860 lines
33 KiB
C++
860 lines
33 KiB
C++
/* lbb (locally bounded bicubic) resampler
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*
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* N. Robidoux, C. Racette and J. Cupitt, 23-28/03/2010
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*
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* N. Robidoux, 16-19/05/2010
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*/
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/*
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This file is part of VIPS.
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VIPS is free software; you can redistribute it and/or modify it
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under the terms of the GNU Lesser General Public License as
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published by the Free Software Foundation; either version 2 of the
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License, or (at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with this program; if not, write to the Free
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Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
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02111-1307 USA
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*/
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/*
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These files are distributed with VIPS - http://www.vips.ecs.soton.ac.uk
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*/
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/*
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* 2010 (c) Nicolas Robidoux, Chantal Racette, John Cupitt.
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*
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* Nicolas Robidoux thanks Adam Turcotte, Geert Jordaens, Ralf Meyer,
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* Øyvind Kolås, Minglun Gong, Eric Daoust and Sven Neumann for useful
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* comments and code.
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*
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* Chantal Racette's image resampling research and programming funded
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* in part by a NSERC Discovery Grant awarded to Julien Dompierre
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* (20-61098).
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*/
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/*
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* LBB has two versions:
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*
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* A "soft" version, which shows a little less staircasing and a
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* little more haloing, and which is a little more expensive to
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* compute. We recommend this as the default.
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*
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* A "sharp" version, which shows a little more staircasing and a
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* little less haloing, which is a little cheaper (it uses 6 less
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* comparisons and 12 less "? :"), and which appears to lead to less
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* "zebra striping" when two diagonal interfaces are close to each
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* other.
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*
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* The only difference between the two is that the "soft" versions
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* uses local minima and maxima computed over 3x3 square blocks, and
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* the "sharp" version uses local minima and maxima computed over 3x3
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* crosses.
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*
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* If you want to use the "soft" (more expensive) version, comment out
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* the following three pre-processor code lines:
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*/
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#ifndef __LBB_CHEAP_H__
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#define __LBB_CHEAP_H__
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#endif
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/*
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* LBB (Locally Bounded Bicubic) is a high quality nonlinear variant
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* of Catmull-Rom. Images resampled with LBB have much smaller halos
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* than images resampled with windowed sincs or other interpolatory
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* cubic spline filters. Specifically, LBB halos are narrower and the
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* over/undershoot amplitude is smaller. This is accomplished without
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* significantly affecting the smoothness of the result (compared to
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* Catmull-Rom).
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*
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* Another important property is that the resampled values are
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* contained within the range of nearby input values. Consequently, no
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* final clamping is needed to stay "in range" (e.g., 0-255 for
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* standard 8-bit images).
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*
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* LBB was developed by Nicolas Robidoux and Chantal Racette of the
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* Department of Mathematics and Computer Science of Laurentian
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* University in the course of C. Racette's Masters thesis in
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* Computational Sciences. Preliminary work directly leading to the
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* LBB method and code was performed by C. Racette and N. Robidoux in
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* the course of her honours thesis, and by N. Robidoux, A. Turcotte
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* and E. Daoust during Google Summer of Code 2009 (through two awards
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* made to GIMP to improve GEGL).
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*
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* LBB is a novel method with the following properties:
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*
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* --LBB is a Hermite bicubic method: The bicubic surface is defined,
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* one convex hull of four nearby input points at a time, using four
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* point values, four x-derivatives, four y-derivatives, and four
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* cross-derivatives.
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*
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* --The stencil for values in a square patch is the usual 4x4.
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*
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* --LBB is interpolatory.
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*
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* --It is C^1 with continuous cross derivatives.
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*
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* --When the limiters are inactive, LBB gives the same result as
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* Catmull-Rom.
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*
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* --When used on binary images, LBB gives results similar to bicubic
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* Hermite with all first derivatives---but not necessarily the
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* cross derivatives (this last assertion needs to be double
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* checked)--at input pixel locations set to zero.
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*
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* --The LBB reconstruction is locally bounded: Over each square
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* patch, the surface is contained between the minimum and the
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* maximum of the 16 nearest input pixel values.
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*
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* --Consequently, the LBB reconstruction is globally bounded between
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* the very smallest input pixel value and the very largest input
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* pixel value. It is not necessary to clamp results.
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*
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* The LBB method is based on the method of Ken Brodlie, Petros
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* Mashwama and Sohail Butt for constraining Hermite interpolants
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* between globally defined planes:
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*
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* Visualization of surface data to preserve positivity and other
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* simple constraints. Computer & Graphics, Vol. 19, Number 4, pages
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* 585-594, 1995. DOI: 10.1016/0097-8493(95)00036-C.
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*
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* Instead of forcing the reconstructed surface to lie between two
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* GLOBALLY defined planes, LBB constrains one patch at a time to lie
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* between LOCALLY defined planes. This is accomplished by
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* constraining the derivatives (x, y and cross) at each input pixel
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* location so that if the constraint was applied everywhere the
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* surface would fit between the min and max of the values at the 9
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* closest pixel locations. Because this is done with each of the four
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* pixel locations which define the bicubic patch, this forces the
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* reconstructed surface to lie between the min and max of the values
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* at the 16 closest values pixel locations. (Each corner defines its
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* own 3x3 subgroup of the 4x4 stencil. Consequently, the surface is
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* necessarily above the minimum of the four minima, which happens to
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* be the minimum over the 4x4. Similarly with the maxima.)
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*
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* The above paragraph described the "soft" version of LBB. The
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* "sharp" version is similar.
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*/
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#ifdef HAVE_CONFIG_H
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#include <config.h>
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#endif /*HAVE_CONFIG_H*/
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#include <vips/intl.h>
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#include <stdio.h>
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#include <stdlib.h>
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#include <vips/vips.h>
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#include <vips/internal.h>
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#include "templates.h"
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#define VIPS_TYPE_INTERPOLATE_LBB \
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(vips_interpolate_lbb_get_type())
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#define VIPS_INTERPOLATE_LBB( obj ) \
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(G_TYPE_CHECK_INSTANCE_CAST( (obj), \
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VIPS_TYPE_INTERPOLATE_LBB, VipsInterpolateLbb ))
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#define VIPS_INTERPOLATE_LBB_CLASS( klass ) \
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(G_TYPE_CHECK_CLASS_CAST( (klass), \
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VIPS_TYPE_INTERPOLATE_LBB, VipsInterpolateLbbClass))
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#define VIPS_IS_INTERPOLATE_LBB( obj ) \
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(G_TYPE_CHECK_INSTANCE_TYPE( (obj), VIPS_TYPE_INTERPOLATE_LBB ))
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#define VIPS_IS_INTERPOLATE_LBB_CLASS( klass ) \
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(G_TYPE_CHECK_CLASS_TYPE( (klass), VIPS_TYPE_INTERPOLATE_LBB ))
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#define VIPS_INTERPOLATE_LBB_GET_CLASS( obj ) \
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(G_TYPE_INSTANCE_GET_CLASS( (obj), \
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VIPS_TYPE_INTERPOLATE_LBB, VipsInterpolateLbbClass ))
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typedef struct _VipsInterpolateLbb {
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VipsInterpolate parent_object;
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} VipsInterpolateLbb;
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typedef struct _VipsInterpolateLbbClass {
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VipsInterpolateClass parent_class;
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} VipsInterpolateLbbClass;
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#define LBB_ABS(x) ( ((x)>=0.) ? (x) : -(x) )
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#define LBB_SIGN(x) ( ((x)>=0.) ? 1.0 : -1.0 )
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/*
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* MIN and MAX macros set up so that I can put the likely winner in
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* the first argument (forward branch likely blah blah blah):
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*/
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#define LBB_MIN(x,y) ( ((x)<=(y)) ? (x) : (y) )
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#define LBB_MAX(x,y) ( ((x)>=(y)) ? (x) : (y) )
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static inline double
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lbbicubic( const double c00,
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const double c10,
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const double c01,
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const double c11,
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const double c00dx,
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const double c10dx,
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const double c01dx,
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const double c11dx,
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const double c00dy,
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const double c10dy,
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const double c01dy,
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const double c11dy,
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const double c00dxdy,
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const double c10dxdy,
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const double c01dxdy,
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const double c11dxdy,
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const double uno_one,
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const double uno_two,
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const double uno_thr,
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const double uno_fou,
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const double dos_one,
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const double dos_two,
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const double dos_thr,
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const double dos_fou,
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const double tre_one,
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const double tre_two,
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const double tre_thr,
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const double tre_fou,
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const double qua_one,
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const double qua_two,
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const double qua_thr,
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const double qua_fou )
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{
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/*
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* STENCIL (FOOTPRINT) OF INPUT VALUES:
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*
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* The stencil of LBB is the same as for any standard Hermite
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* bicubic (e.g., Catmull-Rom):
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*
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* (ix-1,iy-1) (ix,iy-1) (ix+1,iy-1) (ix+2,iy-1)
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* = uno_one = uno_two = uno_thr = uno_fou
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*
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* (ix-1,iy) (ix,iy) (ix+1,iy) (ix+2,iy)
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* = dos_one = dos_two = dos_thr = dos_fou
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* X
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* (ix-1,iy+1) (ix,iy+1) (ix+1,iy+1) (ix+2,iy+1)
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* = tre_one = tre_two = tre_thr = tre_fou
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*
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* (ix-1,iy+2) (ix,iy+2) (ix+1,iy+2) (ix+2,iy+2)
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* = qua_one = qua_two = qua_thr = qua_fou
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*
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* where ix is the (pseudo-)floor of the requested left-to-right
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* location ("X"), and iy is the floor of the requested up-to-down
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* location.
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*/
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#if defined (__LBB_CHEAP_H__)
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/*
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* Computation of the four min and four max over 3x3 input data
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* sub-crosses of the 4x4 input stencil, performed with only 22
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* comparisons and 28 "? :". If you can figure out how to do this
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* more efficiently, let us know.
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*/
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const double m1 = (dos_two <= dos_thr) ? dos_two : dos_thr ;
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const double M1 = (dos_two <= dos_thr) ? dos_thr : dos_two ;
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const double m2 = (tre_two <= tre_thr) ? tre_two : tre_thr ;
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const double M2 = (tre_two <= tre_thr) ? tre_thr : tre_two ;
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const double m3 = (uno_two <= dos_one) ? uno_two : dos_one ;
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const double M3 = (uno_two <= dos_one) ? dos_one : uno_two ;
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const double m4 = (uno_thr <= dos_fou) ? uno_thr : dos_fou ;
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const double M4 = (uno_thr <= dos_fou) ? dos_fou : uno_thr ;
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const double m5 = (tre_one <= qua_two) ? tre_one : qua_two ;
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const double M5 = (tre_one <= qua_two) ? qua_two : tre_one ;
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const double m6 = (tre_fou <= qua_thr) ? tre_fou : qua_thr ;
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const double M6 = (tre_fou <= qua_thr) ? qua_thr : tre_fou ;
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const double m7 = LBB_MIN( m1, tre_two );
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const double M7 = LBB_MAX( M1, tre_two );
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const double m8 = LBB_MIN( m1, tre_thr );
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const double M8 = LBB_MAX( M1, tre_thr );
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const double m9 = LBB_MIN( m2, dos_two );
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const double M9 = LBB_MAX( M2, dos_two );
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const double m10 = LBB_MIN( m2, dos_thr );
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const double M10 = LBB_MAX( M2, dos_thr );
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const double min00 = LBB_MIN( m7, m3 );
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const double max00 = LBB_MAX( M7, M3 );
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const double min10 = LBB_MIN( m8, m4 );
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const double max10 = LBB_MAX( M8, M4 );
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const double min01 = LBB_MIN( m9, m5 );
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const double max01 = LBB_MAX( M9, M5 );
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const double min11 = LBB_MIN( m10, m6 );
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const double max11 = LBB_MAX( M10, M6 );
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#else
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/*
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* Computation of the four min and four max over 3x3 input data
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* sub-blocks of the 4x4 input stencil, performed with only 28
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* comparisons and 34 "? :". If you can figure how to do this more
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* efficiently, let us know.
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*/
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const double m1 = (dos_two <= dos_thr) ? dos_two : dos_thr ;
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const double M1 = (dos_two <= dos_thr) ? dos_thr : dos_two ;
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const double m2 = (tre_two <= tre_thr) ? tre_two : tre_thr ;
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const double M2 = (tre_two <= tre_thr) ? tre_thr : tre_two ;
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const double m6 = (dos_one <= tre_one) ? dos_one : tre_one ;
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const double M6 = (dos_one <= tre_one) ? tre_one : dos_one ;
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const double m7 = (dos_fou <= tre_fou) ? dos_fou : tre_fou ;
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const double M7 = (dos_fou <= tre_fou) ? tre_fou : dos_fou ;
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const double m3 = (uno_two <= uno_thr) ? uno_two : uno_thr ;
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const double M3 = (uno_two <= uno_thr) ? uno_thr : uno_two ;
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const double m4 = (qua_two <= qua_thr) ? qua_two : qua_thr ;
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const double M4 = (qua_two <= qua_thr) ? qua_thr : qua_two ;
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const double m5 = LBB_MIN( m1, m2 );
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const double M5 = LBB_MAX( M1, M2 );
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const double m10 = LBB_MIN( m6, uno_one );
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const double M10 = LBB_MAX( M6, uno_one );
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const double m11 = LBB_MIN( m6, qua_one );
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const double M11 = LBB_MAX( M6, qua_one );
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const double m12 = LBB_MIN( m7, uno_fou );
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const double M12 = LBB_MAX( M7, uno_fou );
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const double m13 = LBB_MIN( m7, qua_fou );
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const double M13 = LBB_MAX( M7, qua_fou );
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const double m8 = LBB_MIN( m5, m3 );
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const double M8 = LBB_MAX( M5, M3 );
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const double m9 = LBB_MIN( m5, m4 );
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const double M9 = LBB_MAX( M5, M4 );
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const double min00 = LBB_MIN( m8, m10 );
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const double max00 = LBB_MAX( M8, M10 );
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const double min10 = LBB_MIN( m8, m12 );
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const double max10 = LBB_MAX( M8, M12 );
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const double min01 = LBB_MIN( m9, m11 );
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const double max01 = LBB_MAX( M9, M11 );
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const double min11 = LBB_MIN( m9, m13 );
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const double max11 = LBB_MAX( M9, M13 );
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#endif
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/*
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* The remainder of the "per channel" computation involves the
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* computation of:
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*
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* --8 conditional moves,
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*
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* --8 signs (in which the sign of zero is unimportant),
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*
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* --12 minima of two values,
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*
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* --8 maxima of two values,
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*
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* --8 absolute values,
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*
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* for a grand total of 29 minima, 25 maxima, 8 conditional moves, 8
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* signs, and 8 absolute values. If everything is done with
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* conditional moves, "only" 28+8+8+12+8+8=72 flags are involved
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* (because initial min and max can be computed with one flag).
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*
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* The "per channel" part of the computation also involves 107
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* arithmetic operations (54 *, 21 +, 42 -).
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*/
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/*
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* Distances to the local min and max:
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*/
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const double u00 = dos_two - min00;
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const double v00 = max00 - dos_two;
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const double u10 = dos_thr - min10;
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const double v10 = max10 - dos_thr;
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const double u01 = tre_two - min01;
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const double v01 = max01 - tre_two;
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const double u11 = tre_thr - min11;
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const double v11 = max11 - tre_thr;
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/*
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* Initial values of the derivatives computed with centered
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* differences. Factors of 1/2 are left out because they are folded
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* in later:
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*/
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const double dble_dzdx00i = dos_thr - dos_one;
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const double dble_dzdy11i = qua_thr - dos_thr;
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const double dble_dzdx10i = dos_fou - dos_two;
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const double dble_dzdy01i = qua_two - dos_two;
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const double dble_dzdx01i = tre_thr - tre_one;
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const double dble_dzdy10i = tre_thr - uno_thr;
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const double dble_dzdx11i = tre_fou - tre_two;
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const double dble_dzdy00i = tre_two - uno_two;
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/*
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* Signs of the derivatives. The upcoming clamping does not change
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* them (except if the clamping sends a negative derivative to 0, in
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* which case the sign does not matter anyway).
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*/
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const double sign_dzdx00 = LBB_SIGN( dble_dzdx00i );
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const double sign_dzdx10 = LBB_SIGN( dble_dzdx10i );
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const double sign_dzdx01 = LBB_SIGN( dble_dzdx01i );
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const double sign_dzdx11 = LBB_SIGN( dble_dzdx11i );
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const double sign_dzdy00 = LBB_SIGN( dble_dzdy00i );
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const double sign_dzdy10 = LBB_SIGN( dble_dzdy10i );
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const double sign_dzdy01 = LBB_SIGN( dble_dzdy01i );
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const double sign_dzdy11 = LBB_SIGN( dble_dzdy11i );
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/*
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* Initial values of the cross-derivatives. Factors of 1/4 are left
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* out because folded in later:
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*/
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const double quad_d2zdxdy00i = uno_one - uno_thr + dble_dzdx01i;
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const double quad_d2zdxdy10i = uno_two - uno_fou + dble_dzdx11i;
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const double quad_d2zdxdy01i = qua_thr - qua_one - dble_dzdx00i;
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const double quad_d2zdxdy11i = qua_fou - qua_two - dble_dzdx10i;
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/*
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* Slope limiters. The key multiplier is 3 but we fold a factor of
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* 2, hence 6:
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*/
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const double dble_slopelimit_00 = 6.0 * LBB_MIN( u00, v00 );
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const double dble_slopelimit_10 = 6.0 * LBB_MIN( u10, v10 );
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const double dble_slopelimit_01 = 6.0 * LBB_MIN( u01, v01 );
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const double dble_slopelimit_11 = 6.0 * LBB_MIN( u11, v11 );
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/*
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* Clamped first derivatives:
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*/
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const double dble_dzdx00 =
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( sign_dzdx00 * dble_dzdx00i <= dble_slopelimit_00 )
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? dble_dzdx00i : sign_dzdx00 * dble_slopelimit_00;
|
|
const double dble_dzdy00 =
|
|
( sign_dzdy00 * dble_dzdy00i <= dble_slopelimit_00 )
|
|
? dble_dzdy00i : sign_dzdy00 * dble_slopelimit_00;
|
|
const double dble_dzdx10 =
|
|
( sign_dzdx10 * dble_dzdx10i <= dble_slopelimit_10 )
|
|
? dble_dzdx10i : sign_dzdx10 * dble_slopelimit_10;
|
|
const double dble_dzdy10 =
|
|
( sign_dzdy10 * dble_dzdy10i <= dble_slopelimit_10 )
|
|
? dble_dzdy10i : sign_dzdy10 * dble_slopelimit_10;
|
|
const double dble_dzdx01 =
|
|
( sign_dzdx01 * dble_dzdx01i <= dble_slopelimit_01 )
|
|
? dble_dzdx01i : sign_dzdx01 * dble_slopelimit_01;
|
|
const double dble_dzdy01 =
|
|
( sign_dzdy01 * dble_dzdy01i <= dble_slopelimit_01 )
|
|
? dble_dzdy01i : sign_dzdy01 * dble_slopelimit_01;
|
|
const double dble_dzdx11 =
|
|
( sign_dzdx11 * dble_dzdx11i <= dble_slopelimit_11 )
|
|
? dble_dzdx11i : sign_dzdx11 * dble_slopelimit_11;
|
|
const double dble_dzdy11 =
|
|
( sign_dzdy11 * dble_dzdy11i <= dble_slopelimit_11 )
|
|
? dble_dzdy11i : sign_dzdy11 * dble_slopelimit_11;
|
|
|
|
/*
|
|
* Sums and differences of first derivatives:
|
|
*/
|
|
const double twelve_sum00 = 6.0 * ( dble_dzdx00 + dble_dzdy00 );
|
|
const double twelve_dif00 = 6.0 * ( dble_dzdx00 - dble_dzdy00 );
|
|
const double twelve_sum10 = 6.0 * ( dble_dzdx10 + dble_dzdy10 );
|
|
const double twelve_dif10 = 6.0 * ( dble_dzdx10 - dble_dzdy10 );
|
|
const double twelve_sum01 = 6.0 * ( dble_dzdx01 + dble_dzdy01 );
|
|
const double twelve_dif01 = 6.0 * ( dble_dzdx01 - dble_dzdy01 );
|
|
const double twelve_sum11 = 6.0 * ( dble_dzdx11 + dble_dzdy11 );
|
|
const double twelve_dif11 = 6.0 * ( dble_dzdx11 - dble_dzdy11 );
|
|
|
|
/*
|
|
* Absolute values of the sums:
|
|
*/
|
|
const double twelve_abs_sum00 = LBB_ABS( twelve_sum00 );
|
|
const double twelve_abs_sum10 = LBB_ABS( twelve_sum10 );
|
|
const double twelve_abs_sum01 = LBB_ABS( twelve_sum01 );
|
|
const double twelve_abs_sum11 = LBB_ABS( twelve_sum11 );
|
|
|
|
/*
|
|
* Scaled distances to the min:
|
|
*/
|
|
const double u00_times_36 = 36.0 * u00;
|
|
const double u10_times_36 = 36.0 * u10;
|
|
const double u01_times_36 = 36.0 * u01;
|
|
const double u11_times_36 = 36.0 * u11;
|
|
|
|
/*
|
|
* First cross-derivative limiter:
|
|
*/
|
|
const double first_limit00 = twelve_abs_sum00 - u00_times_36;
|
|
const double first_limit10 = twelve_abs_sum10 - u10_times_36;
|
|
const double first_limit01 = twelve_abs_sum01 - u01_times_36;
|
|
const double first_limit11 = twelve_abs_sum11 - u11_times_36;
|
|
|
|
const double quad_d2zdxdy00ii = LBB_MAX( quad_d2zdxdy00i, first_limit00 );
|
|
const double quad_d2zdxdy10ii = LBB_MAX( quad_d2zdxdy10i, first_limit10 );
|
|
const double quad_d2zdxdy01ii = LBB_MAX( quad_d2zdxdy01i, first_limit01 );
|
|
const double quad_d2zdxdy11ii = LBB_MAX( quad_d2zdxdy11i, first_limit11 );
|
|
|
|
/*
|
|
* Scaled distances to the max:
|
|
*/
|
|
const double v00_times_36 = 36.0 * v00;
|
|
const double v10_times_36 = 36.0 * v10;
|
|
const double v01_times_36 = 36.0 * v01;
|
|
const double v11_times_36 = 36.0 * v11;
|
|
|
|
/*
|
|
* Second cross-derivative limiter:
|
|
*/
|
|
const double second_limit00 = v00_times_36 - twelve_abs_sum00;
|
|
const double second_limit10 = v10_times_36 - twelve_abs_sum10;
|
|
const double second_limit01 = v01_times_36 - twelve_abs_sum01;
|
|
const double second_limit11 = v11_times_36 - twelve_abs_sum11;
|
|
|
|
const double quad_d2zdxdy00iii = LBB_MIN( quad_d2zdxdy00ii, second_limit00 );
|
|
const double quad_d2zdxdy10iii = LBB_MIN( quad_d2zdxdy10ii, second_limit10 );
|
|
const double quad_d2zdxdy01iii = LBB_MIN( quad_d2zdxdy01ii, second_limit01 );
|
|
const double quad_d2zdxdy11iii = LBB_MIN( quad_d2zdxdy11ii, second_limit11 );
|
|
|
|
/*
|
|
* Absolute values of the differences:
|
|
*/
|
|
const double twelve_abs_dif00 = LBB_ABS( twelve_dif00 );
|
|
const double twelve_abs_dif10 = LBB_ABS( twelve_dif10 );
|
|
const double twelve_abs_dif01 = LBB_ABS( twelve_dif01 );
|
|
const double twelve_abs_dif11 = LBB_ABS( twelve_dif11 );
|
|
|
|
/*
|
|
* Third cross-derivative limiter:
|
|
*/
|
|
const double third_limit00 = twelve_abs_dif00 - v00_times_36;
|
|
const double third_limit10 = twelve_abs_dif10 - v10_times_36;
|
|
const double third_limit01 = twelve_abs_dif01 - v01_times_36;
|
|
const double third_limit11 = twelve_abs_dif11 - v11_times_36;
|
|
|
|
const double quad_d2zdxdy00iiii = LBB_MAX( quad_d2zdxdy00iii, third_limit00);
|
|
const double quad_d2zdxdy10iiii = LBB_MAX( quad_d2zdxdy10iii, third_limit10);
|
|
const double quad_d2zdxdy01iiii = LBB_MAX( quad_d2zdxdy01iii, third_limit01);
|
|
const double quad_d2zdxdy11iiii = LBB_MAX( quad_d2zdxdy11iii, third_limit11);
|
|
|
|
/*
|
|
* Fourth cross-derivative limiter:
|
|
*/
|
|
const double fourth_limit00 = u00_times_36 - twelve_abs_dif00;
|
|
const double fourth_limit10 = u10_times_36 - twelve_abs_dif10;
|
|
const double fourth_limit01 = u01_times_36 - twelve_abs_dif01;
|
|
const double fourth_limit11 = u11_times_36 - twelve_abs_dif11;
|
|
|
|
const double quad_d2zdxdy00 = LBB_MIN( quad_d2zdxdy00iiii, fourth_limit00);
|
|
const double quad_d2zdxdy10 = LBB_MIN( quad_d2zdxdy10iiii, fourth_limit10);
|
|
const double quad_d2zdxdy01 = LBB_MIN( quad_d2zdxdy01iiii, fourth_limit01);
|
|
const double quad_d2zdxdy11 = LBB_MIN( quad_d2zdxdy11iiii, fourth_limit11);
|
|
|
|
/*
|
|
* Part of the result which does not need derivatives:
|
|
*/
|
|
const double newval1 = c00 * dos_two + c10 * dos_thr +
|
|
c01 * tre_two + c11 * tre_thr;
|
|
|
|
/*
|
|
* Twice the part of the result which only needs first derivatives.
|
|
*/
|
|
const double newval2 = c00dx * dble_dzdx00 + c10dx * dble_dzdx10 +
|
|
c01dx * dble_dzdx01 + c11dx * dble_dzdx11 +
|
|
c00dy * dble_dzdy00 + c10dy * dble_dzdy10 +
|
|
c01dy * dble_dzdy01 + c11dy * dble_dzdy11;
|
|
|
|
/*
|
|
* Four times the part of the result which only uses cross
|
|
* derivatives:
|
|
*/
|
|
const double newval3 = c00dxdy * quad_d2zdxdy00 + c10dxdy * quad_d2zdxdy10 +
|
|
c01dxdy * quad_d2zdxdy01 + c11dxdy * quad_d2zdxdy11;
|
|
|
|
const double newval = newval1 + .5 * newval2 + .25 * newval3;
|
|
|
|
return newval;
|
|
}
|
|
|
|
/*
|
|
* Call lbb with a type conversion operator as a parameter.
|
|
*
|
|
* It would be nice to do this with templates but we can't figure out
|
|
* how to do it cleanly. Suggestions welcome!
|
|
*/
|
|
#define LBB_CONVERSION( conversion ) \
|
|
template <typename T> static void inline \
|
|
lbb_ ## conversion( PEL* restrict pout, \
|
|
const PEL* restrict pin, \
|
|
const int bands, \
|
|
const int lskip, \
|
|
const double relative_x, \
|
|
const double relative_y ) \
|
|
{ \
|
|
T* restrict out = (T *) pout; \
|
|
\
|
|
const T* restrict in = (T *) pin; \
|
|
\
|
|
const int one_shift = -bands; \
|
|
const int thr_shift = bands; \
|
|
const int fou_shift = 2*bands; \
|
|
\
|
|
const int uno_two_shift = -lskip; \
|
|
\
|
|
const int tre_two_shift = lskip; \
|
|
const int qua_two_shift = 2*lskip; \
|
|
\
|
|
const int uno_one_shift = uno_two_shift + one_shift; \
|
|
const int dos_one_shift = one_shift; \
|
|
const int tre_one_shift = tre_two_shift + one_shift; \
|
|
const int qua_one_shift = qua_two_shift + one_shift; \
|
|
\
|
|
const int uno_thr_shift = uno_two_shift + thr_shift; \
|
|
const int dos_thr_shift = thr_shift; \
|
|
const int tre_thr_shift = tre_two_shift + thr_shift; \
|
|
const int qua_thr_shift = qua_two_shift + thr_shift; \
|
|
\
|
|
const int uno_fou_shift = uno_two_shift + fou_shift; \
|
|
const int dos_fou_shift = fou_shift; \
|
|
const int tre_fou_shift = tre_two_shift + fou_shift; \
|
|
const int qua_fou_shift = qua_two_shift + fou_shift; \
|
|
\
|
|
const double xp1over2 = relative_x; \
|
|
const double xm1over2 = xp1over2 - 1.0; \
|
|
const double onepx = 0.5 + xp1over2; \
|
|
const double onemx = 1.5 - xp1over2; \
|
|
const double xp1over2sq = xp1over2 * xp1over2; \
|
|
\
|
|
const double yp1over2 = relative_y; \
|
|
const double ym1over2 = yp1over2 - 1.0; \
|
|
const double onepy = 0.5 + yp1over2; \
|
|
const double onemy = 1.5 - yp1over2; \
|
|
const double yp1over2sq = yp1over2 * yp1over2; \
|
|
\
|
|
const double xm1over2sq = xm1over2 * xm1over2; \
|
|
const double ym1over2sq = ym1over2 * ym1over2; \
|
|
\
|
|
const double twice1px = onepx + onepx; \
|
|
const double twice1py = onepy + onepy; \
|
|
const double twice1mx = onemx + onemx; \
|
|
const double twice1my = onemy + onemy; \
|
|
\
|
|
const double xm1over2sq_times_ym1over2sq = xm1over2sq * ym1over2sq; \
|
|
const double xp1over2sq_times_ym1over2sq = xp1over2sq * ym1over2sq; \
|
|
const double xp1over2sq_times_yp1over2sq = xp1over2sq * yp1over2sq; \
|
|
const double xm1over2sq_times_yp1over2sq = xm1over2sq * yp1over2sq; \
|
|
\
|
|
const double four_times_1px_times_1py = twice1px * twice1py; \
|
|
const double four_times_1mx_times_1py = twice1mx * twice1py; \
|
|
const double twice_xp1over2_times_1py = xp1over2 * twice1py; \
|
|
const double twice_xm1over2_times_1py = xm1over2 * twice1py; \
|
|
\
|
|
const double twice_xm1over2_times_1my = xm1over2 * twice1my; \
|
|
const double twice_xp1over2_times_1my = xp1over2 * twice1my; \
|
|
const double four_times_1mx_times_1my = twice1mx * twice1my; \
|
|
const double four_times_1px_times_1my = twice1px * twice1my; \
|
|
\
|
|
const double twice_1px_times_ym1over2 = twice1px * ym1over2; \
|
|
const double twice_1mx_times_ym1over2 = twice1mx * ym1over2; \
|
|
const double xp1over2_times_ym1over2 = xp1over2 * ym1over2; \
|
|
const double xm1over2_times_ym1over2 = xm1over2 * ym1over2; \
|
|
\
|
|
const double xm1over2_times_yp1over2 = xm1over2 * yp1over2; \
|
|
const double xp1over2_times_yp1over2 = xp1over2 * yp1over2; \
|
|
const double twice_1mx_times_yp1over2 = twice1mx * yp1over2; \
|
|
const double twice_1px_times_yp1over2 = twice1px * yp1over2; \
|
|
\
|
|
const double c00 = \
|
|
four_times_1px_times_1py * xm1over2sq_times_ym1over2sq; \
|
|
const double c00dx = \
|
|
twice_xp1over2_times_1py * xm1over2sq_times_ym1over2sq; \
|
|
const double c00dy = \
|
|
twice_1px_times_yp1over2 * xm1over2sq_times_ym1over2sq; \
|
|
const double c00dxdy = \
|
|
xp1over2_times_yp1over2 * xm1over2sq_times_ym1over2sq; \
|
|
\
|
|
const double c10 = \
|
|
four_times_1mx_times_1py * xp1over2sq_times_ym1over2sq; \
|
|
const double c10dx = \
|
|
twice_xm1over2_times_1py * xp1over2sq_times_ym1over2sq; \
|
|
const double c10dy = \
|
|
twice_1mx_times_yp1over2 * xp1over2sq_times_ym1over2sq; \
|
|
const double c10dxdy = \
|
|
xm1over2_times_yp1over2 * xp1over2sq_times_ym1over2sq; \
|
|
\
|
|
const double c01 = \
|
|
four_times_1px_times_1my * xm1over2sq_times_yp1over2sq; \
|
|
const double c01dx = \
|
|
twice_xp1over2_times_1my * xm1over2sq_times_yp1over2sq; \
|
|
const double c01dy = \
|
|
twice_1px_times_ym1over2 * xm1over2sq_times_yp1over2sq; \
|
|
const double c01dxdy = \
|
|
xp1over2_times_ym1over2 * xm1over2sq_times_yp1over2sq; \
|
|
\
|
|
const double c11 = \
|
|
four_times_1mx_times_1my * xp1over2sq_times_yp1over2sq; \
|
|
const double c11dx = \
|
|
twice_xm1over2_times_1my * xp1over2sq_times_yp1over2sq; \
|
|
const double c11dy = \
|
|
twice_1mx_times_ym1over2 * xp1over2sq_times_yp1over2sq; \
|
|
const double c11dxdy = \
|
|
xm1over2_times_ym1over2 * xp1over2sq_times_yp1over2sq; \
|
|
\
|
|
int band = bands; \
|
|
\
|
|
do \
|
|
{ \
|
|
const double double_result = \
|
|
lbbicubic( c00, \
|
|
c10, \
|
|
c01, \
|
|
c11, \
|
|
c00dx, \
|
|
c10dx, \
|
|
c01dx, \
|
|
c11dx, \
|
|
c00dy, \
|
|
c10dy, \
|
|
c01dy, \
|
|
c11dy, \
|
|
c00dxdy, \
|
|
c10dxdy, \
|
|
c01dxdy, \
|
|
c11dxdy, \
|
|
in[ uno_one_shift ], \
|
|
in[ uno_two_shift ], \
|
|
in[ uno_thr_shift ], \
|
|
in[ uno_fou_shift ], \
|
|
in[ dos_one_shift ], \
|
|
in[ 0 ], \
|
|
in[ dos_thr_shift ], \
|
|
in[ dos_fou_shift ], \
|
|
in[ tre_one_shift ], \
|
|
in[ tre_two_shift ], \
|
|
in[ tre_thr_shift ], \
|
|
in[ tre_fou_shift ], \
|
|
in[ qua_one_shift ], \
|
|
in[ qua_two_shift ], \
|
|
in[ qua_thr_shift ], \
|
|
in[ qua_fou_shift ] ); \
|
|
\
|
|
const T result = to_ ## conversion<T>( double_result ); \
|
|
in++; \
|
|
*out++ = result; \
|
|
} while (--band); \
|
|
}
|
|
|
|
LBB_CONVERSION( fptypes )
|
|
LBB_CONVERSION( withsign )
|
|
LBB_CONVERSION( nosign )
|
|
|
|
#define CALL( T, conversion ) \
|
|
lbb_ ## conversion<T>( out, \
|
|
p, \
|
|
bands, \
|
|
lskip, \
|
|
relative_x, \
|
|
relative_y );
|
|
|
|
/*
|
|
* We need C linkage:
|
|
*/
|
|
extern "C" {
|
|
G_DEFINE_TYPE( VipsInterpolateLbb, vips_interpolate_lbb,
|
|
VIPS_TYPE_INTERPOLATE );
|
|
}
|
|
|
|
static void
|
|
vips_interpolate_lbb_interpolate( VipsInterpolate* restrict interpolate,
|
|
PEL* restrict out,
|
|
REGION* restrict in,
|
|
double absolute_x,
|
|
double absolute_y )
|
|
{
|
|
/*
|
|
* Floor's surrogate FAST_PSEUDO_FLOOR is used to make sure that the
|
|
* transition through 0 is smooth. If it is known that absolute_x
|
|
* and absolute_y will never be less than 0, plain cast---that is,
|
|
* const int ix = absolute_x---should be used instead. Actually,
|
|
* any function which agrees with floor for non-integer values, and
|
|
* picks one of the two possibilities for integer values, can be
|
|
* used. FAST_PSEUDO_FLOOR fits the bill.
|
|
*
|
|
* Then, x is the x-coordinate of the sampling point relative to the
|
|
* position of the top left corner of the convex hull of the 2x2
|
|
* block of closest pixels. Similarly for y. Range of values: [0,1).
|
|
*/
|
|
const int ix = FAST_PSEUDO_FLOOR( absolute_x );
|
|
const int iy = FAST_PSEUDO_FLOOR( absolute_y );
|
|
|
|
/*
|
|
* Move the pointer to (the first band of) the top/left pixel of the
|
|
* 2x2 group of pixel centers which contains the sampling location
|
|
* in its convex hull:
|
|
*/
|
|
const PEL* restrict p = (PEL *) IM_REGION_ADDR( in, ix, iy );
|
|
|
|
const double relative_x = absolute_x - ix;
|
|
const double relative_y = absolute_y - iy;
|
|
|
|
/*
|
|
* VIPS versions of Nicolas's pixel addressing values.
|
|
*/
|
|
const int actual_bands = in->im->Bands;
|
|
const int lskip = IM_REGION_LSKIP( in ) / IM_IMAGE_SIZEOF_ELEMENT( in->im );
|
|
/*
|
|
* Double the bands for complex images to account for the real and
|
|
* imaginary parts being computed independently:
|
|
*/
|
|
const int bands =
|
|
vips_bandfmt_iscomplex( in->im->BandFmt ) ? 2 * actual_bands : actual_bands;
|
|
|
|
switch( in->im->BandFmt ) {
|
|
case IM_BANDFMT_UCHAR:
|
|
CALL( unsigned char, nosign );
|
|
break;
|
|
|
|
case IM_BANDFMT_CHAR:
|
|
CALL( signed char, withsign );
|
|
break;
|
|
|
|
case IM_BANDFMT_USHORT:
|
|
CALL( unsigned short, nosign );
|
|
break;
|
|
|
|
case IM_BANDFMT_SHORT:
|
|
CALL( signed short, withsign );
|
|
break;
|
|
|
|
case IM_BANDFMT_UINT:
|
|
CALL( unsigned int, nosign );
|
|
break;
|
|
|
|
case IM_BANDFMT_INT:
|
|
CALL( signed int, withsign );
|
|
break;
|
|
|
|
/*
|
|
* Complex images are handled by doubling of bands.
|
|
*/
|
|
case IM_BANDFMT_FLOAT:
|
|
case IM_BANDFMT_COMPLEX:
|
|
CALL( float, fptypes );
|
|
break;
|
|
|
|
case IM_BANDFMT_DOUBLE:
|
|
case IM_BANDFMT_DPCOMPLEX:
|
|
CALL( double, fptypes );
|
|
break;
|
|
|
|
default:
|
|
g_assert( 0 );
|
|
break;
|
|
}
|
|
}
|
|
|
|
static void
|
|
vips_interpolate_lbb_class_init( VipsInterpolateLbbClass *klass )
|
|
{
|
|
VipsObjectClass *object_class = VIPS_OBJECT_CLASS( klass );
|
|
VipsInterpolateClass *interpolate_class =
|
|
VIPS_INTERPOLATE_CLASS( klass );
|
|
|
|
object_class->nickname = "lbb";
|
|
object_class->description = _( "Reduced halo bicubic" );
|
|
|
|
interpolate_class->interpolate = vips_interpolate_lbb_interpolate;
|
|
interpolate_class->window_size = 4;
|
|
}
|
|
|
|
static void
|
|
vips_interpolate_lbb_init( VipsInterpolateLbb *lbb )
|
|
{
|
|
}
|