[vlc-devel] [PATCH 2/6] Add monotone cubic interpolation support
Rémi Denis-Courmont
remi at remlab.net
Thu Jul 24 19:33:12 CEST 2014
Le jeudi 24 juillet 2014, 12:19:18 Ronald Wright a écrit :
> ---
> include/vlc_interpolation.h | 122 ++++++++++++++++++++++++
> po/POTFILES.in | 2 +
> src/Makefile.am | 2 +
> src/libvlccore.sym | 3 +
> src/misc/interpolation.c | 219
> ++++++++++++++++++++++++++++++++++++++++++++ 5 files changed, 348
> insertions(+)
> create mode 100644 include/vlc_interpolation.h
> create mode 100644 src/misc/interpolation.c
>
> diff --git a/include/vlc_interpolation.h b/include/vlc_interpolation.h
> new file mode 100644
> index 0000000..58c491b
> --- /dev/null
> +++ b/include/vlc_interpolation.h
> @@ -0,0 +1,122 @@
> +/**************************************************************************
> *** + * vlc_interpolation.h: Interpolation utility
> +
> ***************************************************************************
> ** + * Copyright (C) 2014 Ronald Wright
> + * $Id$
> + *
> + * Author: Ronald Wright <logiconcepts819 at gmail.com>
> + *
> + * This program is free software; you can redistribute it and/or modify it
> + * under the terms of the GNU Lesser General Public License as published by
> + * the Free Software Foundation; either version 2.1 of the License, or + *
> (at your option) any later version.
> + *
> + * This program is distributed in the hope that it will be useful,
> + * but WITHOUT ANY WARRANTY; without even the implied warranty of
> + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
> + * GNU Lesser General Public License for more details.
> + *
> + * You should have received a copy of the GNU Lesser General Public License
> + * along with this program; if not, write to the Free Software Foundation,
> + * Inc., 51 Franklin Street, Fifth Floor, Boston MA 02110-1301, USA. +
> ***************************************************************************
> **/ +
> +#ifndef VLC_INTERPOLATION_H
> +#define VLC_INTERPOLATION_H
> +
> +/**
> + * \file
> + * This file is the interface definition for a modification of
> Fritsch-Carlson + * monotone cubic spline interpolation (implementation in
> + * src/misc/interpolation.c)
> + */
> +
> +/**************************************************************************
> *** + * Documentation
> +
> ***************************************************************************
> **/ +/*
> + **** Background
> + *
> + * This implements a modification of Fritsch-Carlson monotone cubic spline
> + * interpolation. Fritsch-Carlson interpolation creates an interpolant as
> + * follows:
> + *
> + * 1. The slopes between successive data points are computed.
> + * 2. The tangents at each data point is computed as the average of the
> + * secants.
> + * 3. To preserve monotonicity, slopes are set to zero wherever two
> successive + * points are equal.
> + * 4. To prevent overshoot, two successive slopes, normalized by the
> tangent + * at the leftmost point, are restricted so that the sum of
> their squares do + * not exceed a certain threshold (9 in this
> algorithm).
> + *
> + * The interpolation is modified such that all sample points left of the
> spline + * have values equal to the left-most data point and all sample
> points right of + * the spline have values equal to the right-most data
> point. Hence, the + * resulting line extending outward from the left-most
> data point has zero + * slope, and the resulting line extending outward
> from the right-most data + * point has zero slope.
> + *
> + **** Example usage
> + *
> + * #define NUM_POINTS 4
> + * ...
> + * my_function()
> + * {
> + * ...
> + * float points[NUM_POINTS] = { -0.5, 1.0, 2.5, 5.0 };
> + * float values[NUM_POINTS] = { 8.0, -5.0, 0.0, 3.0 };
> + * ...
> + * vlc_interpolant_t itp;
> + * if( vlc_create_interpolant( points, values, NUM_POINTS, &itp ) ==
> VLC_SUCCESS ) + * {
> + * ...
> + * float y = vlc_interpolate( &itp, 0.5 );
> + * ...
> + * vlc_destroy_interpolant( &itp );
> + * ...
> + * }
> + * ...
> + * }
> + * */
> +
> +/**************************************************************************
> *** + * Interpolant type
> +
> ***************************************************************************
> **/ +
> +typedef struct
> +{
> + float * pf_points;
> + float * pf_values;
> +
> + float * pf_c1s;
> + float * pf_c2s;
> + float * pf_c3s;
> +
> + int i_point_count;
> +} vlc_interpolant_t;
This should probably not be public. You are allocating dynamically anyway.
> +
> +/**************************************************************************
> *** + * Interpolation routines
> +
> ***************************************************************************
> **/ +
> +/*
> + * Create a new interpolant from the given data points and data point
> values.
> + */
Doxygen style please.
> +VLC_API int vlc_create_interpolant( vlc_interpolant_t * p_interpolant,
> + const float * pf_points,
> + const float * pf_values,
> + int i_point_count );
> +
> +/*
> + * Sample the spline at the given sample point.
> + */
> +VLC_API float vlc_interpolate( const vlc_interpolant_t * p_interpolant,
> + float f_sample_point );
> +
> +/*
> + * Destroy an interpolant that is no longer in use.
> + */
> +VLC_API void vlc_destroy_interpolant( vlc_interpolant_t * p_interpolant );
> +
> +#endif
> diff --git a/po/POTFILES.in b/po/POTFILES.in
> index 09b2369..4a0405d 100644
> --- a/po/POTFILES.in
> +++ b/po/POTFILES.in
> @@ -26,6 +26,7 @@ include/vlc_httpd.h
> include/vlc_image.h
> include/vlc_input.h
> include/vlc_interface.h
> +include/vlc_interpolation.h
> include/vlc_intf_strings.h
> include/vlc_iso_lang.h
> include/vlc_keys.h
> @@ -112,6 +113,7 @@ src/misc/es_format.c
> src/misc/events.c
> src/misc/filter_chain.c
> src/misc/image.c
> +src/misc/interpolation.c
> src/misc/md5.c
> src/misc/messages.c
> src/misc/mtime.c
> diff --git a/src/Makefile.am b/src/Makefile.am
> index fbe7ec2..82a3b63 100644
> --- a/src/Makefile.am
> +++ b/src/Makefile.am
> @@ -56,6 +56,7 @@ pluginsinclude_HEADERS = \
> ../include/vlc_inhibit.h \
> ../include/vlc_input.h \
> ../include/vlc_input_item.h \
> + ../include/vlc_interpolation.h \
> ../include/vlc_keys.h \
> ../include/vlc_main.h \
> ../include/vlc_md5.h \
> @@ -439,6 +440,7 @@ SOURCES_libvlc_common = \
> misc/block.c \
> misc/fourcc.c \
> misc/es_format.c \
> + misc/interpolation.c \
> misc/picture.c \
> misc/picture_fifo.c \
> misc/picture_pool.c \
> diff --git a/src/libvlccore.sym b/src/libvlccore.sym
> index 325c8f6..29a204c 100644
> --- a/src/libvlccore.sym
> +++ b/src/libvlccore.sym
> @@ -501,6 +501,8 @@ vlc_sem_destroy
> vlc_sem_post
> vlc_sem_wait
> vlc_control_cancel
> +vlc_create_interpolant
> +vlc_destroy_interpolant
> vlc_GetCPUCount
> vlc_CPU
> vlc_error
> @@ -528,6 +530,7 @@ vlc_ngettext
> vlc_iconv
> vlc_iconv_close
> vlc_iconv_open
> +vlc_interpolate
> vlc_join
> vlc_list_children
> vlc_list_release
> diff --git a/src/misc/interpolation.c b/src/misc/interpolation.c
> new file mode 100644
> index 0000000..31c80d3
> --- /dev/null
> +++ b/src/misc/interpolation.c
> @@ -0,0 +1,219 @@
> +/**************************************************************************
> *** + * vlc_interpolation.h: Interpolation utility
> +
> ***************************************************************************
> ** + * Copyright (C) 2014 Ronald Wright
> + * $Id$
> + *
> + * Author: Ronald Wright <logiconcepts819 at gmail.com>
> + *
> + * This program is free software; you can redistribute it and/or modify it
> + * under the terms of the GNU Lesser General Public License as published by
> + * the Free Software Foundation; either version 2.1 of the License, or + *
> (at your option) any later version.
> + *
> + * This program is distributed in the hope that it will be useful,
> + * but WITHOUT ANY WARRANTY; without even the implied warranty of
> + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
> + * GNU Lesser General Public License for more details.
> + *
> + * You should have received a copy of the GNU Lesser General Public License
> + * along with this program; if not, write to the Free Software Foundation,
> + * Inc., 51 Franklin Street, Fifth Floor, Boston MA 02110-1301, USA. +
> ***************************************************************************
> **/ +
> +/**************************************************************************
> *** + * Preamble
> +
> ***************************************************************************
> **/ +
> +#ifdef HAVE_CONFIG_H
> +# include "config.h"
> +#endif
> +
> +#include <vlc_common.h>
> +#include <vlc_interpolation.h>
> +
> +/**************************************************************************
> *** + * Documentation : Read vlc_interpolation.h
> +
> ***************************************************************************
> **/ +
> +/**************************************************************************
> *** + * Implementation of interpolation routines.
> +
> ***************************************************************************
> **/ +
> +int vlc_create_interpolant( vlc_interpolant_t * p_interpolant,
> + const float * pf_points, const float *
> pf_values, + int i_point_count )
> +{
> + /* This subroutine assumes that each sample point in the sequence
> + * referenced by pf_points is unique and that the sequence is sorted.
> */ +
> + /* We should have at least two data points for the computation */
> + if( i_point_count < 2 )
> + return VLC_EBADVAR;
> +
> + int i_ret_val = VLC_ENOMEM;
> +
> + /* Allocate memory */
> +
> + float * pf_dys = malloc( ( i_point_count - 1 ) * sizeof( *pf_dys ) );
> + if( unlikely( !pf_dys ) )
> + goto return_i_ret_val;
> +
> + float * pf_dxs = malloc( ( i_point_count - 1 ) * sizeof( *pf_dxs ) );
> + if( unlikely( !pf_dxs ) )
> + goto free_pf_dys;
> +
> + float * pf_ms = malloc( ( i_point_count - 1 ) * sizeof( *pf_ms ) );
> + if( unlikely( !pf_ms ) )
> + goto free_pf_dxs;
> +
> + float * pf_c1s = malloc( i_point_count * sizeof( *pf_c1s ) );
> + if( unlikely( !pf_c1s ) )
> + goto free_pf_ms;
> +
> + float * pf_c2s = malloc( ( i_point_count - 1 ) * sizeof( *pf_c2s ) );
> + if( unlikely( !pf_c2s ) )
> + goto free_pf_c1s;
> +
> + float * pf_c3s = malloc( ( i_point_count - 1 ) * sizeof( *pf_c3s ) );
> + if( unlikely( !pf_c3s ) )
> + goto free_pf_c2s;
> +
> + float * pf_points_ = malloc( i_point_count * sizeof( *pf_points_ ) );
> + if( unlikely( !pf_points_ ) )
> + goto free_pf_c3s;
> +
> + float * pf_values_ = malloc( i_point_count * sizeof( *pf_values_ ) );
> + if( unlikely( !pf_values_ ) )
> + goto free_pf_points;
Defining a structure for each point and allocating a single table should be
much simpler. In fact you can even combine the table and interpolant as a
single allocation.
> +
> + /* Get consecutive differences and slopes */
> + for( int i = 0; i < i_point_count - 1; i++ )
> + {
> + float f_dx = pf_points[i + 1] - pf_points[i];
> + float f_dy = pf_values[i + 1] - pf_values[i];
> + pf_dxs[i] = f_dx;
> + pf_dys[i] = f_dy;
> + pf_ms[i] = f_dy / f_dx;
> + }
> +
> + /* Get degree-1 coefficients */
> + pf_c1s[0] = pf_ms[0];
> + for( int i = 0; i < i_point_count - 2; i++ )
> + {
> + float f_m = pf_ms[i];
> + float f_mNext = pf_ms[i + 1];
> + float f_c1;
> + if( f_m * f_mNext <= 0 )
> + {
> + f_c1 = 0.0f;
> + }
> + else
> + {
> + float f_dx = pf_dxs[i];
> + float f_dxNext = pf_dxs[i + 1];
> + float f_common = f_dx + f_dxNext;
> + f_c1 = 3.0f * f_common / ( ( f_common + f_dxNext ) / f_m
> + + ( f_common + f_dx ) / f_mNext );
> + }
> + pf_c1s[i + 1] = f_c1;
> + }
> + pf_c1s[i_point_count - 1] = pf_ms[i_point_count - 2];
> +
> + /* Get degree-2 and degree-3 coefficients */
> + for( int i = 0; i < i_point_count - 1; i++ )
> + {
> + float f_c1 = pf_c1s[i];
> + float f_m = pf_ms[i];
> + float f_invDx = 1.0f / pf_dxs[i];
> + float f_common = f_c1 + pf_c1s[i + 1] - f_m - f_m;
> + pf_c2s[i] = ( f_m - f_c1 - f_common ) * f_invDx;
> + pf_c3s[i] = f_common * f_invDx * f_invDx;
> + }
> +
> + /* Set up structure */
> + memcpy( pf_points_, pf_points, i_point_count * sizeof( *pf_points ) );
> + memcpy( pf_values_, pf_values, i_point_count * sizeof( *pf_values ) );
> + p_interpolant->pf_c1s = pf_c1s;
> + p_interpolant->pf_c2s = pf_c2s;
> + p_interpolant->pf_c3s = pf_c3s;
> + p_interpolant->pf_points = pf_points_;
> + p_interpolant->pf_values = pf_values_;
> + p_interpolant->i_point_count = i_point_count;
> + i_ret_val = VLC_SUCCESS;
> + goto free_pf_ms;
> +
> +free_pf_points:
> + free( pf_points_ );
> +free_pf_c3s:
> + free( pf_c3s );
> +free_pf_c2s:
> + free( pf_c2s );
> +free_pf_c1s:
> + free( pf_c1s );
> +free_pf_ms:
> + free( pf_ms );
> +free_pf_dxs:
> + free( pf_dxs );
> +free_pf_dys:
> + free( pf_dys );
> +return_i_ret_val:
> + return i_ret_val;
> +}
> +
> +float vlc_interpolate( const vlc_interpolant_t * p_interpolant,
> + float f_sample_point )
> +{
> + const float * pf_points = p_interpolant->pf_points;
> + const float * pf_values = p_interpolant->pf_values;
> +
> + /* Here, the implementation is modified to give the closest endpoints
> for + * sample points that lie outside the spline region */
> + int i = p_interpolant->i_point_count - 1;
> + if( f_sample_point >= pf_points[i] )
> + {
> + return pf_values[i];
> + }
> + if( f_sample_point <= pf_points[0] )
> + {
> + return pf_values[0];
> + }
> +
> + /* Use binary search to find the matching data value or the region
> where
> + * the matching value is to be interpolated */
> + int i_low = 0;
> + int i_high = i - 1;
> + while( i_low <= i_high )
> + {
> + int i_mid = ( i_low + i_high ) >> 1;
> + float f_point_here = pf_points[i_mid];
> + if( f_point_here < f_sample_point )
> + {
> + i_low = i_mid + 1;
> + }
> + else if( f_point_here > f_sample_point )
> + {
> + i_high = i_mid - 1;
> + }
> + else
> + {
> + return pf_values[i_mid];
> + }
> + }
> + i = i_high > 0 ? i_high : 0;
> +
> + /* Interpolate */
> + float f_diff = f_sample_point - pf_points[i];
> + return pf_values[i] + f_diff * ( p_interpolant->pf_c1s[i]
> + + f_diff * ( p_interpolant->pf_c2s[i]
> + + f_diff * p_interpolant->pf_c3s[i] ) );
> +}
> +
> +void vlc_destroy_interpolant( vlc_interpolant_t * p_interpolant )
> +{
> + free( p_interpolant->pf_values );
> + free( p_interpolant->pf_points );
> + free( p_interpolant->pf_c3s );
> + free( p_interpolant->pf_c2s );
> + free( p_interpolant->pf_c1s );
> +}
--
Rémi Denis-Courmont
http://www.remlab.net/
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