/*====================================================================*

 -  Copyright (C) 2001 Leptonica.  All rights reserved.

 -

 -  Redistribution and use in source and binary forms, with or without

 -  modification, are permitted provided that the following conditions

 -  are met:

 -  1. Redistributions of source code must retain the above copyright

 -     notice, this list of conditions and the following disclaimer.

 -  2. Redistributions in binary form must reproduce the above

 -     copyright notice, this list of conditions and the following

 -     disclaimer in the documentation and/or other materials

 -     provided with the distribution.

 -

 -  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS

 -  ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT

 -  LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR

 -  A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL ANY

 -  CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,

 -  EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,

 -  PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR

 -  PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY

 -  OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING

 -  NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS

 -  SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

 *====================================================================*/

/*!

 * \file rotateam.c

 * <pre>

 *

 *     Grayscale and color rotation for area mapping (== interpolation)

 *

 *         Rotation about the image center

 *                PIX         *pixRotateAM()

 *                PIX         *pixRotateAMColor()

 *                PIX         *pixRotateAMGray()

 *                static void  rotateAMColorLow()

 *                static void  rotateAMGrayLow()

 *

 *         Rotation about the UL corner of the image

 *                PIX         *pixRotateAMCorner()

 *                PIX         *pixRotateAMColorCorner()

 *                PIX         *pixRotateAMGrayCorner()

 *                static void  rotateAMColorCornerLow()

 *                static void  rotateAMGrayCornerLow()

 *

 *         Faster color rotation about the image center

 *                PIX         *pixRotateAMColorFast()

 *                static void  rotateAMColorFastLow()

 *

 *     Rotations are measured in radians; clockwise is positive.

 *

 *     The basic area mapping grayscale rotation works on 8 bpp images.

 *     For color, the same method is applied to each color separately.

 *     This can be done in two ways: (1) as here, computing each dest

 *     rgb pixel from the appropriate four src rgb pixels, or (2) separating

 *     the color image into three 8 bpp images, rotate each of these,

 *     and then combine the result.  Method (1) is about 2.5x faster.

 *     We have also implemented a fast approximation for color area-mapping

 *     rotation (pixRotateAMColorFast()), which is about 25% faster

 *     than the standard color rotator.  If you need the extra speed,

 *     use it.

 *

 *     Area mapping works as follows.  For each dest

 *     pixel you find the 4 source pixels that it partially

 *     covers.  You then compute the dest pixel value as

 *     the area-weighted average of those 4 source pixels.

 *     We make two simplifying approximations:

 *

 *       ~  For simplicity, compute the areas as if the dest

 *          pixel were translated but not rotated.

 *

 *       ~  Compute area overlaps on a discrete sub-pixel grid.

 *          Because we are using 8 bpp images with 256 levels,

 *          it is convenient to break each pixel into a

 *          16x16 sub-pixel grid, and count the number of

 *          overlapped sub-pixels.

 *

 *     It is interesting to note that the digital filter that

 *     implements the area mapping algorithm for rotation

 *     is identical to the digital filter used for linear

 *     interpolation when arbitrarily scaling grayscale images.

 *

 *     The advantage of area mapping over pixel sampling

 *     in grayscale rotation is that the former naturally

 *     blurs sharp edges ("anti-aliasing"), so that stair-step

 *     artifacts are not introduced.  The disadvantage is that

 *     it is significantly slower.

 *

 *     But it is still pretty fast.  With standard 3 GHz hardware,

 *     the anti-aliased (area-mapped) color rotation speed is

 *     about 15 million pixels/sec.

 *

 *     The function pixRotateAMColorFast() is about 10-20% faster

 *     than pixRotateAMColor().  The quality is slightly worse,

 *     and if you make many successive small rotations, with a

 *     total angle of 360 degrees, it has been noted that the

 *     center wanders -- it seems to be doing a 1 pixel translation

 *     in addition to the rotation.

 *

 *     Consider again the comparison of image quality between sampling

 *     and area mapping.  With sampling, sharp edges such as found in

 *     text images remain sharp.  However, sampling artifacts such as

 *     characters randomly bouncing up and down by one pixel, or

 *     one pixel horizontal shear lines going through a line of text

 *     (causing the characters to look like badly rendered italic),

 *     are highly visible.  It does not help to sample the source pixel

 *     with the largest area covering each dest pixel; the result has

 *     the same ugly sampling artifacts.

 *

 *     With area mapping, these annoying artifacts are avoided, but the

 *     blurring of edges makes small text a bit more difficult to read.

 *     However, if you are willing to do more computation, you can have

 *     the best of both worlds: no sampling artifacts and sharp edges.

 *     Use area mapping to avoid sampling issues, and follow it with

 *     unsharp masking.  Experiment with the sharpening parameters.

 *     I have found that a small amount of sharpening is sufficient to

 *     restore the sharp edges in text; e.g.,

 *         pix2 = pixUnsharpMasking(pix1, 1, 0.3);

 * </pre>

 */

#ifdef HAVE_CONFIG_H

#include <config_auto.h>

#endif  /* HAVE_CONFIG_H */

#include <string.h>

#include <math.h>   /* required for sin and tan */

#include "allheaders.h"

static void rotateAMColorLow(l_uint32 *datad, l_int32 w, l_int32 h,

                             l_int32 wpld, l_uint32 *datas, l_int32 wpls,

                             l_float32 angle, l_uint32 colorval);

static void rotateAMGrayLow(l_uint32 *datad, l_int32 w, l_int32 h,

                            l_int32 wpld, l_uint32 *datas, l_int32 wpls,

                            l_float32 angle, l_uint8 grayval);

static void rotateAMColorCornerLow(l_uint32 *datad, l_int32 w, l_int32 h,

                                   l_int32 wpld, l_uint32 *datas,

                                   l_int32 wpls, l_float32 angle,

                                   l_uint32 colorval);

static void rotateAMGrayCornerLow(l_uint32 *datad, l_int32 w, l_int32 h,

                                  l_int32 wpld, l_uint32 *datas, l_int32 wpls,

                                  l_float32 angle, l_uint8 grayval);

static void rotateAMColorFastLow(l_uint32 *datad, l_int32 w, l_int32 h,

                                 l_int32 wpld, l_uint32 *datas, l_int32 wpls,

                                 l_float32 angle, l_uint32 colorval);

static const l_float32  MinAngleToRotate = 0.001f;  /* radians; ~0.06 deg */

/*------------------------------------------------------------------*

 *                     Rotation about the center                    *

 *------------------------------------------------------------------*/

/*!

 * \brief   pixRotateAM()

 *

 * \param[in]    pixs 2, 4, 8 bpp gray or colormapped, or 32 bpp RGB

 * \param[in]    angle radians; clockwise is positive

 * \param[in]    incolor L_BRING_IN_WHITE, L_BRING_IN_BLACK

 * \return  pixd, or NULL on error

 *

 * <pre>

 * Notes:

 *      (1) Rotates about image center.

 *      (2) A positive angle gives a clockwise rotation.

 *      (3) Brings in either black or white pixels from the boundary.

 * </pre>

 */

PIX *

pixRotateAM(PIX       *pixs,

            l_float32  angle,

            l_int32    incolor)

{

l_int32   d;

l_uint32  fillval;

PIX      *pixt1, *pixt2, *pixd;

    if (!pixs)

        return (PIX *)ERROR_PTR("pixs not defined", __func__, NULL);

    if (pixGetDepth(pixs) == 1)

        return (PIX *)ERROR_PTR("pixs is 1 bpp", __func__, NULL);

    if (L_ABS(angle) < MinAngleToRotate)

        return pixClone(pixs);

        /* Remove cmap if it exists, and unpack to 8 bpp if necessary */

    pixt1 = pixRemoveColormap(pixs, REMOVE_CMAP_BASED_ON_SRC);

    d = pixGetDepth(pixt1);

    if (d < 8)

        pixt2 = pixConvertTo8(pixt1, FALSE);

    else

        pixt2 = pixClone(pixt1);

    d = pixGetDepth(pixt2);

        /* Compute actual incoming color */

    fillval = 0;

    if (incolor == L_BRING_IN_WHITE) {

        if (d == 8)

            fillval = 255;

        else  /* d == 32 */

            fillval = 0xffffff00;

    }

    if (d == 8)

        pixd = pixRotateAMGray(pixt2, angle, fillval);

    else   /* d == 32 */

        pixd = pixRotateAMColor(pixt2, angle, fillval);

    pixDestroy(&pixt1);

    pixDestroy(&pixt2);

    return pixd;

}

/*!

 * \brief   pixRotateAMColor()

 *

 * \param[in]    pixs 32 bpp

 * \param[in]    angle radians; clockwise is positive

 * \param[in]    colorval e.g., 0 to bring in BLACK, 0xffffff00 for WHITE

 * \return  pixd, or NULL on error

 *

 * <pre>

 * Notes:

 *      (1) Rotates about image center.

 *      (2) A positive angle gives a clockwise rotation.

 *      (3) Specify the color to be brought in from outside the image.

 * </pre>

 */

PIX *

pixRotateAMColor(PIX       *pixs,

                 l_float32  angle,

                 l_uint32   colorval)

{

l_int32    w, h, wpls, wpld;

l_uint32  *datas, *datad;

PIX       *pix1, *pix2, *pixd;

    if (!pixs)

        return (PIX *)ERROR_PTR("pixs not defined", __func__, NULL);

    if (pixGetDepth(pixs) != 32)

        return (PIX *)ERROR_PTR("pixs must be 32 bpp", __func__, NULL);

    if (L_ABS(angle) < MinAngleToRotate)

        return pixClone(pixs);

    pixGetDimensions(pixs, &w, &h, NULL);

    datas = pixGetData(pixs);

    wpls = pixGetWpl(pixs);

    pixd = pixCreateTemplate(pixs);

    datad = pixGetData(pixd);

    wpld = pixGetWpl(pixd);

    rotateAMColorLow(datad, w, h, wpld, datas, wpls, angle, colorval);

    if (pixGetSpp(pixs) == 4) {

        pix1 = pixGetRGBComponent(pixs, L_ALPHA_CHANNEL);

        pix2 = pixRotateAMGray(pix1, angle, 255);  /* bring in opaque */

        pixSetRGBComponent(pixd, pix2, L_ALPHA_CHANNEL);

        pixDestroy(&pix1);

        pixDestroy(&pix2);

    }

    return pixd;

}

/*!

 * \brief   pixRotateAMGray()

 *

 * \param[in]    pixs 8 bpp

 * \param[in]    angle radians; clockwise is positive

 * \param[in]    grayval 0 to bring in BLACK, 255 for WHITE

 * \return  pixd, or NULL on error

 *

 * <pre>

 * Notes:

 *      (1) Rotates about image center.

 *      (2) A positive angle gives a clockwise rotation.

 *      (3) Specify the grayvalue to be brought in from outside the image.

 * </pre>

 */

PIX *

pixRotateAMGray(PIX       *pixs,

                l_float32  angle,

                l_uint8    grayval)

{

l_int32    w, h, wpls, wpld;

l_uint32  *datas, *datad;

PIX        *pixd;

    if (!pixs)

        return (PIX *)ERROR_PTR("pixs not defined", __func__, NULL);

    if (pixGetDepth(pixs) != 8)

        return (PIX *)ERROR_PTR("pixs must be 8 bpp", __func__, NULL);

    if (L_ABS(angle) < MinAngleToRotate)

        return pixClone(pixs);

    pixGetDimensions(pixs, &w, &h, NULL);

    datas = pixGetData(pixs);

    wpls = pixGetWpl(pixs);

    pixd = pixCreateTemplate(pixs);

    datad = pixGetData(pixd);

    wpld = pixGetWpl(pixd);

    rotateAMGrayLow(datad, w, h, wpld, datas, wpls, angle, grayval);

    return pixd;

}

static void

rotateAMColorLow(l_uint32  *datad,

                 l_int32    w,

                 l_int32    h,

                 l_int32    wpld,

                 l_uint32  *datas,

                 l_int32    wpls,

                 l_float32  angle,

                 l_uint32   colorval)

{

l_int32    i, j, xcen, ycen, wm2, hm2;

l_int32    xdif, ydif, xpm, ypm, xp, yp, xf, yf;

l_int32    rval, gval, bval;

l_uint32   word00, word01, word10, word11;

l_uint32  *lines, *lined;

l_float32  sina, cosa;

    xcen = w / 2;

    wm2 = w - 2;

    ycen = h / 2;

    hm2 = h - 2;

    sina = 16.f * sin(angle);

    cosa = 16.f * cos(angle);

    for (i = 0; i < h; i++) {

        ydif = ycen - i;

        lined = datad + i * wpld;

        for (j = 0; j < w; j++) {

            xdif = xcen - j;

            xpm = (l_int32)(-xdif * cosa - ydif * sina);

            ypm = (l_int32)(-ydif * cosa + xdif * sina);

            xp = xcen + (xpm >> 4);

            yp = ycen + (ypm >> 4);

            xf = xpm & 0x0f;

            yf = ypm & 0x0f;

                /* if off the edge, write input colorval */

            if (xp < 0 || yp < 0 || xp > wm2 || yp > hm2) {

                *(lined + j) = colorval;

                continue;

            }

            lines = datas + yp * wpls;

                /* do area weighting.  Without this, we would

                 * simply do:

                 *   *(lined + j) = *(lines + xp);

                 * which is faster but gives lousy results!

                 */

            word00 = *(lines + xp);

            word10 = *(lines + xp + 1);

            word01 = *(lines + wpls + xp);

            word11 = *(lines + wpls + xp + 1);

            rval = ((16 - xf) * (16 - yf) * ((word00 >> L_RED_SHIFT) & 0xff) +

                    xf * (16 - yf) * ((word10 >> L_RED_SHIFT) & 0xff) +

                    (16 - xf) * yf * ((word01 >> L_RED_SHIFT) & 0xff) +

                    xf * yf * ((word11 >> L_RED_SHIFT) & 0xff) + 128) / 256;

            gval = ((16 - xf) * (16 - yf) * ((word00 >> L_GREEN_SHIFT) & 0xff) +

                    xf * (16 - yf) * ((word10 >> L_GREEN_SHIFT) & 0xff) +

                    (16 - xf) * yf * ((word01 >> L_GREEN_SHIFT) & 0xff) +

                    xf * yf * ((word11 >> L_GREEN_SHIFT) & 0xff) + 128) / 256;

            bval = ((16 - xf) * (16 - yf) * ((word00 >> L_BLUE_SHIFT) & 0xff) +

                    xf * (16 - yf) * ((word10 >> L_BLUE_SHIFT) & 0xff) +

                    (16 - xf) * yf * ((word01 >> L_BLUE_SHIFT) & 0xff) +

                    xf * yf * ((word11 >> L_BLUE_SHIFT) & 0xff) + 128) / 256;

            composeRGBPixel(rval, gval, bval, lined + j);

        }

    }

}

static void

rotateAMGrayLow(l_uint32  *datad,

                l_int32    w,

                l_int32    h,

                l_int32    wpld,

                l_uint32  *datas,

                l_int32    wpls,

                l_float32  angle,

                l_uint8    grayval)

{

l_int32    i, j, xcen, ycen, wm2, hm2;

l_int32    xdif, ydif, xpm, ypm, xp, yp, xf, yf;

l_int32    v00, v01, v10, v11;

l_uint8    val;

l_uint32  *lines, *lined;

l_float32  sina, cosa;

    xcen = w / 2;

    wm2 = w - 2;

    ycen = h / 2;

    hm2 = h - 2;

    sina = 16.f * sin(angle);

    cosa = 16.f * cos(angle);

    for (i = 0; i < h; i++) {

        ydif = ycen - i;

        lined = datad + i * wpld;

        for (j = 0; j < w; j++) {

            xdif = xcen - j;

            xpm = (l_int32)(-xdif * cosa - ydif * sina);

            ypm = (l_int32)(-ydif * cosa + xdif * sina);

            xp = xcen + (xpm >> 4);

            yp = ycen + (ypm >> 4);

            xf = xpm & 0x0f;

            yf = ypm & 0x0f;

                /* if off the edge, write input grayval */

            if (xp < 0 || yp < 0 || xp > wm2 || yp > hm2) {

                SET_DATA_BYTE(lined, j, grayval);

                continue;

            }

            lines = datas + yp * wpls;

                /* do area weighting.  Without this, we would

                 * simply do:

                 *   SET_DATA_BYTE(lined, j, GET_DATA_BYTE(lines, xp));

                 * which is faster but gives lousy results!

                 */

            v00 = (16 - xf) * (16 - yf) * GET_DATA_BYTE(lines, xp);

            v10 = xf * (16 - yf) * GET_DATA_BYTE(lines, xp + 1);

            v01 = (16 - xf) * yf * GET_DATA_BYTE(lines + wpls, xp);

            v11 = xf * yf * GET_DATA_BYTE(lines + wpls, xp + 1);

            val = (l_uint8)((v00 + v01 + v10 + v11 + 128) / 256);

            SET_DATA_BYTE(lined, j, val);

        }

    }

}

/*------------------------------------------------------------------*

 *                    Rotation about the UL corner                  *

 *------------------------------------------------------------------*/

/*!

 * \brief   pixRotateAMCorner()

 *

 * \param[in]    pixs 1, 2, 4, 8 bpp gray or colormapped, or 32 bpp RGB

 * \param[in]    angle radians; clockwise is positive

 * \param[in]    incolor L_BRING_IN_WHITE, L_BRING_IN_BLACK

 * \return  pixd, or NULL on error

 *

 * <pre>

 * Notes:

 *      (1) Rotates about the UL corner of the image.

 *      (2) A positive angle gives a clockwise rotation.

 *      (3) Brings in either black or white pixels from the boundary.

 * </pre>

 */

PIX *

pixRotateAMCorner(PIX       *pixs,

                  l_float32  angle,

                  l_int32    incolor)

{

l_int32   d;

l_uint32  fillval;

PIX      *pixt1, *pixt2, *pixd;

    if (!pixs)

        return (PIX *)ERROR_PTR("pixs not defined", __func__, NULL);

    if (L_ABS(angle) < MinAngleToRotate)

        return pixClone(pixs);

        /* Remove cmap if it exists, and unpack to 8 bpp if necessary */

    pixt1 = pixRemoveColormap(pixs, REMOVE_CMAP_BASED_ON_SRC);

    d = pixGetDepth(pixt1);

    if (d < 8)

        pixt2 = pixConvertTo8(pixt1, FALSE);

    else

        pixt2 = pixClone(pixt1);

    d = pixGetDepth(pixt2);

        /* Compute actual incoming color */

    fillval = 0;

    if (incolor == L_BRING_IN_WHITE) {

        if (d == 8)

            fillval = 255;

        else  /* d == 32 */

            fillval = 0xffffff00;

    }

    if (d == 8)

        pixd = pixRotateAMGrayCorner(pixt2, angle, fillval);

    else   /* d == 32 */

        pixd = pixRotateAMColorCorner(pixt2, angle, fillval);

    pixDestroy(&pixt1);

    pixDestroy(&pixt2);

    return pixd;

}

/*!

 * \brief   pixRotateAMColorCorner()

 *

 * \param[in]    pixs

 * \param[in]    angle radians; clockwise is positive

 * \param[in]    fillval e.g., 0 to bring in BLACK, 0xffffff00 for WHITE

 * \return  pixd, or NULL on error

 *

 * <pre>

 * Notes:

 *      (1) Rotates the image about the UL corner.

 *      (2) A positive angle gives a clockwise rotation.

 *      (3) Specify the color to be brought in from outside the image.

 * </pre>

 */

PIX *

pixRotateAMColorCorner(PIX       *pixs,

                       l_float32  angle,

                       l_uint32   fillval)

{

l_int32    w, h, wpls, wpld;

l_uint32  *datas, *datad;

PIX       *pix1, *pix2, *pixd;

    if (!pixs)

        return (PIX *)ERROR_PTR("pixs not defined", __func__, NULL);

    if (pixGetDepth(pixs) != 32)

        return (PIX *)ERROR_PTR("pixs must be 32 bpp", __func__, NULL);

    if (L_ABS(angle) < MinAngleToRotate)

        return pixClone(pixs);

    pixGetDimensions(pixs, &w, &h, NULL);

    datas = pixGetData(pixs);

    wpls = pixGetWpl(pixs);

    pixd = pixCreateTemplate(pixs);

    datad = pixGetData(pixd);

    wpld = pixGetWpl(pixd);

    rotateAMColorCornerLow(datad, w, h, wpld, datas, wpls, angle, fillval);

    if (pixGetSpp(pixs) == 4) {

        pix1 = pixGetRGBComponent(pixs, L_ALPHA_CHANNEL);

        pix2 = pixRotateAMGrayCorner(pix1, angle, 255);  /* bring in opaque */

        pixSetRGBComponent(pixd, pix2, L_ALPHA_CHANNEL);

        pixDestroy(&pix1);

        pixDestroy(&pix2);

    }

    return pixd;

}

/*!

 * \brief   pixRotateAMGrayCorner()

 *

 * \param[in]    pixs

 * \param[in]    angle radians; clockwise is positive

 * \param[in]    grayval 0 to bring in BLACK, 255 for WHITE

 * \return  pixd, or NULL on error

 *

 * <pre>

 * Notes:

 *      (1) Rotates the image about the UL corner.

 *      (2) A positive angle gives a clockwise rotation.

 *      (3) Specify the grayvalue to be brought in from outside the image.

 * </pre>

 */

PIX *

pixRotateAMGrayCorner(PIX       *pixs,

                      l_float32  angle,

                      l_uint8    grayval)

{

l_int32    w, h, wpls, wpld;

l_uint32  *datas, *datad;

PIX       *pixd;

    if (!pixs)

        return (PIX *)ERROR_PTR("pixs not defined", __func__, NULL);

    if (pixGetDepth(pixs) != 8)

        return (PIX *)ERROR_PTR("pixs must be 8 bpp", __func__, NULL);

    if (L_ABS(angle) < MinAngleToRotate)

        return pixClone(pixs);

    pixGetDimensions(pixs, &w, &h, NULL);

    datas = pixGetData(pixs);

    wpls = pixGetWpl(pixs);

    pixd = pixCreateTemplate(pixs);

    datad = pixGetData(pixd);

    wpld = pixGetWpl(pixd);

    rotateAMGrayCornerLow(datad, w, h, wpld, datas, wpls, angle, grayval);

    return pixd;

}

static void

rotateAMColorCornerLow(l_uint32  *datad,

                       l_int32    w,

                       l_int32    h,

                       l_int32    wpld,

                       l_uint32  *datas,

                       l_int32    wpls,

                       l_float32  angle,

                       l_uint32   colorval)

{

l_int32    i, j, wm2, hm2;

l_int32    xpm, ypm, xp, yp, xf, yf;

l_int32    rval, gval, bval;

l_uint32   word00, word01, word10, word11;

l_uint32  *lines, *lined;

l_float32  sina, cosa;

    wm2 = w - 2;

    hm2 = h - 2;

    sina = 16.f * sin(angle);

    cosa = 16.f * cos(angle);

    for (i = 0; i < h; i++) {

        lined = datad + i * wpld;

        for (j = 0; j < w; j++) {

            xpm = (l_int32)(j * cosa + i * sina);

            ypm = (l_int32)(i * cosa - j * sina);

            xp = xpm >> 4;

            yp = ypm >> 4;

            xf = xpm & 0x0f;

            yf = ypm & 0x0f;

                /* if off the edge, write input colorval */

            if (xp < 0 || yp < 0 || xp > wm2 || yp > hm2) {

                *(lined + j) = colorval;

                continue;

            }

            lines = datas + yp * wpls;

                /* do area weighting.  Without this, we would

                 * simply do:

                 *   *(lined + j) = *(lines + xp);

                 * which is faster but gives lousy results!

                 */

            word00 = *(lines + xp);

            word10 = *(lines + xp + 1);

            word01 = *(lines + wpls + xp);

            word11 = *(lines + wpls + xp + 1);

            rval = ((16 - xf) * (16 - yf) * ((word00 >> L_RED_SHIFT) & 0xff) +

                    xf * (16 - yf) * ((word10 >> L_RED_SHIFT) & 0xff) +

                    (16 - xf) * yf * ((word01 >> L_RED_SHIFT) & 0xff) +

                    xf * yf * ((word11 >> L_RED_SHIFT) & 0xff) + 128) / 256;

            gval = ((16 - xf) * (16 - yf) * ((word00 >> L_GREEN_SHIFT) & 0xff) +

                    xf * (16 - yf) * ((word10 >> L_GREEN_SHIFT) & 0xff) +

                    (16 - xf) * yf * ((word01 >> L_GREEN_SHIFT) & 0xff) +

                    xf * yf * ((word11 >> L_GREEN_SHIFT) & 0xff) + 128) / 256;

            bval = ((16 - xf) * (16 - yf) * ((word00 >> L_BLUE_SHIFT) & 0xff) +

                    xf * (16 - yf) * ((word10 >> L_BLUE_SHIFT) & 0xff) +

                    (16 - xf) * yf * ((word01 >> L_BLUE_SHIFT) & 0xff) +

                    xf * yf * ((word11 >> L_BLUE_SHIFT) & 0xff) + 128) / 256;

            composeRGBPixel(rval, gval, bval, lined + j);

        }

    }

}

static void

rotateAMGrayCornerLow(l_uint32  *datad,

                      l_int32    w,

                      l_int32    h,

                      l_int32    wpld,

                      l_uint32  *datas,

                      l_int32    wpls,

                      l_float32  angle,

                      l_uint8    grayval)

{

l_int32    i, j, wm2, hm2;

l_int32    xpm, ypm, xp, yp, xf, yf;

l_int32    v00, v01, v10, v11;

l_uint8    val;

l_uint32  *lines, *lined;

l_float32  sina, cosa;

    wm2 = w - 2;

    hm2 = h - 2;

    sina = 16.f * sin(angle);

    cosa = 16.f * cos(angle);

    for (i = 0; i < h; i++) {

        lined = datad + i * wpld;

        for (j = 0; j < w; j++) {

            xpm = (l_int32)(j * cosa + i * sina);

            ypm = (l_int32)(i * cosa - j * sina);

            xp = xpm >> 4;

            yp = ypm >> 4;

            xf = xpm & 0x0f;

            yf = ypm & 0x0f;

                /* if off the edge, write input grayval */

            if (xp < 0 || yp < 0 || xp > wm2 || yp > hm2) {

                SET_DATA_BYTE(lined, j, grayval);

                continue;

            }

            lines = datas + yp * wpls;

                /* do area weighting.  Without this, we would

                 * simply do:

                 *   SET_DATA_BYTE(lined, j, GET_DATA_BYTE(lines, xp));

                 * which is faster but gives lousy results!

                 */

            v00 = (16 - xf) * (16 - yf) * GET_DATA_BYTE(lines, xp);

            v10 = xf * (16 - yf) * GET_DATA_BYTE(lines, xp + 1);

            v01 = (16 - xf) * yf * GET_DATA_BYTE(lines + wpls, xp);

            v11 = xf * yf * GET_DATA_BYTE(lines + wpls, xp + 1);

            val = (l_uint8)((v00 + v01 + v10 + v11 + 128) / 256);

            SET_DATA_BYTE(lined, j, val);

        }

    }

}

/*------------------------------------------------------------------*

 *               Fast RGB color rotation about center               *

 *------------------------------------------------------------------*/

/*!

 * \brief   pixRotateAMColorFast()

 *

 * \param[in]    pixs

 * \param[in]    angle radians; clockwise is positive

 * \param[in]    colorval e.g., 0 to bring in BLACK, 0xffffff00 for WHITE

 * \return  pixd, or NULL on error

 *

 * <pre>

 * Notes:

 *      (1) This rotates a color image about the image center.

 *      (2) A positive angle gives a clockwise rotation.

 *      (3) It uses area mapping, dividing each pixel into

 *          16 subpixels.

 *      (4) It is about 10% to 20% faster than the more accurate linear

 *          interpolation function pixRotateAMColor(),

 *          which uses 256 subpixels.

 *      (5) For some reason it shifts the image center.

 *          No attempt is made to rotate the alpha component.

 * </pre>

 */

PIX *

pixRotateAMColorFast(PIX       *pixs,

                     l_float32  angle,

                     l_uint32   colorval)

{

l_int32    w, h, wpls, wpld;

l_uint32  *datas, *datad;

PIX       *pixd;

    if (!pixs)

        return (PIX *)ERROR_PTR("pixs not defined", __func__, NULL);

    if (pixGetDepth(pixs) != 32)

        return (PIX *)ERROR_PTR("pixs must be 32 bpp", __func__, NULL);

    if (L_ABS(angle) < MinAngleToRotate)

        return pixClone(pixs);

    pixGetDimensions(pixs, &w, &h, NULL);

    datas = pixGetData(pixs);

    wpls = pixGetWpl(pixs);

    pixd = pixCreateTemplate(pixs);

    datad = pixGetData(pixd);

    wpld = pixGetWpl(pixd);

    rotateAMColorFastLow(datad, w, h, wpld, datas, wpls, angle, colorval);

    return pixd;

}

/*!

 * \brief   rotateAMColorFastLow()

 *

 *     This is a special simplification of area mapping with division

 *     of each pixel into 16 sub-pixels.  The exact coefficients that

 *     should be used are the same as for the 4x linear interpolation

 *     scaling case, and are given there.  I tried to approximate these

 *     as weighted coefficients with a maximum sum of 4, which

 *     allows us to do the arithmetic in parallel for the R, G and B

 *     components in a 32 bit pixel.  However, there are three reasons

 *     for not doing that:

 *        (1) the loss of accuracy in the parallel implementation

 *            is visually significant

 *        (2) the parallel implementation (described below) is slower

 *        (3) the parallel implementation requires allocation of

 *            a temporary color image

 *

 *     There are 16 cases for the choice of the subpixel, and

 *     for each, the mapping to the relevant source

 *     pixels is as follows:

 *

 *      subpixel      src pixel weights

 *      --------      -----------------

 *         0          sp1

 *         1          (3 * sp1 + sp2) / 4

 *         2          (sp1 + sp2) / 2

 *         3          (sp1 + 3 * sp2) / 4

 *         4          (3 * sp1 + sp3) / 4

 *         5          (9 * sp1 + 3 * sp2 + 3 * sp3 + sp4) / 16

 *         6          (3 * sp1 + 3 * sp2 + sp3 + sp4) / 8

 *         7          (3 * sp1 + 9 * sp2 + sp3 + 3 * sp4) / 16

 *         8          (sp1 + sp3) / 2

 *         9          (3 * sp1 + sp2 + 3 * sp3 + sp4) / 8

 *         10         (sp1 + sp2 + sp3 + sp4) / 4

 *         11         (sp1 + 3 * sp2 + sp3 + 3 * sp4) / 8

 *         12         (sp1 + 3 * sp3) / 4

 *         13         (3 * sp1 + sp2 + 9 * sp3 + 3 * sp4) / 16

 *         14         (sp1 + sp2 + 3 * sp3 + 3 * sp4) / 8

 *         15         (sp1 + 3 * sp2 + 3 * sp3 + 9 * sp4) / 16

 *

 *     Another way to visualize this is to consider the area mapping

 *     (or linear interpolation) coefficients  for the pixel sp1.

 *     Expressed in fourths, they can be written as asymmetric matrix:

 *

 *           4      3      2      1

 *           3      2.25   1.5    0.75

 *           2      1.5    1      0.5

 *           1      0.75   0.5    0.25

 *

 *     The coefficients for the three neighboring pixels can be

 *     similarly written.

 *

 *     This is implemented here, where, for each color component,

 *     we inline its extraction from each participating word,

 *     construct the linear combination, and combine the results

 *     into the destination 32 bit RGB pixel, using the appropriate shifts.

 *

 *     It is interesting to note that an alternative method, where

 *     we do the arithmetic on the 32 bit pixels directly (after

 *     shifting the components so they won't overflow into each other)

 *     is significantly inferior.  Because we have only 8 bits for

 *     internal overflows, which can be distributed as 2, 3, 3, it

 *     is impossible to add these with the correct linear

 *     interpolation coefficients, which require a sum of up to 16.

 *     Rounding off to a sum of 4 causes appreciable visual artifacts

 *     in the rotated image.  The code for the inferior method

 *     can be found in prog/rotatefastalt.c, for reference.

 */

static void

rotateAMColorFastLow(l_uint32  *datad,

                     l_int32    w,

                     l_int32    h,

                     l_int32    wpld,

                     l_uint32  *datas,

                     l_int32    wpls,

                     l_float32  angle,

                     l_uint32   colorval)

{

l_int32    i, j, xcen, ycen, wm2, hm2;

l_int32    xdif, ydif, xpm, ypm, xp, yp, xf, yf;

l_uint32   word1, word2, word3, word4, red, blue, green;

l_uint32  *pword, *lines, *lined;

l_float32  sina, cosa;

    xcen = w / 2;

    wm2 = w - 2;

    ycen = h / 2;

    hm2 = h - 2;

    sina = 4.f * sin(angle);

    cosa = 4.f * cos(angle);

    for (i = 0; i < h; i++) {

        ydif = ycen - i;

        lined = datad + i * wpld;

        for (j = 0; j < w; j++) {

            xdif = xcen - j;

            xpm = (l_int32)(-xdif * cosa - ydif * sina);

            ypm = (l_int32)(-ydif * cosa + xdif * sina);

            xp = xcen + (xpm >> 2);

            yp = ycen + (ypm >> 2);

            xf = xpm & 0x03;

            yf = ypm & 0x03;

                /* if off the edge, write input grayval */

            if (xp < 0 || yp < 0 || xp > wm2 || yp > hm2) {

                *(lined + j) = colorval;

                continue;

            }

            lines = datas + yp * wpls;

            pword = lines + xp;

            switch (xf + 4 * yf)

            {

            case 0:

                *(lined + j) = *pword;

                break;

            case 1:

                word1 = *pword;

                word2 = *(pword + 1);

                red = 3 * (word1 >> 24) + (word2 >> 24);

                green = 3 * ((word1 >> 16) & 0xff) +

                            ((word2 >> 16) & 0xff);

                blue = 3 * ((word1 >> 8) & 0xff) +

                            ((word2 >> 8) & 0xff);

                *(lined + j) = ((red << 22) & 0xff000000) |

                               ((green << 14) & 0x00ff0000) |

                               ((blue << 6) & 0x0000ff00);

                break;

            case 2:

                word1 = *pword;

                word2 = *(pword + 1);

                red = (word1 >> 24) + (word2 >> 24);

                green = ((word1 >> 16) & 0xff) + ((word2 >> 16) & 0xff);

                blue = ((word1 >> 8) & 0xff) + ((word2 >> 8) & 0xff);

                *(lined + j) = ((red << 23) & 0xff000000) |

                               ((green << 15) & 0x00ff0000) |

                               ((blue << 7) & 0x0000ff00);

                break;

            case 3:

                word1 = *pword;

                word2 = *(pword + 1);

                red = (word1 >> 24) + 3 * (word2 >> 24);

                green = ((word1 >> 16) & 0xff) +

                          3 * ((word2 >> 16) & 0xff);

                blue = ((word1 >> 8) & 0xff) +

                          3 * ((word2 >> 8) & 0xff);

                *(lined + j) = ((red << 22) & 0xff000000) |

                               ((green << 14) & 0x00ff0000) |

                               ((blue << 6) & 0x0000ff00);

                break;

            case 4:

                word1 = *pword;

                word3 = *(pword + wpls);

                red = 3 * (word1 >> 24) + (word3 >> 24);

                green = 3 * ((word1 >> 16) & 0xff) +

                            ((word3 >> 16) & 0xff);

                blue = 3 * ((word1 >> 8) & 0xff) +

                            ((word3 >> 8) & 0xff);

                *(lined + j) = ((red << 22) & 0xff000000) |

                               ((green << 14) & 0x00ff0000) |

                               ((blue << 6) & 0x0000ff00);

                break;

            case 5:

                word1 = *pword;

                word2 = *(pword + 1);

                word3 = *(pword + wpls);

                word4 = *(pword + wpls + 1);

                red = 9 * (word1 >> 24) + 3 * (word2 >> 24) +

                      3 * (word3 >> 24) + (word4 >> 24);

                green = 9 * ((word1 >> 16) & 0xff) +

                        3 * ((word2 >> 16) & 0xff) +

                        3 * ((word3 >> 16) & 0xff) +

                        ((word4 >> 16) & 0xff);

                blue = 9 * ((word1 >> 8) & 0xff) +

                       3 * ((word2 >> 8) & 0xff) +

                       3 * ((word3 >> 8) & 0xff) +

                       ((word4 >> 8) & 0xff);

                *(lined + j) = ((red << 20) & 0xff000000) |

                               ((green << 12) & 0x00ff0000) |

                               ((blue << 4) & 0x0000ff00);

                break;

            case 6:

                word1 = *pword;

                word2 = *(pword + 1);

                word3 = *(pword + wpls);

                word4 = *(pword + wpls + 1);

                red = 3 * (word1 >> 24) +  3 * (word2 >> 24) +