/*====================================================================*
- Copyright (C) 2001 Leptonica. All rights reserved.
- This software is distributed in the hope that it will be
- useful, but with NO WARRANTY OF ANY KIND.
- No author or distributor accepts responsibility to anyone for the
- consequences of using this software, or for whether it serves any
- particular purpose or works at all, unless he or she says so in
- writing. Everyone is granted permission to copy, modify and
- redistribute this source code, for commercial or non-commercial
- purposes, with the following restrictions: (1) the origin of this
- source code must not be misrepresented; (2) modified versions must
- be plainly marked as such; and (3) this notice may not be removed
- or altered from any source or modified source distribution.
*====================================================================*/
/*
* bilinear.c
*
* Bilinear (4 pt) image transformation using a sampled
* (to nearest integer) transform on each dest point
* PIX *pixBilinearSampledPta()
* PIX *pixBilinearSampled()
*
* Bilinear (4 pt) image transformation using interpolation
* (or area mapping) for anti-aliasing images that are
* 2, 4, or 8 bpp gray, or colormapped, or 32 bpp RGB
* PIX *pixBilinearPta()
* PIX *pixBilinear()
* PIX *pixBilinearPtaColor()
* PIX *pixBilinearColor()
* PIX *pixBilinearPtaGray()
* PIX *pixBilinearGray()
*
* Bilinear coordinate transformation
* l_int32 getBilinearXformCoeffs()
* l_int32 bilinearXformSampledPt()
* l_int32 bilinearXformPt()
*
* A bilinear transform can be specified as a specific functional
* mapping between 4 points in the source and 4 points in the dest.
* It can be used as an approximation to a (nonlinear) projective
* transform, because for small warps it is very similar and
* it is more stable. (Projective transforms have a division
* by a quantity that can get arbitrarily small.)
*
* We give both a bilinear coordinate transformation and
* a bilinear image transformation.
*
* For the former, we ask for the coordinate value (x',y')
* in the transformed space for any point (x,y) in the original
* space. The coefficients of the transformation are found by
* solving 8 simultaneous equations for the 8 coordinates of
* the 4 points in src and dest. The transformation can then
* be used to compute the associated image transform, by
* computing, for each dest pixel, the relevant pixel(s) in
* the source. This can be done either by taking the closest
* src pixel to each transformed dest pixel ("sampling") or
* by doing an interpolation and averaging over 4 source
* pixels with appropriate weightings ("interpolated").
*
* A typical application would be to remove some of the
* keystoning due to a projective transform in the imaging system.
*
* The bilinear transform is given by specifying two equations:
*
* x' = ax + by + cxy + d
* y' = ex + fy + gxy + h
*
* where the eight coefficients have been computed from four
* sets of these equations, each for two corresponding data pts.
* In practice, for each point (x,y) in the dest image, this
* equation is used to compute the corresponding point (x',y')
* in the src. That computed point in the src is then used
* to determine the dest value in one of two ways:
*
* - sampling: take the value of the src pixel in which this
* point falls
* - interpolation: take appropriate linear combinations of the
* four src pixels that this dest pixel would
* overlap, with the coefficients proportional
* to the amount of overlap
*
* For small warp, like rotation, area mapping in the
* interpolation is equivalent to linear interpolation.
*
* Typical relative timing of transforms (sampled = 1.0):
* 8 bpp: sampled 1.0
* interpolated 1.6
* 32 bpp: sampled 1.0
* interpolated 1.8
* Additionally, the computation time/pixel is nearly the same
* for 8 bpp and 32 bpp, for both sampled and interpolated.
*/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include "allheaders.h"
/*-------------------------------------------------------------*
* Sampled bilinear image transformation *
*-------------------------------------------------------------*/
/*!
* pixBilinearSampledPta()
*
* Input: pixs (all depths)
* ptad (4 pts of final coordinate space)
* ptas (4 pts of initial coordinate space)
* incolor (L_BRING_IN_WHITE, L_BRING_IN_BLACK)
* Return: pixd, or null on error
*
* Notes:
* (1) Brings in either black or white pixels from the boundary.
* (2) Retains colormap, which you can do for a sampled transform..
* (3) No 3 of the 4 points may be collinear.
* (4) For 8 and 32 bpp pix, better quality is obtained by the
* somewhat slower pixBilinearPta(). See that
* function for relative timings between sampled and interpolated.
*/
PIX *
pixBilinearSampledPta(PIX *pixs,
PTA *ptad,
PTA *ptas,
l_int32 incolor)
{
l_float32 *vc;
PIX *pixd;
PROCNAME("pixBilinearSampledPta");
if (!pixs)
return (PIX *)ERROR_PTR("pixs not defined", procName, NULL);
if (!ptas)
return (PIX *)ERROR_PTR("ptas not defined", procName, NULL);
if (!ptad)
return (PIX *)ERROR_PTR("ptad not defined", procName, NULL);
if (incolor != L_BRING_IN_WHITE && incolor != L_BRING_IN_BLACK)
return (PIX *)ERROR_PTR("invalid incolor", procName, NULL);
if (ptaGetCount(ptas) != 4)
return (PIX *)ERROR_PTR("ptas count not 4", procName, NULL);
if (ptaGetCount(ptad) != 4)
return (PIX *)ERROR_PTR("ptad count not 4", procName, NULL);
/* Get backwards transform from dest to src, and apply it */
getBilinearXformCoeffs(ptad, ptas, &vc);
pixd = pixBilinearSampled(pixs, vc, incolor);
FREE(vc);
return pixd;
}
/*!
* pixBilinearSampled()
*
* Input: pixs (all depths)
* vc (vector of 8 coefficients for bilinear transformation)
* incolor (L_BRING_IN_WHITE, L_BRING_IN_BLACK)
* Return: pixd, or null on error
*
* Notes:
* (1) Brings in either black or white pixels from the boundary.
* (2) Retains colormap, which you can do for a sampled transform..
* (3) For 8 or 32 bpp, much better quality is obtained by the
* somewhat slower pixBilinear(). See that function
* for relative timings between sampled and interpolated.
*/
PIX *
pixBilinearSampled(PIX *pixs,
l_float32 *vc,
l_int32 incolor)
{
l_int32 i, j, w, h, d, x, y, wpls, wpld, color, cmapindex;
l_uint32 val;
l_uint32 *datas, *datad, *lines, *lined;
PIX *pixd;
PIXCMAP *cmap;
PROCNAME("pixBilinearSampled");
if (!pixs)
return (PIX *)ERROR_PTR("pixs not defined", procName, NULL);
if (!vc)
return (PIX *)ERROR_PTR("vc not defined", procName, NULL);
if (incolor != L_BRING_IN_WHITE && incolor != L_BRING_IN_BLACK)
return (PIX *)ERROR_PTR("invalid incolor", procName, NULL);
pixGetDimensions(pixs, &w, &h, &d);
if (d != 1 && d != 2 && d != 4 && d != 8 && d != 32)
return (PIX *)ERROR_PTR("depth not 1, 2, 4, 8 or 16", procName, NULL);
/* Init all dest pixels to color to be brought in from outside */
pixd = pixCreateTemplate(pixs);
if ((cmap = pixGetColormap(pixs)) != NULL) {
if (incolor == L_BRING_IN_WHITE)
color = 1;
else
color = 0;
pixcmapAddBlackOrWhite(cmap, color, &cmapindex);
pixSetAllArbitrary(pixd, cmapindex);
}
else {
if ((d == 1 && incolor == L_BRING_IN_WHITE) ||
(d > 1 && incolor == L_BRING_IN_BLACK))
pixClearAll(pixd);
else
pixSetAll(pixd);
}
/* Scan over the dest pixels */
datas = pixGetData(pixs);
wpls = pixGetWpl(pixs);
datad = pixGetData(pixd);
wpld = pixGetWpl(pixd);
for (i = 0; i < h; i++) {
lined = datad + i * wpld;
for (j = 0; j < w; j++) {
bilinearXformSampledPt(vc, j, i, &x, &y);
if (x < 0 || y < 0 || x >=w || y >= h)
continue;
lines = datas + y * wpls;
if (d == 1) {
val = GET_DATA_BIT(lines, x);
SET_DATA_BIT_VAL(lined, j, val);
}
else if (d == 8) {
val = GET_DATA_BYTE(lines, x);
SET_DATA_BYTE(lined, j, val);
}
else if (d == 32) {
lined[j] = lines[x];
}
else if (d == 2) {
val = GET_DATA_DIBIT(lines, x);
SET_DATA_DIBIT(lined, j, val);
}
else if (d == 4) {
val = GET_DATA_QBIT(lines, x);
SET_DATA_QBIT(lined, j, val);
}
}
}
return pixd;
}
/*---------------------------------------------------------------------*
* Interpolated bilinear image transformation *
*---------------------------------------------------------------------*/
/*!
* pixBilinearPta()
*
* Input: pixs (all depths; colormap ok)
* ptad (4 pts of final coordinate space)
* ptas (4 pts of initial coordinate space)
* incolor (L_BRING_IN_WHITE, L_BRING_IN_BLACK)
* Return: pixd, or null on error
*
* Notes:
* (1) Brings in either black or white pixels from the boundary
* (2) Removes any existing colormap, if necessary, before transforming
*/
PIX *
pixBilinearPta(PIX *pixs,
PTA *ptad,
PTA *ptas,
l_int32 incolor)
{
l_int32 d;
l_uint32 colorval;
PIX *pixt1, *pixt2, *pixd;
PROCNAME("pixBilinearPta");
if (!pixs)
return (PIX *)ERROR_PTR("pixs not defined", procName, NULL);
if (!ptas)
return (PIX *)ERROR_PTR("ptas not defined", procName, NULL);
if (!ptad)
return (PIX *)ERROR_PTR("ptad not defined", procName, NULL);
if (incolor != L_BRING_IN_WHITE && incolor != L_BRING_IN_BLACK)
return (PIX *)ERROR_PTR("invalid incolor", procName, NULL);
if (ptaGetCount(ptas) != 4)
return (PIX *)ERROR_PTR("ptas count not 4", procName, NULL);
if (ptaGetCount(ptad) != 4)
return (PIX *)ERROR_PTR("ptad count not 4", procName, NULL);
if (pixGetDepth(pixs) == 1)
return pixBilinearSampledPta(pixs, ptad, ptas, incolor);
/* 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 color to bring in from edges */
colorval = 0;
if (incolor == L_BRING_IN_WHITE) {
if (d == 8)
colorval = 255;
else /* d == 32 */
colorval = 0xffffff00;
}
if (d == 8)
pixd = pixBilinearPtaGray(pixt2, ptad, ptas, colorval);
else /* d == 32 */
pixd = pixBilinearPtaColor(pixt2, ptad, ptas, colorval);
pixDestroy(&pixt1);
pixDestroy(&pixt2);
return pixd;
}
/*!
* pixBilinear()
*
* Input: pixs (all depths; colormap ok)
* vc (vector of 8 coefficients for affine transformation)
* incolor (L_BRING_IN_WHITE, L_BRING_IN_BLACK)
* Return: pixd, or null on error
*
* Notes:
* (1) Brings in either black or white pixels from the boundary
* (2) Removes any existing colormap, if necessary, before transforming
*/
PIX *
pixBilinear(PIX *pixs,
l_float32 *vc,
l_int32 incolor)
{
l_int32 d;
l_uint32 colorval;
PIX *pixt1, *pixt2, *pixd;
PROCNAME("pixBilinear");
if (!pixs)
return (PIX *)ERROR_PTR("pixs not defined", procName, NULL);
if (!vc)
return (PIX *)ERROR_PTR("vc not defined", procName, NULL);
if (pixGetDepth(pixs) == 1)
return pixBilinearSampled(pixs, vc, incolor);
/* 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 color to bring in from edges */
colorval = 0;
if (incolor == L_BRING_IN_WHITE) {
if (d == 8)
colorval = 255;
else /* d == 32 */
colorval = 0xffffff00;
}
if (d == 8)
pixd = pixBilinearGray(pixt2, vc, colorval);
else /* d == 32 */
pixd = pixBilinearColor(pixt2, vc, colorval);
pixDestroy(&pixt1);
pixDestroy(&pixt2);
return pixd;
}
/*!
* pixBilinearPtaColor()
*
* Input: pixs (32 bpp)
* ptad (4 pts of final coordinate space)
* ptas (4 pts of initial coordinate space)
* colorval (e.g., 0 to bring in BLACK, 0xffffff00 for WHITE)
* Return: pixd, or null on error
*/
PIX *
pixBilinearPtaColor(PIX *pixs,
PTA *ptad,
PTA *ptas,
l_uint32 colorval)
{
l_float32 *vc;
PIX *pixd;
PROCNAME("pixBilinearPtaColor");
if (!pixs)
return (PIX *)ERROR_PTR("pixs not defined", procName, NULL);
if (!ptas)
return (PIX *)ERROR_PTR("ptas not defined", procName, NULL);
if (!ptad)
return (PIX *)ERROR_PTR("ptad not defined", procName, NULL);
if (pixGetDepth(pixs) != 32)
return (PIX *)ERROR_PTR("pixs must be 32 bpp", procName, NULL);
if (ptaGetCount(ptas) != 4)
return (PIX *)ERROR_PTR("ptas count not 4", procName, NULL);
if (ptaGetCount(ptad) != 4)
return (PIX *)ERROR_PTR("ptad count not 4", procName, NULL);
/* Get backwards transform from dest to src, and apply it */
getBilinearXformCoeffs(ptad, ptas, &vc);
pixd = pixBilinearColor(pixs, vc, colorval);
FREE(vc);
return pixd;
}
/*!
* pixBilinearColor()
*
* Input: pixs (32 bpp)
* vc (vector of 6 coefficients for affine transformation)
* colorval (e.g., 0 to bring in BLACK, 0xffffff00 for WHITE)
* Return: pixd, or null on error
*/
PIX *
pixBilinearColor(PIX *pixs,
l_float32 *vc,
l_uint32 colorval)
{
l_int32 i, j, w, h, d, wpls, wpld;
l_uint32 val;
l_uint32 *datas, *datad, *lined;
l_float32 x, y;
PIX *pixd;
PROCNAME("pixBilinearColor");
if (!pixs)
return (PIX *)ERROR_PTR("pixs not defined", procName, NULL);
pixGetDimensions(pixs, &w, &h, &d);
if (d != 32)
return (PIX *)ERROR_PTR("pixs must be 32 bpp", procName, NULL);
if (!vc)
return (PIX *)ERROR_PTR("vc not defined", procName, NULL);
datas = pixGetData(pixs);
wpls = pixGetWpl(pixs);
pixd = pixCreateTemplate(pixs);
pixSetAllArbitrary(pixd, colorval);
datad = pixGetData(pixd);
wpld = pixGetWpl(pixd);
/* Iterate over destination pixels */
for (i = 0; i < h; i++) {
lined = datad + i * wpld;
for (j = 0; j < w; j++) {
/* Compute float src pixel location corresponding to (i,j) */
bilinearXformPt(vc, j, i, &x, &y);
linearInterpolatePixelColor(datas, wpls, w, h, x, y, colorval,
&val);
*(lined + j) = val;
}
}
return pixd;
}
/*!
* pixBilinearPtaGray()
*
* Input: pixs (8 bpp)
* ptad (4 pts of final coordinate space)
* ptas (4 pts of initial coordinate space)
* grayval (0 to bring in BLACK, 255 for WHITE)
* Return: pixd, or null on error
*/
PIX *
pixBilinearPtaGray(PIX *pixs,
PTA *ptad,
PTA *ptas,
l_uint8 grayval)
{
l_float32 *vc;
PIX *pixd;
PROCNAME("pixBilinearPtaGray");
if (!pixs)
return (PIX *)ERROR_PTR("pixs not defined", procName, NULL);
if (!ptas)
return (PIX *)ERROR_PTR("ptas not defined", procName, NULL);
if (!ptad)
return (PIX *)ERROR_PTR("ptad not defined", procName, NULL);
if (pixGetDepth(pixs) != 8)
return (PIX *)ERROR_PTR("pixs must be 8 bpp", procName, NULL);
if (ptaGetCount(ptas) != 4)
return (PIX *)ERROR_PTR("ptas count not 4", procName, NULL);
if (ptaGetCount(ptad) != 4)
return (PIX *)ERROR_PTR("ptad count not 4", procName, NULL);
/* Get backwards transform from dest to src, and apply it */
getBilinearXformCoeffs(ptad, ptas, &vc);
pixd = pixBilinearGray(pixs, vc, grayval);
FREE(vc);
return pixd;
}
/*!
* pixBilinearGray()
*
* Input: pixs (8 bpp)
* vc (vector of 8 coefficients for affine transformation)
* grayval (0 to bring in BLACK, 255 for WHITE)
* Return: pixd, or null on error
*/
PIX *
pixBilinearGray(PIX *pixs,
l_float32 *vc,
l_uint8 grayval)
{
l_int32 i, j, w, h, wpls, wpld, val;
l_uint32 *datas, *datad, *lined;
l_float32 x, y;
PIX *pixd;
PROCNAME("pixBilinearGray");
if (!pixs)
return (PIX *)ERROR_PTR("pixs not defined", procName, NULL);
pixGetDimensions(pixs, &w, &h, NULL);
if (pixGetDepth(pixs) != 8)
return (PIX *)ERROR_PTR("pixs must be 8 bpp", procName, NULL);
if (!vc)
return (PIX *)ERROR_PTR("vc not defined", procName, NULL);
datas = pixGetData(pixs);
wpls = pixGetWpl(pixs);
pixd = pixCreateTemplate(pixs);
pixSetAllArbitrary(pixd, grayval);
datad = pixGetData(pixd);
wpld = pixGetWpl(pixd);
/* Iterate over destination pixels */
for (i = 0; i < h; i++) {
lined = datad + i * wpld;
for (j = 0; j < w; j++) {
/* Compute float src pixel location corresponding to (i,j) */
bilinearXformPt(vc, j, i, &x, &y);
linearInterpolatePixelGray(datas, wpls, w, h, x, y, grayval, &val);
SET_DATA_BYTE(lined, j, val);
}
}
return pixd;
}
/*-------------------------------------------------------------*
* Bilinear coordinate transformation *
*-------------------------------------------------------------*/
/*!
* getBilinearXformCoeffs()
*
* Input: ptas (source 4 points; unprimed)
* ptad (transformed 4 points; primed)
* &vc (<return> vector of coefficients of transform)
* Return: 0 if OK; 1 on error
*
* We have a set of 8 equations, describing the bilinear
* transformation that takes 4 points (ptas) into 4 other
* points (ptad). These equations are:
*
* x1' = c[0]*x1 + c[1]*y1 + c[2]*x1*y1 + c[3]
* y1' = c[4]*x1 + c[5]*y1 + c[6]*x1*y1 + c[7]
* x2' = c[0]*x2 + c[1]*y2 + c[2]*x2*y2 + c[3]
* y2' = c[4]*x2 + c[5]*y2 + c[6]*x2*y2 + c[7]
* x3' = c[0]*x3 + c[1]*y3 + c[2]*x3*y3 + c[3]
* y3' = c[4]*x3 + c[5]*y3 + c[6]*x3*y3 + c[7]
* x4' = c[0]*x4 + c[1]*y4 + c[2]*x4*y4 + c[3]
* y4' = c[4]*x4 + c[5]*y4 + c[6]*x4*y4 + c[7]
*
* This can be represented as
*
* AC = B
*
* where B and C are column vectors
*
* B = [ x1' y1' x2' y2' x3' y3' x4' y4' ]
* C = [ c[0] c[1] c[2] c[3] c[4] c[5] c[6] c[7] ]
*
* and A is the 8x8 matrix
*
* x1 y1 x1*y1 1 0 0 0 0
* 0 0 0 0 x1 y1 x1*y1 1
* x2 y2 x2*y2 1 0 0 0 0
* 0 0 0 0 x2 y2 x2*y2 1
* x3 y3 x3*y3 1 0 0 0 0
* 0 0 0 0 x3 y3 x3*y3 1
* x4 y4 x4*y4 1 0 0 0 0
* 0 0 0 0 x4 y4 x4*y4 1
*
* These eight equations are solved here for the coefficients C.
*
* These eight coefficients can then be used to find the mapping
* (x,y) --> (x',y'):
*
* x' = c[0]x + c[1]y + c[2]xy + c[3]
* y' = c[4]x + c[5]y + c[6]xy + c[7]
*
* that are implemented in bilinearXformSampledPt() and
* bilinearXFormPt().
*/
l_int32
getBilinearXformCoeffs(PTA *ptas,
PTA *ptad,
l_float32 **pvc)
{
l_int32 i;
l_float32 x1, y1, x2, y2, x3, y3, x4, y4;
l_float32 *b; /* rhs vector of primed coords X'; coeffs returned in *pvc */
l_float32 *a[8]; /* 8x8 matrix A */
PROCNAME("getBilinearXformCoeffs");
if (!ptas)
return ERROR_INT("ptas not defined", procName, 1);
if (!ptad)
return ERROR_INT("ptad not defined", procName, 1);
if (!pvc)
return ERROR_INT("&vc not defined", procName, 1);
if ((b = (l_float32 *)CALLOC(8, sizeof(l_float32))) == NULL)
return ERROR_INT("b not made", procName, 1);
*pvc = b;
ptaGetPt(ptas, 0, &x1, &y1);
ptaGetPt(ptas, 1, &x2, &y2);
ptaGetPt(ptas, 2, &x3, &y3);
ptaGetPt(ptas, 3, &x4, &y4);
ptaGetPt(ptad, 0, &b[0], &b[1]);
ptaGetPt(ptad, 1, &b[2], &b[3]);
ptaGetPt(ptad, 2, &b[4], &b[5]);
ptaGetPt(ptad, 3, &b[6], &b[7]);
for (i = 0; i < 8; i++) {
if ((a[i] = (l_float32 *)CALLOC(8, sizeof(l_float32))) == NULL)
return ERROR_INT("a[i] not made", procName, 1);
}
a[0][0] = x1;
a[0][1] = y1;
a[0][2] = x1 * y1;
a[0][3] = 1.;
a[1][4] = x1;
a[1][5] = y1;
a[1][6] = x1 * y1;
a[1][7] = 1.;
a[2][0] = x2;
a[2][1] = y2;
a[2][2] = x2 * y2;
a[2][3] = 1.;
a[3][4] = x2;
a[3][5] = y2;
a[3][6] = x2 * y2;
a[3][7] = 1.;
a[4][0] = x3;
a[4][1] = y3;
a[4][2] = x3 * y3;
a[4][3] = 1.;
a[5][4] = x3;
a[5][5] = y3;
a[5][6] = x3 * y3;
a[5][7] = 1.;
a[6][0] = x4;
a[6][1] = y4;
a[6][2] = x4 * y4;
a[6][3] = 1.;
a[7][4] = x4;
a[7][5] = y4;
a[7][6] = x4 * y4;
a[7][7] = 1.;
gaussjordan(a, b, 8);
for (i = 0; i < 8; i++)
FREE(a[i]);
return 0;
}
/*!
* bilinearXformSampledPt()
*
* Input: vc (vector of 8 coefficients)
* (x, y) (initial point)
* (&xp, &yp) (<return> transformed point)
* Return: 0 if OK; 1 on error
*
* Notes:
* (1) This finds the nearest pixel coordinates of the transformed point.
* (2) It does not check ptrs for returned data!
*/
l_int32
bilinearXformSampledPt(l_float32 *vc,
l_int32 x,
l_int32 y,
l_int32 *pxp,
l_int32 *pyp)
{
PROCNAME("bilinearXformSampledPt");
if (!vc)
return ERROR_INT("vc not defined", procName, 1);
*pxp = (l_int32)(vc[0] * x + vc[1] * y + vc[2] * x * y + vc[3] + 0.5);
*pyp = (l_int32)(vc[4] * x + vc[5] * y + vc[6] * x * y + vc[7] + 0.5);
return 0;
}
/*!
* bilinearXformPt()
*
* Input: vc (vector of 8 coefficients)
* (x, y) (initial point)
* (&xp, &yp) (<return> transformed point)
* Return: 0 if OK; 1 on error
*
* Notes:
* (1) This computes the floating point location of the transformed point.
* (2) It does not check ptrs for returned data!
*/
l_int32
bilinearXformPt(l_float32 *vc,
l_int32 x,
l_int32 y,
l_float32 *pxp,
l_float32 *pyp)
{
PROCNAME("bilinearXformPt");
if (!vc)
return ERROR_INT("vc not defined", procName, 1);
*pxp = vc[0] * x + vc[1] * y + vc[2] * x * y + vc[3];
*pyp = vc[4] * x + vc[5] * y + vc[6] * x * y + vc[7];
return 0;
}