_line_join_t join)
static cairo_int_status_t
_cairo_pdf_operators_emit_stroke_style (cairo_pdf_operators_t *pdf_operators,
cairo_stroke_style_t *style)
cairo_stroke_style_t *style,
double scale)
{
double *dash = style->dash;
int num_dashes = style->num_dashes;
@ -551,7 +552,7 @@ _cairo_pdf_operators_emit_stroke_style (cairo_pdf_operators_t *pdf_operators,
_cairo_output_stream_printf (pdf_operators->stream,
"%f w\n",
style->line_width);
style->line_width * scale);
_cairo_output_stream_printf (pdf_operators->stream,
"%d J\n",
@ -566,9 +567,9 @@ _cairo_pdf_operators_emit_stroke_style (cairo_pdf_operators_t *pdf_operators,
_cairo_output_stream_printf (pdf_operators->stream, "[");
for (d = 0; d < num_dashes; d++)
_cairo_output_stream_printf (pdf_operators->stream, " %f", dash[d]);
_cairo_output_stream_printf (pdf_operators->stream, " %f", dash[d] * scale);
_cairo_output_stream_printf (pdf_operators->stream, "] %f d\n",
dash_offset);
dash_offset * scale);
} else {
_cairo_output_stream_printf (pdf_operators->stream, "[] 0.0 d\n");
}
@ -582,6 +583,31 @@ _cairo_pdf_operators_emit_stroke_style (cairo_pdf_operators_t *pdf_operators,
return _cairo_output_stream_get_status (pdf_operators->stream);
}
/* Scale the matrix so the largest absolute value of the non
* translation components is 1.0. Return the scale required to restore
* the matrix to the original values.
*
* eg the matrix [ 100 0 0 50 20 10 ]
*
* is rescaled to [ 1 0 0 0.5 0.2 0.1 ]
* and the scale returned is 100
*/
static void
_cairo_matrix_factor_out_scale (cairo_matrix_t *m, double *scale)
{
double s;
s = fabs (m->xx);
if (fabs (m->xy) > s)
s = fabs (m->xy);
if (fabs (m->yx) > s)
s = fabs (m->yx);
if (fabs (m->yy) > s)
s = fabs (m->yy);
*scale = s;
s = 1.0/s;
cairo_matrix_scale (m, s, s);
}
static cairo_int_status_t
_cairo_pdf_operators_emit_stroke (cairo_pdf_operators_t *pdf_operators,
@ -594,6 +620,7 @@ _cairo_pdf_operators_emit_stroke (cairo_pdf_operators_t *pdf_operators,
cairo_status_t status;
cairo_matrix_t m, path_transform;
cairo_bool_t has_ctm = TRUE;
double scale = 1.0;
/* Optimize away the stroke ctm when it does not affect the
* stroke. There are other ctm cases that could be optimized
@ -605,15 +632,44 @@ _cairo_pdf_operators_emit_stroke (cairo_pdf_operators_t *pdf_operators,
has_ctm = FALSE;
}
status = _cairo_pdf_operators_emit_stroke_style (pdf_operators, style);
/* The PDF CTM is transformed to the user space CTM when stroking
* so the corect pen shape will be used. This also requires that
* the path be transformed to user space when emitted. The
* conversion of path coordinates to user space may cause rounding
* errors. For example the device space point (1.234, 3.142) when
* transformed to a user space CTM of [100 0 0 100 0 0] will be
* emitted as (0.012, 0.031).
*
* To avoid the rounding problem we scale the user space CTM
* matrix so that all the non translation components of the matrix
* are <= 1. The line width and and dashes are scaled by the
* inverse of the scale applied to the CTM. This maintains the
* shape of the stroke pen while keeping the user space CTM within
* the range that maximizes the precision of the emitted path.
*/
if (has_ctm) {
m = *ctm;
/* Zero out the translation since it does not affect the pen
* shape however it may cause unnecessary digits to be emitted.
*/
m.x0 = 0.0;
m.y0 = 0.0;
_cairo_matrix_factor_out_scale (&m, &scale);
path_transform = m;
status = cairo_matrix_invert (&path_transform);
if (status)
return status;
cairo_matrix_multiply (&m, &m, &pdf_operators->cairo_to_pdf);
}
status = _cairo_pdf_operators_emit_stroke_style (pdf_operators, style, scale);
if (status == CAIRO_INT_STATUS_NOTHING_TO_DO)
return CAIRO_STATUS_SUCCESS;
if (status)
return status;
if (has_ctm) {
cairo_matrix_multiply (&m, ctm, &pdf_operators->cairo_to_pdf);
path_transform = *ctm_inverse;
_cairo_output_stream_printf (pdf_operators->stream,
"q %f %f %f %f %f %f cm\n",
m.xx, m.yx, m.xy, m.yy,