Matrix Inconsistency?

Lawrence D'Oliveiro <[email protected]> Mon, 27 Jun 2016 16:06:35 +1200

Newsgroups	gmane.comp.lib.cairo
Organization	Geek Central
Message-ID	<[email protected]>

The docs for cairo_matrix_multiply(&result, &a, &b)
<https://www.cairographics.org/manual/cairo-cairo-matrix-t.html#cairo-matrix-multiply>
say “The effect of the resulting transformation is to first apply the
transformation in a to the coordinates and then apply the
transformation in b to the coordinates”, while the docs for
cairo_transform
<https://www.cairographics.org/manual/cairo-Transformations.html#cairo-transform>
say “The new transformation of user space takes place after any
existing transformation”.

It seems to me, then that the sequence

    cairo_matrix_multiply(&resultmat, &mat_rotate, &mat_translate);

should put the same thing into resultmat as the sequence

    cairo_identity_matrix(cr);
    cairo_transform(cr, &mat_rotate);
    cairo_transform(cr, &mat_translate);
    cairo_get_matrix(cr, &resultmat);

but it does not. Given the following definitions for mat_rotate and
mat_translate:

    cairo_matrix_init_rotate(&mat_rotate, M_PI / 4.0);
    cairo_matrix_init_translate(&mat_translate, 1.0, 1.0);

I get the following output from my test program:

    * matrix:
    rotate × translate = [[0.707, -0.707, 1] [0.707, 0.707, 1] [0, 0, 1]]
    translate × rotate = [[0.707, -0.707, 1.11e-16] [0.707, 0.707, 1.41] [0, 0, 1]]
    * context:
    rotate × translate = [[0.707, -0.707, 1.11e-16] [0.707, 0.707, 1.41] [0, 0, 1]]
    translate × rotate = [[0.707, -0.707, 1] [0.707, 0.707, 1] [0, 0, 1]]

The output for the cairo_matrix calls looks the right way round,
that for the cairo_transform calls does not.

See the attached source for the full program.

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matrix_order.c (text/x-c++src, 2.7 KB)

/*
    Comparing <https://www.cairographics.org/manual/cairo-Transformations.html>
    with <https://www.cairographics.org/manual/cairo-cairo-matrix-t.html>, is
    the ordering of matrix operations consistent?
*/

#define _XOPEN_SOURCE 500 /* for M_PI, which is not part of standard C */
#include <math.h>
#include <stdio.h>
#include <cairo/cairo.h>

static void print_matrix
  (
    const cairo_matrix_t * mat,
    FILE * out
  )
  {
#define ELT_FMT "%.3g"
    fprintf
      (
        out,
        "[[" ELT_FMT ", " ELT_FMT ", " ELT_FMT "]"
        " [" ELT_FMT ", " ELT_FMT ", " ELT_FMT "]"
        " [0, 0, 1]]",
        mat->xx, mat->xy, mat->x0,
        mat->yx, mat->yy, mat->y0
      );
#undef ELT_FMT
  } /*print_matrix*/

int main
  (
    int argc,
    char ** argv
  )
  {
    const int img_size = 10; /* dummy */
    cairo_surface_t * const pix = cairo_image_surface_create
      (
        /*format =*/ CAIRO_FORMAT_RGB24,
        /*width =*/ img_size,
        /*height =*/ img_size
      );
    cairo_t * const cr = cairo_create(pix);
    cairo_matrix_t mat_rotate, mat_translate, resultmat;
    cairo_matrix_init_rotate(&mat_rotate, M_PI / 4.0);
    cairo_matrix_init_translate(&mat_translate, 1.0, 1.0);
    cairo_matrix_multiply(&resultmat, &mat_rotate, &mat_translate);
      /*
       According to the docs
       <https://www.cairographics.org/manual/cairo-cairo-matrix-t.html#cairo-matrix-multiply>,
       “The effect of [cairo_matrix_multiply(&result, &a, &b)] is to
       first apply the transformation in a to the coordinates and then
       apply the transformation in b to the coordinates.”
      */
    fputs("* matrix:\nrotate × translate = ", stdout);
    print_matrix(&resultmat, stdout);
    fputs("\n", stdout);
    cairo_matrix_multiply(&resultmat, &mat_translate, &mat_rotate);
    fputs("translate × rotate = ", stdout);
    print_matrix(&resultmat, stdout);
    fputs("\n", stdout);
    cairo_identity_matrix(cr);
    cairo_transform(cr, &mat_rotate);
    cairo_transform(cr, &mat_translate);
      /*
        According to the docs
        <https://www.cairographics.org/manual/cairo-Transformations.html#cairo-transform>,
        “The new transformation of user space takes place after any
        existing transformation.”
      */
    cairo_get_matrix(cr, &resultmat);
    fputs("* context:\nrotate × translate = ", stdout);
    print_matrix(&resultmat, stdout);
    fputs("\n", stdout);
    cairo_identity_matrix(cr);
    cairo_transform(cr, &mat_translate);
    cairo_transform(cr, &mat_rotate);
    cairo_get_matrix(cr, &resultmat);
    fputs("translate × rotate = ", stdout);
    print_matrix(&resultmat, stdout);
    fputs("\n", stdout);
    return
        0;
  } /*main*/