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/**********************************************************************
Audacity: A Digital Audio Editor
Envelope.cpp
Dominic Mazzoni (original author)
Dr William Bland (integration - the Calculus kind)
Monty (xiphmont) (important bug fixes)
*******************************************************************//**
\class Envelope
\brief Piecewise linear or piecewise exponential function from double to double
This class manages an envelope - i.e. a function
that the user can edit by dragging control points around. The
envelope is most commonly used to control the amplitude of a
waveform, but it is also used to shape the Equalization curve, and in
TimeTrack to determine a time warp.
*//****************************************************************//**
\class EnvPoint
\brief EnvPoint, derived from XMLTagHandler, provides Envelope with
a draggable point type.
*//*******************************************************************/
#include "Envelope.h"
#include <math.h>
#include <wx/wxcrtvararg.h>
#include <wx/brush.h>
#include <wx/pen.h>
#include <wx/textfile.h>
#include <wx/log.h>
static const double VALUE_TOLERANCE = 0.001;
Envelope::Envelope(bool exponential, double minValue, double maxValue, double defaultValue)
: mDB(exponential)
, mMinValue(minValue)
, mMaxValue(maxValue)
, mDefaultValue { ClampValue(defaultValue) }
{
}
Envelope::~Envelope()
{
}
bool Envelope::ConsistencyCheck()
{
bool consistent = true;
bool disorder;
do {
disorder = false;
for ( size_t ii = 0, count = mEnv.size(); ii < count; ) {
// Find range of points with equal T
const double thisT = mEnv[ii].GetT();
double nextT = 0.0f;
auto nextI = ii + 1;
while ( nextI < count && thisT == ( nextT = mEnv[nextI].GetT() ) )
++nextI;
if ( nextI < count && nextT < thisT )
disorder = true;
while ( nextI - ii > 2 ) {
// too many coincident time values
if ((int)ii == mDragPoint || (int)nextI - 1 == mDragPoint)
// forgivable
;
else {
consistent = false;
// repair it
Delete( nextI - 2 );
if (mDragPoint >= (int)nextI - 2)
--mDragPoint;
--nextI, --count;
// wxLogError
}
}
ii = nextI;
}
if (disorder) {
consistent = false;
// repair it
std::stable_sort( mEnv.begin(), mEnv.end(),
[]( const EnvPoint &a, const EnvPoint &b )
{ return a.GetT() < b.GetT(); } );
}
} while ( disorder );
return consistent;
}
/// Rescale function for time tracks (could also be used for other tracks though).
/// This is used to load old time track project files where the envelope used a 0 to 1
/// range instead of storing the actual time track values. This function will change the range of the envelope
/// and rescale all envelope points accordingly (unlike SetRange, which clamps the envelope points to the NEW range).
/// @minValue - the NEW minimum value
/// @maxValue - the NEW maximum value
void Envelope::RescaleValues(double minValue, double maxValue)
{
double oldMinValue = mMinValue;
double oldMaxValue = mMaxValue;
mMinValue = minValue;
mMaxValue = maxValue;
// rescale the default value
double factor = (mDefaultValue - oldMinValue) / (oldMaxValue - oldMinValue);
mDefaultValue = ClampValue(mMinValue + (mMaxValue - mMinValue) * factor);
// rescale all points
for( unsigned int i = 0; i < mEnv.size(); i++ ) {
factor = (mEnv[i].GetVal() - oldMinValue) / (oldMaxValue - oldMinValue);
mEnv[i].SetVal( this, mMinValue + (mMaxValue - mMinValue) * factor );
}
}
/// Flatten removes all points from the envelope to
/// make it horizontal at a chosen y-value.
/// @value - the y-value for the flat envelope.
void Envelope::Flatten(double value)
{
mEnv.clear();
mDefaultValue = ClampValue(value);
}
void Envelope::SetDragPoint(int dragPoint)
{
mDragPoint = std::max(-1, std::min(int(mEnv.size() - 1), dragPoint));
mDragPointValid = (mDragPoint >= 0);
}
void Envelope::SetDragPointValid(bool valid)
{
mDragPointValid = (valid && mDragPoint >= 0);
if (mDragPoint >= 0 && !valid) {
// We're going to be deleting the point; On
// screen we show this by having the envelope move to
// the position it will have after deletion of the point.
// Without deleting the point we move it left or right
// to the same position as the previous or next point.
static const double big = std::numeric_limits<double>::max();
auto size = mEnv.size();
if( size <= 1) {
// There is only one point - just move it
// off screen and at default height.
// temporary state when dragging only!
mEnv[mDragPoint].SetT(big);
mEnv[mDragPoint].SetVal( this, mDefaultValue );
return;
}
else if ( mDragPoint + 1 == (int)size ) {
// Put the point at the height of the last point, but also off screen.
mEnv[mDragPoint].SetT(big);
mEnv[mDragPoint].SetVal( this, mEnv[ size - 1 ].GetVal() );
}
else {
// Place it exactly on its right neighbour.
// That way the drawing code will overpaint the dark dot with
// a light dot, as if it were deleted.
const auto &neighbor = mEnv[mDragPoint + 1];
mEnv[mDragPoint].SetT(neighbor.GetT());
mEnv[mDragPoint].SetVal( this, neighbor.GetVal() );
}
}
}
void Envelope::MoveDragPoint(double newWhen, double value)
{
SetDragPointValid(true);
if (!mDragPointValid)
return;
// We'll limit the drag point time to be between those of the preceding
// and next envelope point.
double limitLo = 0.0;
double limitHi = mTrackLen;
if (mDragPoint > 0)
limitLo = std::max(limitLo, mEnv[mDragPoint - 1].GetT());
if (mDragPoint + 1 < (int)mEnv.size())
limitHi = std::min(limitHi, mEnv[mDragPoint + 1].GetT());
EnvPoint &dragPoint = mEnv[mDragPoint];
const double tt =
std::max(limitLo, std::min(limitHi, newWhen));
// This might temporary violate the constraint that at most two
// points share a time value.
dragPoint.SetT(tt);
dragPoint.SetVal( this, value );
}
void Envelope::ClearDragPoint()
{
if (!mDragPointValid && mDragPoint >= 0)
Delete(mDragPoint);
mDragPoint = -1;
mDragPointValid = false;
}
void Envelope::SetRange(double minValue, double maxValue) {
mMinValue = minValue;
mMaxValue = maxValue;
mDefaultValue = ClampValue(mDefaultValue);
for( unsigned int i = 0; i < mEnv.size(); i++ )
mEnv[i].SetVal( this, mEnv[i].GetVal() ); // this clamps the value to the NEW range
}
// This is used only during construction of an Envelope by complete or partial
// copy of another, or when truncating a track.
void Envelope::AddPointAtEnd( double t, double val )
{
mEnv.push_back( EnvPoint{ t, val } );
// Assume copied points were stored by nondecreasing time.
// Allow no more than two points at exactly the same time.
// Maybe that happened, because extra points were inserted at the boundary
// of the copied range, which were not in the source envelope.
auto nn = mEnv.size() - 1;
while ( nn >= 2 && mEnv[ nn - 2 ].GetT() == t ) {
// Of three or more points at the same time, erase one in the middle,
// not the one newly added.
mEnv.erase( mEnv.begin() + nn - 1 );
--nn;
}
}
Envelope::Envelope(const Envelope &orig, double t0, double t1)
: mDB(orig.mDB)
, mMinValue(orig.mMinValue)
, mMaxValue(orig.mMaxValue)
, mDefaultValue(orig.mDefaultValue)
{
mOffset = wxMax(t0, orig.mOffset);
mTrackLen = wxMin(t1, orig.mOffset + orig.mTrackLen) - mOffset;
auto range1 = orig.EqualRange( t0 - orig.mOffset, 0 );
auto range2 = orig.EqualRange( t1 - orig.mOffset, 0 );
CopyRange(orig, range1.first, range2.second);
}
Envelope::Envelope(const Envelope &orig)
: mDB(orig.mDB)
, mMinValue(orig.mMinValue)
, mMaxValue(orig.mMaxValue)
, mDefaultValue(orig.mDefaultValue)
{
mOffset = orig.mOffset;
mTrackLen = orig.mTrackLen;
CopyRange(orig, 0, orig.GetNumberOfPoints());
}
void Envelope::CopyRange(const Envelope &orig, size_t begin, size_t end)
{
size_t len = orig.mEnv.size();
size_t i = begin;
// Create the point at 0 if it needs interpolated representation
if ( i > 0 )
AddPointAtEnd(0, orig.GetValue(mOffset));
// Copy points from inside the copied region
for (; i < end; ++i) {
const EnvPoint &point = orig[i];
const double when = point.GetT() + (orig.mOffset - mOffset);
AddPointAtEnd(when, point.GetVal());
}
// Create the final point if it needs interpolated representation
// If the last point of e was exactly at t1, this effectively copies it too.
if (mTrackLen > 0 && i < len)
AddPointAtEnd( mTrackLen, orig.GetValue(mOffset + mTrackLen));
}
#if 0
/// Limit() limits a double value to a range.
/// TODO: Move to a general utilities source file.
static double Limit( double Lo, double Value, double Hi )
{
if( Value < Lo )
return Lo;
if( Value > Hi )
return Hi;
return Value;
}
#endif
bool Envelope::HandleXMLTag(const wxChar *tag, const wxChar **attrs)
{
// Return unless it's the envelope tag.
if (wxStrcmp(tag, wxT("envelope")))
return false;
int numPoints = 0;
long nValue = -1;
while (*attrs) {
const wxChar *attr = *attrs++;
const wxChar *value = *attrs++;
if (!value)
break;
const wxString strValue = value;
if( !wxStrcmp(attr, wxT("numpoints")) &&
XMLValueChecker::IsGoodInt(strValue) && strValue.ToLong(&nValue))
numPoints = nValue;
}
if (numPoints < 0)
return false;
mEnv.clear();
mEnv.reserve(numPoints);
return true;
}
XMLTagHandler *Envelope::HandleXMLChild(const wxChar *tag)
{
if (wxStrcmp(tag, wxT("controlpoint")))
return NULL;
mEnv.push_back( EnvPoint{} );
return &mEnv.back();
}
void Envelope::WriteXML(XMLWriter &xmlFile) const
// may throw
{
unsigned int ctrlPt;
xmlFile.StartTag(wxT("envelope"));
xmlFile.WriteAttr(wxT("numpoints"), mEnv.size());
for (ctrlPt = 0; ctrlPt < mEnv.size(); ctrlPt++) {
const EnvPoint &point = mEnv[ctrlPt];
xmlFile.StartTag(wxT("controlpoint"));
xmlFile.WriteAttr(wxT("t"), point.GetT(), 12);
xmlFile.WriteAttr(wxT("val"), point.GetVal(), 12);
xmlFile.EndTag(wxT("controlpoint"));
}
xmlFile.EndTag(wxT("envelope"));
}
void Envelope::Delete( int point )
{
mEnv.erase(mEnv.begin() + point);
}
void Envelope::Insert(int point, const EnvPoint &p)
{
mEnv.insert(mEnv.begin() + point, p);
}
void Envelope::Insert(double when, double value)
{
mEnv.push_back( EnvPoint{ when, value });
}
/*! @excsafety{No-fail} */
void Envelope::CollapseRegion( double t0, double t1, double sampleDur )
{
if ( t1 <= t0 )
return;
// This gets called when somebody clears samples.
// Snip points in the interval (t0, t1), shift values left at times after t1.
// For the boundaries of the interval, preserve the left-side limit at the
// start and right-side limit at the end.
const auto epsilon = sampleDur / 2;
t0 = std::max( 0.0, std::min( mTrackLen, t0 - mOffset ) );
t1 = std::max( 0.0, std::min( mTrackLen, t1 - mOffset ) );
bool leftPoint = true, rightPoint = true;
// Determine the start of the range of points to remove from the array.
auto range0 = EqualRange( t0, 0 );
auto begin = range0.first;
if ( begin == range0.second ) {
if ( t0 > epsilon ) {
// There was no point exactly at t0;
// insert a point to preserve the value.
auto val = GetValueRelative( t0 );
InsertOrReplaceRelative( t0, val );
++begin;
}
else
leftPoint = false;
}
else
// We will keep the first (or only) point that was at t0.
++begin;
// We want end to be the index one past the range of points to remove from
// the array.
// At first, find index of the first point after t1:
auto range1 = EqualRange( t1, 0 );
auto end = range1.second;
if ( range1.first == end ) {
if ( mTrackLen - t1 > epsilon ) {
// There was no point exactly at t1; insert a point to preserve the value.
auto val = GetValueRelative( t1 );
InsertOrReplaceRelative( t1, val );
// end is now the index of this NEW point and that is correct.
}
else
rightPoint = false;
}
else
// We will keep the last (or only) point that was at t1.
--end;
if ( end < begin ) {
if ( leftPoint )
rightPoint = false;
}
else
mEnv.erase( mEnv.begin() + begin, mEnv.begin() + end );
// Shift points left after deleted region.
auto len = mEnv.size();
for ( size_t i = begin; i < len; ++i ) {
auto &point = mEnv[i];
if (rightPoint && (int)i == begin)
// Avoid roundoff error.
// Make exactly equal times of neighboring points so that we have
// a real discontinuity.
point.SetT( t0 );
else
point.SetT( point.GetT() - (t1 - t0) );
}
// See if the discontinuity is removable.
if ( rightPoint )
RemoveUnneededPoints( begin, true );
if ( leftPoint )
RemoveUnneededPoints( begin - 1, false );
mTrackLen -= ( t1 - t0 );
}
// This operation is trickier than it looks; the basic rub is that
// a track's envelope runs the range from t=0 to t=tracklen; the t=0
// envelope point applies to the first sample, but the t=tracklen
// envelope point applies one-past the last actual sample.
// t0 should be in the domain of this; if not, it is trimmed.
/*! @excsafety{No-fail} */
void Envelope::PasteEnvelope( double t0, const Envelope *e, double sampleDur )
{
const bool wasEmpty = (this->mEnv.size() == 0);
auto otherSize = e->mEnv.size();
const double otherDur = e->mTrackLen;
const auto otherOffset = e->mOffset;
const auto deltat = otherOffset + otherDur;
if ( otherSize == 0 && wasEmpty && e->mDefaultValue == this->mDefaultValue )
{
// msmeyer: The envelope is empty and has the same default value, so
// there is nothing that must be inserted, just return. This avoids
// the creation of unnecessary duplicate control points
// MJS: but the envelope does get longer
// PRL: Assuming t0 is in the domain of the envelope
mTrackLen += deltat;
return;
}
// Make t0 relative to the offset of the envelope we are pasting into,
// and trim it to the domain of this
t0 = std::min( mTrackLen, std::max( 0.0, t0 - mOffset ) );
// Adjust if the insertion point rounds off near a discontinuity in this
if ( true )
{
double newT0;
auto range = EqualRange( t0, sampleDur );
auto index = range.first;
if ( index + 2 == range.second &&
( newT0 = mEnv[ index ].GetT() ) == mEnv[ 1 + index ].GetT() )
t0 = newT0;
}
// Open up a space
double leftVal = e->GetValue( 0 );
double rightVal = e->GetValueRelative( otherDur );
// This range includes the right-side limit of the left end of the space,
// and the left-side limit of the right end:
const auto range = ExpandRegion( t0, deltat, &leftVal, &rightVal );
// Where to put the copied points from e -- after the first of the
// two points in range:
auto insertAt = range.first + 1;
// Copy points from e -- maybe skipping those at the extremes
auto end = e->mEnv.end();
if ( otherSize != 0 && e->mEnv[ otherSize - 1 ].GetT() == otherDur )
// ExpandRegion already made an equivalent limit point
--end, --otherSize;
auto begin = e->mEnv.begin();
if ( otherSize != 0 && otherOffset == 0.0 && e->mEnv[ 0 ].GetT() == 0.0 )
++begin, --otherSize;
mEnv.insert( mEnv.begin() + insertAt, begin, end );
// Adjust their times
for ( size_t index = insertAt, last = insertAt + otherSize;
index < last; ++index ) {
auto &point = mEnv[ index ];
// The mOffset of the envelope-pasted-from is irrelevant.
// The GetT() times in it are relative to its start.
// The new GetT() times are relative to the envelope-pasted-to start.
// We are pasting at t0 relative to the envelope-pasted-to start.
// Hence we adjust by just t0.
// Bug 1844 was that we also adjusted by the envelope-pasted-from offset.
point.SetT( point.GetT() + /*otherOffset +*/ t0 );
}
// Treat removable discontinuities
// Right edge outward:
RemoveUnneededPoints( insertAt + otherSize + 1, true );
// Right edge inward:
RemoveUnneededPoints( insertAt + otherSize, false, false );
// Left edge inward:
RemoveUnneededPoints( range.first, true, false );
// Left edge outward:
RemoveUnneededPoints( range.first - 1, false );
// Guarantee monotonicity of times, against little round-off mistakes perhaps
ConsistencyCheck();
}
/*! @excsafety{No-fail} */
void Envelope::RemoveUnneededPoints
( size_t startAt, bool rightward, bool testNeighbors )
{
// startAt is the index of a recently inserted point which might make no
// difference in envelope evaluation, or else might cause nearby points to
// make no difference.
auto isDiscontinuity = [this]( size_t index ) {
// Assume array accesses are in-bounds
const EnvPoint &point1 = mEnv[ index ];
const EnvPoint &point2 = mEnv[ index + 1 ];
return point1.GetT() == point2.GetT() &&
fabs( point1.GetVal() - point2.GetVal() ) > VALUE_TOLERANCE;
};
auto remove = [this]( size_t index, bool leftLimit ) {
// Assume array accesses are in-bounds
const auto &point = mEnv[ index ];
auto when = point.GetT();
auto val = point.GetVal();
Delete( index ); // try it to see if it's doing anything
auto val1 = GetValueRelative ( when, leftLimit );
if( fabs( val - val1 ) > VALUE_TOLERANCE ) {
// put it back, we needed it
Insert( index, EnvPoint{ when, val } );
return false;
}
else
return true;
};
auto len = mEnv.size();
bool leftLimit =
!rightward && startAt + 1 < len && isDiscontinuity( startAt );
bool removed = remove( startAt, leftLimit );
if ( removed )
// The given point was removable. Done!
return;
if ( !testNeighbors )
return;
// The given point was not removable. But did its insertion make nearby
// points removable?
int index = startAt + ( rightward ? 1 : -1 );
while ( index >= 0 && index < (int)len ) {
// Stop at any discontinuity
if ( index > 0 && isDiscontinuity( index - 1 ) )
break;
if ( (index + 1) < (int)len && isDiscontinuity( index ) )
break;
if ( ! remove( index, false ) )
break;
--len;
if ( ! rightward )
--index;
}
}
/*! @excsafety{No-fail} */
std::pair< int, int > Envelope::ExpandRegion
( double t0, double tlen, double *pLeftVal, double *pRightVal )
{
// t0 is relative time
double val = GetValueRelative( t0 );
const auto range = EqualRange( t0, 0 );
// Preserve the left-side limit.
int index = 1 + range.first;
if ( index <= range.second )
// There is already a control point.
;
else {
// Make a control point.
Insert( range.first, EnvPoint{ t0, val } );
}
// Shift points.
auto len = mEnv.size();
for ( unsigned int ii = index; ii < len; ++ii ) {
auto &point = mEnv[ ii ];
point.SetT( point.GetT() + tlen );
}
mTrackLen += tlen;
// Preserve the right-side limit.
if ( index < range.second )
// There was a control point already.
;
else
// Make a control point.
Insert( index, EnvPoint{ t0 + tlen, val } );
// Make discontinuities at ends, maybe:
if ( pLeftVal )
// Make a discontinuity at the left side of the expansion
Insert( index++, EnvPoint{ t0, *pLeftVal } );
if ( pRightVal )
// Make a discontinuity at the right side of the expansion
Insert( index++, EnvPoint{ t0 + tlen, *pRightVal } );
// Return the range of indices that includes the inside limiting points,
// none, one, or two
return { 1 + range.first, index };
}
/*! @excsafety{No-fail} */
void Envelope::InsertSpace( double t0, double tlen )
{
auto range = ExpandRegion( t0 - mOffset, tlen, nullptr, nullptr );
// Simplify the boundaries if possible
RemoveUnneededPoints( range.second, true );
RemoveUnneededPoints( range.first - 1, false );
}
int Envelope::Reassign(double when, double value)
{
when -= mOffset;
int len = mEnv.size();
if (len == 0)
return -1;
int i = 0;
while (i < len && when > mEnv[i].GetT())
i++;
if (i >= len || when < mEnv[i].GetT())
return -1;
mEnv[i].SetVal( this, value );
return 0;
}
size_t Envelope::GetNumberOfPoints() const
{
return mEnv.size();
}
void Envelope::GetPoints(double *bufferWhen,
double *bufferValue,
int bufferLen) const
{
int n = mEnv.size();
if (n > bufferLen)
n = bufferLen;
int i;
for (i = 0; i < n; i++) {
bufferWhen[i] = mEnv[i].GetT() - mOffset;
bufferValue[i] = mEnv[i].GetVal();
}
}
void Envelope::Cap( double sampleDur )
{
auto range = EqualRange( mTrackLen, sampleDur );
if ( range.first == range.second )
InsertOrReplaceRelative( mTrackLen, GetValueRelative( mTrackLen ) );
}
// Private methods
/** @brief Add a control point to the envelope
*
* @param when the time in seconds when the envelope point should be created.
* @param value the envelope value to use at the given point.
* @return the index of the NEW envelope point within array of envelope points.
*/
int Envelope::InsertOrReplaceRelative(double when, double value)
{
#if defined(_DEBUG)
// in debug builds, do a spot of argument checking
if(when > mTrackLen + 0.0000001)
{
wxString msg;
msg = wxString::Format(wxT("when %.20f mTrackLen %.20f diff %.20f"), when, mTrackLen, when-mTrackLen);
wxASSERT_MSG(when <= (mTrackLen), msg);
}
if(when < 0)
{
wxString msg;
msg = wxString::Format(wxT("when %.20f mTrackLen %.20f"), when, mTrackLen);
wxASSERT_MSG(when >= 0, msg);
}
#endif
when = std::max( 0.0, std::min( mTrackLen, when ) );
auto range = EqualRange( when, 0 );
int index = range.first;
if ( index < range.second )
// modify existing
// In case of a discontinuity, ALWAYS CHANGING LEFT LIMIT ONLY!
mEnv[ index ].SetVal( this, value );
else
// Add NEW
Insert( index, EnvPoint { when, value } );
return index;
}
std::pair<int, int> Envelope::EqualRange( double when, double sampleDur ) const
{
// Find range of envelope points matching the given time coordinate
// (within an interval of length sampleDur)
// by binary search; if empty, it still indicates where to
// insert.
const auto tolerance = sampleDur / 2;
auto begin = mEnv.begin();
auto end = mEnv.end();
auto first = std::lower_bound(
begin, end,
EnvPoint{ when - tolerance, 0.0 },
[]( const EnvPoint &point1, const EnvPoint &point2 )
{ return point1.GetT() < point2.GetT(); }
);
auto after = first;
while ( after != end && after->GetT() <= when + tolerance )
++after;
return { first - begin, after - begin };
}
// Control
/*! @excsafety{No-fail} */
void Envelope::SetOffset(double newOffset)
{
mOffset = newOffset;
}
/*! @excsafety{No-fail} */
void Envelope::SetTrackLen( double trackLen, double sampleDur )
{
// Preserve the left-side limit at trackLen.
auto range = EqualRange( trackLen, sampleDur );
bool needPoint = ( range.first == range.second && trackLen < mTrackLen );
double value=0.0;
if ( needPoint )
value = GetValueRelative( trackLen );
mTrackLen = trackLen;
// Shrink the array.
// If more than one point already at the end, keep only the first of them.
int newLen = std::min( 1 + range.first, range.second );
mEnv.resize( newLen );
if ( needPoint )
AddPointAtEnd( mTrackLen, value );
}
/*! @excsafety{No-fail} */
void Envelope::RescaleTimes( double newLength )
{
if ( mTrackLen == 0 ) {
for ( auto &point : mEnv )
point.SetT( 0 );
}
else {
auto ratio = newLength / mTrackLen;
for ( auto &point : mEnv )
point.SetT( point.GetT() * ratio );
}
mTrackLen = newLength;
}
// Accessors
double Envelope::GetValue( double t, double sampleDur ) const
{
// t is absolute time
double temp;
GetValues( &temp, 1, t, sampleDur );
return temp;
}
double Envelope::GetValueRelative(double t, bool leftLimit) const
{
double temp;
GetValuesRelative(&temp, 1, t, 0.0, leftLimit);
return temp;
}
// relative time
/// @param Lo returns last index at or before this time, maybe -1
/// @param Hi returns first index after this time, maybe past the end
void Envelope::BinarySearchForTime( int &Lo, int &Hi, double t ) const
{
// Optimizations for the usual pattern of repeated calls with
// small increases of t.
{
if (mSearchGuess >= 0 && mSearchGuess < (int)mEnv.size()) {
if (t >= mEnv[mSearchGuess].GetT() &&
(1 + mSearchGuess == (int)mEnv.size() ||
t < mEnv[1 + mSearchGuess].GetT())) {
Lo = mSearchGuess;
Hi = 1 + mSearchGuess;
return;
}
}
++mSearchGuess;
if (mSearchGuess >= 0 && mSearchGuess < (int)mEnv.size()) {
if (t >= mEnv[mSearchGuess].GetT() &&
(1 + mSearchGuess == (int)mEnv.size() ||
t < mEnv[1 + mSearchGuess].GetT())) {
Lo = mSearchGuess;
Hi = 1 + mSearchGuess;
return;
}
}
}
Lo = -1;
Hi = mEnv.size();
// Invariants: Lo is not less than -1, Hi not more than size
while (Hi > (Lo + 1)) {
int mid = (Lo + Hi) / 2;
// mid must be strictly between Lo and Hi, therefore a valid index
if (t < mEnv[mid].GetT())
Hi = mid;
else
Lo = mid;
}
wxASSERT( Hi == ( Lo+1 ));
mSearchGuess = Lo;
}
// relative time
/// @param Lo returns last index before this time, maybe -1
/// @param Hi returns first index at or after this time, maybe past the end
void Envelope::BinarySearchForTime_LeftLimit( int &Lo, int &Hi, double t ) const
{
Lo = -1;
Hi = mEnv.size();
// Invariants: Lo is not less than -1, Hi not more than size
while (Hi > (Lo + 1)) {
int mid = (Lo + Hi) / 2;
// mid must be strictly between Lo and Hi, therefore a valid index
if (t <= mEnv[mid].GetT())
Hi = mid;
else
Lo = mid;
}
wxASSERT( Hi == ( Lo+1 ));
mSearchGuess = Lo;
}
/// GetInterpolationStartValueAtPoint() is used to select either the
/// envelope value or its log depending on whether we are doing linear
/// or log interpolation.
/// @param iPoint index in env array to look at.
/// @return value there, or its (safe) log10.
double Envelope::GetInterpolationStartValueAtPoint( int iPoint ) const
{
double v = mEnv[ iPoint ].GetVal();
if( !mDB )
return v;
else
return log10(v);
}
void Envelope::GetValues( double *buffer, int bufferLen,
double t0, double tstep ) const
{
// Convert t0 from absolute to clip-relative time
t0 -= mOffset;
GetValuesRelative( buffer, bufferLen, t0, tstep);
}
void Envelope::GetValuesRelative
(double *buffer, int bufferLen, double t0, double tstep, bool leftLimit)
const
{
// JC: If bufferLen ==0 we have probably just allocated a zero sized buffer.
// wxASSERT( bufferLen > 0 );
const auto epsilon = tstep / 2;
int len = mEnv.size();
double t = t0;
double increment = 0;
if ( len > 1 && t <= mEnv[0].GetT() && mEnv[0].GetT() == mEnv[1].GetT() )
increment = leftLimit ? -epsilon : epsilon;
double tprev, vprev, tnext = 0, vnext, vstep = 0;
for (int b = 0; b < bufferLen; b++) {
// Get easiest cases out the way first...
// IF empty envelope THEN default value
if (len <= 0) {
buffer[b] = mDefaultValue;
t += tstep;
continue;
}
auto tplus = t + increment;
// IF before envelope THEN first value
if ( leftLimit ? tplus <= mEnv[0].GetT() : tplus < mEnv[0].GetT() ) {
buffer[b] = mEnv[0].GetVal();
t += tstep;
continue;
}
// IF after envelope THEN last value
if ( leftLimit
? tplus > mEnv[len - 1].GetT() : tplus >= mEnv[len - 1].GetT() ) {
buffer[b] = mEnv[len - 1].GetVal();
t += tstep;
continue;
}
// be careful to get the correct limit even in case epsilon == 0
if ( b == 0 ||
( leftLimit ? tplus > tnext : tplus >= tnext ) ) {
// We're beyond our tnext, so find the next one.
// Don't just increment lo or hi because we might
// be zoomed far out and that could be a large number of
// points to move over. That's why we binary search.
int lo,hi;
if ( leftLimit )
BinarySearchForTime_LeftLimit( lo, hi, tplus );
else
BinarySearchForTime( lo, hi, tplus );
// mEnv[0] is before tplus because of eliminations above, therefore lo >= 0
// mEnv[len - 1] is after tplus, therefore hi <= len - 1
wxASSERT( lo >= 0 && hi <= len - 1 );
tprev = mEnv[lo].GetT();
tnext = mEnv[hi].GetT();
if ( hi + 1 < len && tnext == mEnv[ hi + 1 ].GetT() )
// There is a discontinuity after this point-to-point interval.
// Usually will stop evaluating in this interval when time is slightly
// before tNext, then use the right limit.
// This is the right intent
// in case small roundoff errors cause a sample time to be a little
// before the envelope point time.
// Less commonly we want a left limit, so we continue evaluating in
// this interval until shortly after the discontinuity.
increment = leftLimit ? -epsilon : epsilon;
else
increment = 0;
vprev = GetInterpolationStartValueAtPoint( lo );
vnext = GetInterpolationStartValueAtPoint( hi );
// Interpolate, either linear or log depending on mDB.
double dt = (tnext - tprev);
double to = t - tprev;
double v;
if (dt > 0.0)
{
v = (vprev * (dt - to) + vnext * to) / dt;
vstep = (vnext - vprev) * tstep / dt;
}
else
{
v = vnext;
vstep = 0.0;
}
// An adjustment if logarithmic scale.
if( mDB )
{
v = pow(10.0, v);
vstep = pow( 10.0, vstep );
}
buffer[b] = v;
} else {
if (mDB){
buffer[b] = buffer[b - 1] * vstep;
}else{
buffer[b] = buffer[b - 1] + vstep;
}
}
t += tstep;
}
}
// relative time
int Envelope::NumberOfPointsAfter(double t) const
{
int lo,hi;
BinarySearchForTime( lo, hi, t );
return mEnv.size() - hi;
}
// relative time
double Envelope::NextPointAfter(double t) const
{
int lo,hi;
BinarySearchForTime( lo, hi, t );
if (hi >= (int)mEnv.size())
return t;
else
return mEnv[hi].GetT();
}
double Envelope::Average( double t0, double t1 ) const
{
if( t0 == t1 )
return GetValue( t0 );
else
return Integral( t0, t1 ) / (t1 - t0);
}
double Envelope::AverageOfInverse( double t0, double t1 ) const
{
if( t0 == t1 )
return 1.0 / GetValue( t0 );
else
return IntegralOfInverse( t0, t1 ) / (t1 - t0);
}
//
// Integration and debugging functions
//
// The functions below are used by the TimeTrack and possibly for
// other debugging. They do not affect normal amplitude envelopes
// for waveforms, nor frequency envelopes for equalization.
// The 'Average' function also uses 'Integral'.
//
// A few helper functions to make the code below more readable.
static double InterpolatePoints(double y1, double y2, double factor, bool logarithmic)
{
if(logarithmic)
// you can use any base you want, it doesn't change the result
return exp(log(y1) * (1.0 - factor) + log(y2) * factor);
else
return y1 * (1.0 - factor) + y2 * factor;
}
static double IntegrateInterpolated(double y1, double y2, double time, bool logarithmic)
{
// Calculates: integral(interpolate(y1, y2, x), x = 0 .. time)
// Integrating logarithmic interpolated segments is surprisingly simple. You can check this formula here:
// http://www.wolframalpha.com/input/?i=integrate+10%5E%28log10%28y1%29*%28T-x%29%2FT%2Blog10%28y2%29*x%2FT%29+from+0+to+T
// Again, the base you use for interpolation is irrelevant, the formula below should always use the natural
// logarithm (i.e. 'log' in C/C++). If the denominator is too small, it's better to use linear interpolation
// because the rounding errors would otherwise get too large. The threshold value is 1.0e-5 because at that
// point the rounding errors become larger than the difference between linear and logarithmic (I tested this in Octave).
if(logarithmic)
{
double l = log(y1 / y2);
if(fabs(l) < 1.0e-5) // fall back to linear interpolation
return (y1 + y2) * 0.5 * time;
return (y1 - y2) / l * time;
}
else
{
return (y1 + y2) * 0.5 * time;
}
}
static double IntegrateInverseInterpolated(double y1, double y2, double time, bool logarithmic)
{
// Calculates: integral(1 / interpolate(y1, y2, x), x = 0 .. time)
// This one is a bit harder. Linear:
// http://www.wolframalpha.com/input/?i=integrate+1%2F%28y1*%28T-x%29%2FT%2By2*x%2FT%29+from+0+to+T
// Logarithmic:
// http://www.wolframalpha.com/input/?i=integrate+1%2F%2810%5E%28log10%28y1%29*%28T-x%29%2FT%2Blog10%28y2%29*x%2FT%29%29+from+0+to+T
// Here both cases need a special case for y1 == y2. The threshold is 1.0e5 again, this is still the
// best value in both cases.
double l = log(y1 / y2);
if(fabs(l) < 1.0e-5) // fall back to average
return 2.0 / (y1 + y2) * time;
if(logarithmic)
return (y1 - y2) / (l * y1 * y2) * time;
else
return l / (y1 - y2) * time;
}
static double SolveIntegrateInverseInterpolated(double y1, double y2, double time, double area, bool logarithmic)
{
// Calculates: solve (integral(1 / interpolate(y1, y2, x), x = 0 .. res) = area) for res
// Don't try to derive these formulas by hand :). The threshold is 1.0e5 again.
double a = area / time, res;
if(logarithmic)
{
double l = log(y1 / y2);
if(fabs(l) < 1.0e-5) // fall back to average
res = a * (y1 + y2) * 0.5;
else if(1.0 + a * y1 * l <= 0.0)
res = 1.0;
else
res = log1p(a * y1 * l) / l;
}
else
{
if(fabs(y2 - y1) < 1.0e-5) // fall back to average
res = a * (y1 + y2) * 0.5;
else
res = y1 * expm1(a * (y2 - y1)) / (y2 - y1);
}
return std::max(0.0, std::min(1.0, res)) * time;
}
// We should be able to write a very efficient memoizer for this
// but make sure it gets reset when the envelope is changed.
double Envelope::Integral( double t0, double t1 ) const
{
if(t0 == t1)
return 0.0;
if(t0 > t1)
{
return -Integral(t1, t0); // this makes more sense than returning the default value
}
unsigned int count = mEnv.size();
if(count == 0) // 'empty' envelope
return (t1 - t0) * mDefaultValue;
t0 -= mOffset;
t1 -= mOffset;
double total = 0.0, lastT, lastVal;
unsigned int i; // this is the next point to check
if(t0 < mEnv[0].GetT()) // t0 preceding the first point
{
if(t1 <= mEnv[0].GetT())
return (t1 - t0) * mEnv[0].GetVal();
i = 1;
lastT = mEnv[0].GetT();
lastVal = mEnv[0].GetVal();
total += (lastT - t0) * lastVal;
}
else if(t0 >= mEnv[count - 1].GetT()) // t0 at or following the last point
{
return (t1 - t0) * mEnv[count - 1].GetVal();
}
else // t0 enclosed by points
{
// Skip any points that come before t0 using binary search
int lo, hi;
BinarySearchForTime(lo, hi, t0);
lastVal = InterpolatePoints(mEnv[lo].GetVal(), mEnv[hi].GetVal(), (t0 - mEnv[lo].GetT()) / (mEnv[hi].GetT() - mEnv[lo].GetT()), mDB);
lastT = t0;
i = hi; // the point immediately after t0.
}
// loop through the rest of the envelope points until we get to t1
while (1)
{
if(i >= count) // the requested range extends beyond the last point
{
return total + (t1 - lastT) * lastVal;
}
else if(mEnv[i].GetT() >= t1) // this point follows the end of the range
{
double thisVal = InterpolatePoints(mEnv[i - 1].GetVal(), mEnv[i].GetVal(), (t1 - mEnv[i - 1].GetT()) / (mEnv[i].GetT() - mEnv[i - 1].GetT()), mDB);
return total + IntegrateInterpolated(lastVal, thisVal, t1 - lastT, mDB);
}
else // this point precedes the end of the range
{
total += IntegrateInterpolated(lastVal, mEnv[i].GetVal(), mEnv[i].GetT() - lastT, mDB);
lastT = mEnv[i].GetT();
lastVal = mEnv[i].GetVal();
i++;
}
}
}
double Envelope::IntegralOfInverse( double t0, double t1 ) const
{
if(t0 == t1)
return 0.0;
if(t0 > t1)
{
return -IntegralOfInverse(t1, t0); // this makes more sense than returning the default value
}
unsigned int count = mEnv.size();
if(count == 0) // 'empty' envelope
return (t1 - t0) / mDefaultValue;
t0 -= mOffset;
t1 -= mOffset;
double total = 0.0, lastT, lastVal;
unsigned int i; // this is the next point to check
if(t0 < mEnv[0].GetT()) // t0 preceding the first point
{
if(t1 <= mEnv[0].GetT())
return (t1 - t0) / mEnv[0].GetVal();
i = 1;
lastT = mEnv[0].GetT();
lastVal = mEnv[0].GetVal();
total += (lastT - t0) / lastVal;
}
else if(t0 >= mEnv[count - 1].GetT()) // t0 at or following the last point
{
return (t1 - t0) / mEnv[count - 1].GetVal();
}
else // t0 enclosed by points
{
// Skip any points that come before t0 using binary search
int lo, hi;
BinarySearchForTime(lo, hi, t0);
lastVal = InterpolatePoints(mEnv[lo].GetVal(), mEnv[hi].GetVal(), (t0 - mEnv[lo].GetT()) / (mEnv[hi].GetT() - mEnv[lo].GetT()), mDB);
lastT = t0;
i = hi; // the point immediately after t0.
}
// loop through the rest of the envelope points until we get to t1
while (1)
{
if(i >= count) // the requested range extends beyond the last point
{
return total + (t1 - lastT) / lastVal;
}
else if(mEnv[i].GetT() >= t1) // this point follows the end of the range
{
double thisVal = InterpolatePoints(mEnv[i - 1].GetVal(), mEnv[i].GetVal(), (t1 - mEnv[i - 1].GetT()) / (mEnv[i].GetT() - mEnv[i - 1].GetT()), mDB);
return total + IntegrateInverseInterpolated(lastVal, thisVal, t1 - lastT, mDB);
}
else // this point precedes the end of the range
{
total += IntegrateInverseInterpolated(lastVal, mEnv[i].GetVal(), mEnv[i].GetT() - lastT, mDB);
lastT = mEnv[i].GetT();
lastVal = mEnv[i].GetVal();
i++;
}
}
}
double Envelope::SolveIntegralOfInverse( double t0, double area ) const
{
if(area == 0.0)
return t0;
const auto count = mEnv.size();
if(count == 0) // 'empty' envelope
return t0 + area * mDefaultValue;
// Correct for offset!
t0 -= mOffset;
return mOffset + [&] {
// Now we can safely assume t0 is relative time!
double lastT, lastVal;
int i; // this is the next point to check
if(t0 < mEnv[0].GetT()) // t0 preceding the first point
{
if (area < 0) {
return t0 + area * mEnv[0].GetVal();
}
else {
i = 1;
lastT = mEnv[0].GetT();
lastVal = mEnv[0].GetVal();
double added = (lastT - t0) / lastVal;
if(added >= area)
return t0 + area * mEnv[0].GetVal();
area -= added;
}
}
else if(t0 >= mEnv[count - 1].GetT()) // t0 at or following the last point
{
if (area < 0) {
i = (int)count - 2;
lastT = mEnv[count - 1].GetT();
lastVal = mEnv[count - 1].GetVal();
double added = (lastT - t0) / lastVal; // negative
if(added <= area)
return t0 + area * mEnv[count - 1].GetVal();
area -= added;
}
else {
return t0 + area * mEnv[count - 1].GetVal();
}
}
else // t0 enclosed by points
{
// Skip any points that come before t0 using binary search
int lo, hi;
BinarySearchForTime(lo, hi, t0);
lastVal = InterpolatePoints(mEnv[lo].GetVal(), mEnv[hi].GetVal(), (t0 - mEnv[lo].GetT()) / (mEnv[hi].GetT() - mEnv[lo].GetT()), mDB);
lastT = t0;
if (area < 0)
i = lo;
else
i = hi; // the point immediately after t0.
}
if (area < 0) {
// loop BACKWARDS through the rest of the envelope points until we get to t1
// (which is less than t0)
while (1)
{
if(i < 0) // the requested range extends beyond the leftmost point
{
return lastT + area * lastVal;
}
else
{
double added =
-IntegrateInverseInterpolated(mEnv[i].GetVal(), lastVal, lastT - mEnv[i].GetT(), mDB);
if(added <= area)
return lastT - SolveIntegrateInverseInterpolated(lastVal, mEnv[i].GetVal(), lastT - mEnv[i].GetT(), -area, mDB);
area -= added;
lastT = mEnv[i].GetT();
lastVal = mEnv[i].GetVal();
--i;
}
}
}
else {
// loop through the rest of the envelope points until we get to t1
while (1)
{
if(i >= (int)count) // the requested range extends beyond the last point
{
return lastT + area * lastVal;
}
else
{
double added = IntegrateInverseInterpolated(lastVal, mEnv[i].GetVal(), mEnv[i].GetT() - lastT, mDB);
if(added >= area)
return lastT + SolveIntegrateInverseInterpolated(lastVal, mEnv[i].GetVal(), mEnv[i].GetT() - lastT, area, mDB);
area -= added;
lastT = mEnv[i].GetT();
lastVal = mEnv[i].GetVal();
i++;
}
}
}
}();
}
void Envelope::print() const
{
for( unsigned int i = 0; i < mEnv.size(); i++ )
wxPrintf( "(%.2f, %.2f)\n", mEnv[i].GetT(), mEnv[i].GetVal() );
}
static void checkResult( int n, double a, double b )
{
if( (a-b > 0 ? a-b : b-a) > 0.0000001 )
{
wxPrintf( "Envelope: Result #%d is: %f, should be %f\n", n, a, b );
//exit( -1 );
}
}
void Envelope::testMe()
{
double t0=0, t1=0;
SetExponential(false);
Flatten(0.5);
checkResult( 1, Integral(0.0,100.0), 50);
checkResult( 2, Integral(-10.0,10.0), 10);
Flatten(0.5);
checkResult( 3, Integral(0.0,100.0), 50);
checkResult( 4, Integral(-10.0,10.0), 10);
checkResult( 5, Integral(-20.0,-10.0), 5);
Flatten(0.5);
InsertOrReplaceRelative( 5.0, 0.5 );
checkResult( 6, Integral(0.0,100.0), 50);
checkResult( 7, Integral(-10.0,10.0), 10);
Flatten(0.0);
InsertOrReplaceRelative( 0.0, 0.0 );
InsertOrReplaceRelative( 5.0, 1.0 );
InsertOrReplaceRelative( 10.0, 0.0 );
t0 = 10.0 - .1;
t1 = 10.0 + .1;
double result = Integral(0.0,t1);
double resulta = Integral(0.0,t0);
double resultb = Integral(t0,t1);
// Integrals should be additive
checkResult( 8, result - resulta - resultb, 0);
Flatten(0.0);
InsertOrReplaceRelative( 0.0, 0.0 );
InsertOrReplaceRelative( 5.0, 1.0 );
InsertOrReplaceRelative( 10.0, 0.0 );
t0 = 10.0 - .1;
t1 = 10.0 + .1;
checkResult( 9, Integral(0.0,t1), 5);
checkResult( 10, Integral(0.0,t0), 4.999);
checkResult( 11, Integral(t0,t1), .001);
mEnv.clear();
InsertOrReplaceRelative( 0.0, 0.0 );
InsertOrReplaceRelative( 5.0, 1.0 );
InsertOrReplaceRelative( 10.0, 0.0 );
checkResult( 12, NumberOfPointsAfter( -1 ), 3 );
checkResult( 13, NumberOfPointsAfter( 0 ), 2 );
checkResult( 14, NumberOfPointsAfter( 1 ), 2 );
checkResult( 15, NumberOfPointsAfter( 5 ), 1 );
checkResult( 16, NumberOfPointsAfter( 7 ), 1 );
checkResult( 17, NumberOfPointsAfter( 10 ), 0 );
checkResult( 18, NextPointAfter( 0 ), 5 );
checkResult( 19, NextPointAfter( 5 ), 10 );
}
#include "ZoomInfo.h"
void Envelope::GetValues
( const Envelope &env,
double alignedTime, double sampleDur,
double *buffer, int bufferLen, int leftOffset,
const ZoomInfo &zoomInfo )
{
// Getting many envelope values, corresponding to pixel columns, which may
// not be uniformly spaced in time when there is a fisheye.
double prevDiscreteTime=0.0, prevSampleVal=0.0, nextSampleVal=0.0;
for ( int xx = 0; xx < bufferLen; ++xx ) {
auto time = zoomInfo.PositionToTime( xx, -leftOffset );
if ( sampleDur <= 0 )
// Sample interval not defined (as for time track)
buffer[xx] = env.GetValue( time );
else {
// The level of zoom-in may resolve individual samples.
// If so, then instead of evaluating the envelope directly,
// we draw a piecewise curve with knees at each sample time.
// This actually makes clearer what happens as you drag envelope
// points and make discontinuities.
auto leftDiscreteTime = alignedTime +
sampleDur * floor( ( time - alignedTime ) / sampleDur );
if ( xx == 0 || leftDiscreteTime != prevDiscreteTime ) {
prevDiscreteTime = leftDiscreteTime;
prevSampleVal =
env.GetValue( prevDiscreteTime, sampleDur );
nextSampleVal =
env.GetValue( prevDiscreteTime + sampleDur, sampleDur );
}
auto ratio = ( time - leftDiscreteTime ) / sampleDur;
if ( env.GetExponential() )
buffer[ xx ] = exp(
( 1.0 - ratio ) * log( prevSampleVal )
+ ratio * log( nextSampleVal ) );
else
buffer[ xx ] =
( 1.0 - ratio ) * prevSampleVal + ratio * nextSampleVal;
}
}
}
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