[vlc-devel] [PATCH 2/6] Add monotone cubic interpolation support

Ronald Wright logiconcepts819 at gmail.com
Thu Jul 24 19:19:18 CEST 2014


---
 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;
+
+/*****************************************************************************
+ * Interpolation routines
+ *****************************************************************************/
+
+/*
+ * Create a new interpolant from the given data points and data point values.
+ */
+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;
+
+    /* 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 );
+}
-- 
1.9.1




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