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/* Libart_LGPL - library of basic graphic primitives
* Copyright (C) 1998 Raph Levien
*
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Library General Public
* License as published by the Free Software Foundation; either
* version 2 of the License, or (at your option) any later version.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Library General Public License for more details.
*
* You should have received a copy of the GNU Library General Public
* License along with this library; if not, write to the
* Free Software Foundation, Inc., 59 Temple Place - Suite 330,
* Boston, MA 02111-1307, USA.
*/
/* Simple manipulations with affine transformations */
#include "config.h"
#include "art_affine.h"
#include "art_misc.h" /* for M_PI */
#include <math.h>
#include <stdio.h> /* for sprintf */
#include <string.h> /* for strcpy */
/* According to a strict interpretation of the libart structure, this
routine should go into its own module, art_point_affine. However,
it's only two lines of code, and it can be argued that it is one of
the natural basic functions of an affine transformation.
*/
/**
* art_affine_point: Do an affine transformation of a point.
* @dst: Where the result point is stored.
* @src: The original point.
@ @affine: The affine transformation.
**/
void
art_affine_point (ArtPoint *dst, const ArtPoint *src,
const gdouble affine[6])
{
gdouble x, y;
x = src->x;
y = src->y;
dst->x = x * affine[0] + y * affine[2] + affine[4];
dst->y = x * affine[1] + y * affine[3] + affine[5];
}
/**
* art_affine_invert: Find the inverse of an affine transformation.
* @dst: Where the resulting affine is stored.
* @src: The original affine transformation.
*
* All non-degenerate affine transforms are invertible. If the original
* affine is degenerate or nearly so, expect numerical instability and
* very likely core dumps on Alpha and other fp-picky architectures.
* Otherwise, @dst multiplied with @src, or @src multiplied with @dst
* will be (to within roundoff error) the identity affine.
**/
void
art_affine_invert (gdouble dst[6], const gdouble src[6])
{
gdouble r_det;
r_det = 1.0 / (src[0] * src[3] - src[1] * src[2]);
dst[0] = src[3] * r_det;
dst[1] = -src[1] * r_det;
dst[2] = -src[2] * r_det;
dst[3] = src[0] * r_det;
dst[4] = -src[4] * dst[0] - src[5] * dst[2];
dst[5] = -src[4] * dst[1] - src[5] * dst[3];
}
/**
* art_affine_multiply: Multiply two affine transformation matrices.
* @dst: Where to store the result.
* @src1: The first affine transform to multiply.
* @src2: The second affine transform to multiply.
*
* Multiplies two affine transforms together, i.e. the resulting @dst
* is equivalent to doing first @src1 then @src2. Note that the
* PostScript concat operator multiplies on the left, i.e. "M concat"
* is equivalent to "CTM = multiply (M, CTM)";
*
* It is safe to call this function with @dst equal to @src1 or @src2.
**/
void
art_affine_multiply (gdouble dst[6], const gdouble src1[6], const gdouble src2[6])
{
gdouble d0, d1, d2, d3, d4, d5;
d0 = src1[0] * src2[0] + src1[1] * src2[2];
d1 = src1[0] * src2[1] + src1[1] * src2[3];
d2 = src1[2] * src2[0] + src1[3] * src2[2];
d3 = src1[2] * src2[1] + src1[3] * src2[3];
d4 = src1[4] * src2[0] + src1[5] * src2[2] + src2[4];
d5 = src1[4] * src2[1] + src1[5] * src2[3] + src2[5];
dst[0] = d0;
dst[1] = d1;
dst[2] = d2;
dst[3] = d3;
dst[4] = d4;
dst[5] = d5;
}
/**
* art_affine_identity: Set up the identity matrix.
* @dst: Where to store the resulting affine transform.
*
* Sets up an identity matrix.
**/
void
art_affine_identity (gdouble dst[6])
{
dst[0] = 1;
dst[1] = 0;
dst[2] = 0;
dst[3] = 1;
dst[4] = 0;
dst[5] = 0;
}
/**
* art_affine_scale: Set up a scaling matrix.
* @dst: Where to store the resulting affine transform.
* @sx: X scale factor.
* @sy: Y scale factor.
*
* Sets up a scaling matrix.
**/
void
art_affine_scale (gdouble dst[6], gdouble sx, gdouble sy)
{
dst[0] = sx;
dst[1] = 0;
dst[2] = 0;
dst[3] = sy;
dst[4] = 0;
dst[5] = 0;
}
/**
* art_affine_translate: Set up a translation matrix.
* @dst: Where to store the resulting affine transform.
* @tx: X translation amount.
* @tx: Y translation amount.
*
* Sets up a translation matrix.
**/
void
art_affine_translate (gdouble dst[6], gdouble tx, gdouble ty)
{
dst[0] = 1;
dst[1] = 0;
dst[2] = 0;
dst[3] = 1;
dst[4] = tx;
dst[5] = ty;
}
/**
* art_affine_expansion: Find the affine's expansion factor.
* @src: The affine transformation.
*
* Finds the expansion factor, i.e. the square root of the factor
* by which the affine transform affects area. In an affine transform
* composed of scaling, rotation, shearing, and translation, returns
* the amount of scaling.
*
* Return value: the expansion factor.
**/
gdouble
art_affine_expansion (const gdouble src[6])
{
return sqrt (fabs (src[0] * src[3] - src[1] * src[2]));
}
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