// ---------------------------------------------------------------------------
// fixPhaseForward
//
//! Recompute phases of all Breakpoints on the closed range [pos, stopHere]
//! so that the synthesized phases of those Breakpoints matches
//! the stored phase, as long as the synthesized phase at pos
//! matches the stored (not recomputed) phase. The phase at pos
//! is modified only if pos is the position of a null Breakpoint
//! and the Breakpoint that follows is non-null.
//!
//! Phase fixing is only applied to non-null (nonzero-amplitude) Breakpoints,
//! because null Breakpoints are interpreted as phase reset points in
//! Loris. If a null is encountered, its phase is corrected from its non-Null
//! successor, if it has one, otherwise it is unmodified.
//!
//! \pre pos and stopHere are iterators on the same Partial, and
//! pos must be not later than stopHere.
//! \pre stopHere cannot be end of the Partial, it must be the postion
//! of a valid Breakpoint.
//! \param pos the position of the first Breakpoint whose phase might be
//! recomputed.
//! \param stopHere the position of the last Breakpoint whose phase might
//! be modified.
//
void fixPhaseForward( Partial::iterator pos, Partial::iterator stopHere )
{
while ( pos != stopHere )
{
Partial::iterator posPrev = pos++;
if ( NoNulls || BreakpointUtils::isNonNull( pos.breakpoint() ) )
{
// pos is the position of a non-Null Breakpoint
double travel = phaseTravel( posPrev, pos );
if ( NoNulls || BreakpointUtils::isNonNull( posPrev.breakpoint() ) )
{
// if its predecessor of pos is non-Null, then fix
// the phase of the Breakpoint at pos.
pos.breakpoint().setPhase( wrapPi( posPrev.breakpoint().phase() + travel ) );
}
else
{
// if the predecessor of pos is Null, then
// correct the predecessor's phase so that
// it correctly resets the synthesis phase
// so that the phase of the Breakpoint at
// pos is achieved in synthesis.
posPrev.breakpoint().setPhase( wrapPi( pos.breakpoint().phase() - travel ) );
}
}
}
}
// 变换为“限制集”欧拉角
void EulerAngles::cononize()
{
pitch = wrapPi(pitch);
if (pitch < -kPiOver2)
{
pitch = -kPi - pitch;
heading += kPi;
bank += kPi;
}
else if (pitch>kPiOver2)
{
pitch = kPi - pitch;
heading += kPi;
bank += kPi;
}
if (fabs(pitch) > kPiOver2 - 1e-4)
{
heading += bank;
bank = 0.0f;
}
else
{
bank = wrapPi(bank);
}
heading = wrapPi(heading);
}
void EulerAngles::canonize()
{
pitch = wrapPi(pitch);
if (pitch < -PI_OVER_2)
{
pitch = -PI - pitch;
heading += PI;
bank += PI;
}
else if (pitch > -PI_OVER_2)
{
pitch = PI - pitch;
heading += PI;
bank += PI;
}
//检测万向锁，即pitch是否等于pi/2,允许有误差
if (fabs(pitch) > PI_OVER_2 - EPSINON)
{
heading += bank;
bank = 0.0f;
}
else
{
bank = wrapPi(bank);
}
heading = wrapPi(heading);
}
void EulerAngles::canonize() {
// 首先，回绕pitch到-pi到pi
// First, wrap pitch in range -pi ... pi
pitch = wrapPi(pitch);
// 现在，检查矩阵的“后面”，pitch超出标准范围-pi/2到pi/2
// Now, check for "the back side" of the matrix, pitch outside
// the canonical range of -pi/2 ... pi/2
if (pitch < -kPiOver2) {
pitch = -kPi - pitch;
heading += kPi;
bank += kPi;
} else if (pitch > kPiOver2) {
pitch = kPi - pitch;
heading += kPi;
bank += kPi;
}
// 好了，现在检查万向锁情况（需要一点容忍度）
// OK, now check for the gimbel lock case (within a slight
// tolerance)
if (fabs(pitch) > kPiOver2 - 1e-4) {
// 我们遇到了万向锁。将所有竖直轴的旋转交给heading
// We are in gimbel lock. Assign all rotation
// about the vertical axis to heading
heading += bank;
bank = 0.0f;
} else {
// 没有遇到万向锁。回绕到标准范围的bank角度。
// Not in gimbel lock. Wrap the bank angle in
// canonical range
bank = wrapPi(bank);
}
// 将heading回绕到标准范围
// Wrap heading in canonical range
heading = wrapPi(heading);
}
// ---------------------------------------------------------------------------
// fixPhaseBackward
//
//! Recompute phases of all Breakpoints on the half-open range [stopHere, pos)
//! so that the synthesized phases of those Breakpoints matches
//! the stored phase, as long as the synthesized phase at stopHere
//! matches the stored (not recomputed) phase.
//!
//! The phase is corrected beginning at the end of the range, maintaining
//! the stored phase in the Breakpoint at pos.
//!
//! Backward phase-fixing stops if a null (zero-amplitude) Breakpoint
//! is encountered, because nulls are interpreted as phase reset points
//! in Loris. If a null is encountered, the remainder of the range
//! (the front part) is fixed in the forward direction, beginning at
//! the start of the stopHere.
//!
//! \pre pos and stopHere are iterators on the same Partial, and
//! pos must be not later than stopHere.
//! \pre pos cannot be end of the Partial, it must be the postion
//! of a valid Breakpoint.
//! \param stopHere the position of the earliest Breakpoint whose phase might be
//! recomputed.
//! \param pos the position of a (later) Breakpoint whose phase is to be matched.
//! The phase at pos is not modified.
//
void fixPhaseBackward( Partial::iterator stopHere, Partial::iterator pos )
{
while ( pos != stopHere &&
( NoNulls || BreakpointUtils::isNonNull( pos.breakpoint() ) ) )
{
// pos is not the first Breakpoint in the Partial,
// and pos is not a Null Breakpoint.
// Compute the correct phase for the
// predecessor of pos.
Partial::iterator posFwd = pos--;
double travel = phaseTravel( pos, posFwd );
pos.breakpoint().setPhase( wrapPi( posFwd.breakpoint().phase() - travel ) );
}
// if a null was encountered, then stop fixing backwards,
// and fix the front of the Partial in the forward direction:
if ( pos != stopHere )
{
// pos is not the first Breakpoint in the Partial,
// and it is a Null Breakpoint (zero amplitude),
// so it will be used to reset the phase during
// synthesis.
// The phase of all Breakpoints starting with pos
// and ending with the Breakpoint nearest to time t
// has been corrected.
// Fix phases before pos starting at the beginning
// of the Partial.
//
// Dont fix pos, it has already been fixed.
fixPhaseForward( stopHere, --pos );
}
}
/// Determines the canonical Euler angle triple for this
/// set of angles and canonizes it. Note that while this
/// doesn't affect the rotation represented by the triplet,
/// if your code uses the angles for some other purpose
/// (e.g., angular velocity), the results may be unexpected.
/// \note See section 10.3 for more information.
void EulerAngles::canonize() {
// First, wrap pitch in range -pi ... pi
pitch = wrapPi(pitch);
// Now, check for "the back side" of the matrix, pitch outside
// the canonical range of -pi/2 ... pi/2
if (pitch < -kPiOver2) {
pitch = -kPi - pitch;
heading += kPi;
bank += kPi;
} else if (pitch > kPiOver2) {
pitch = kPi - pitch;
heading += kPi;
bank += kPi;
}
// OK, now check for the gimbal lock case (within a slight
// tolerance)
if (fabs(pitch) > kPiOver2 - 1e-4) {
// We are in gimbal lock. Assign all rotation
// about the vertical axis to heading
heading += bank;
bank = 0.0f;
} else {
// Not in gimbal lock. Wrap the bank angle in
// canonical range
bank = wrapPi(bank);
}
// Wrap heading in canonical range
heading = wrapPi(heading);
}
// processes movement and input
/// \param elapsed time in seconds since the last call to this function
void FreeCamera::process(float elapsed)
{
Matrix4x3 view;
Vector3 movement = Vector3(0.0f,0.0f,0.0f);
if (gInput.keyDown(DIK_UPARROW))
movement.z = 1.0f;
if (gInput.keyDown(DIK_DOWNARROW))
movement.z = -1.0f;
if (gInput.keyDown(DIK_LEFTARROW))
movement.x = -1.0f;
if (gInput.keyDown(DIK_RIGHTARROW))
movement.x = 1.0f;
if (gInput.keyDown(DIK_PGUP))
movement.y = 1.0f;
if (gInput.keyDown(DIK_PGDN))
movement.y = -1.0f;
// get mouse movement from input manager
float lx = gInput.getMouseLX();
float ly = gInput.getMouseLY();
m_cameraOrientMoving.pitch += ly / 100.0f;
m_cameraOrientMoving.heading += lx / 100.0f;
// add 80% of cameraOrientMoving to cameraOrient
// then remove 80% of cameraOrientMoving
cameraOrient += m_cameraOrientMoving * 0.8f;
m_cameraOrientMoving += m_cameraOrientMoving * -0.8f;
// constrain pitch
if (cameraOrient.pitch > kPiOver2)
cameraOrient.pitch = kPiOver2;
if (cameraOrient.pitch < -kPiOver2)
cameraOrient.pitch = -kPiOver2;
// wrap heading btw -pi and pi
cameraOrient.heading = wrapPi(cameraOrient.heading);
// create a matrix to transform the movement to world space
view.setupParentToLocal(Vector3::kZeroVector, cameraOrient);
view = view.inverse();
movement = movement*view;
cameraPos += movement * elapsed * m_speed;
}
// ---------------------------------------------------------------------------
// matchPhaseFwd
//
//! Compute the target frequency that will affect the
//! predicted (by the Breakpoint phases) amount of
//! sinusoidal phase travel between two breakpoints,
//! and assign that frequency to the target Breakpoint.
//! After computing the new frequency, update the phase of
//! the later Breakpoint.
//!
//! If the earlier Breakpoint is null and the later one
//! is non-null, then update the phase of the earlier
//! Breakpoint, and do not modify its frequency or the
//! later Breakpoint.
//!
//! The most common kinds of errors are local (or burst) errors in
//! frequency and phase. These errors are best corrected by correcting
//! less than half the detected error at any time. Correcting more
//! than that will produce frequency oscillations for the remainder of
//! the Partial, in the case of a single bad frequency (as is common
//! at the onset of a tone). Any damping factor less then one will
//! converge eventually, .5 or less will converge without oscillating.
//! Use the damping argument to control the damping of the correction.
//! Specify 1 for no damping.
//!
//! \pre The two Breakpoints are assumed to be consecutive in
//! a Partial.
//! \param bp0 The earlier Breakpoint.
//! \param bp1 The later Breakpoint.
//! \param dt The time (in seconds) between bp0 and bp1.
//! \param damping The fraction of the amount of phase error that will
//! be corrected (.5 or less will prevent frequency oscilation
//! due to burst errors in phase).
//! \param maxFixPct The maximum amount of frequency adjustment
//! that can be made to the frequency of bp1, expressed
//! as a precentage of the unmodified frequency of bp1.
//! If the necessary amount of frequency adjustment exceeds
//! this amount, then the phase will not be matched,
//! but will be updated as well to be consistent with
//! the frequencies. (default is 0.2%)
//
void matchPhaseFwd( Breakpoint & bp0, Breakpoint & bp1,
double dt, double damping, double maxFixPct )
{
double travel = phaseTravel( bp0, bp1, dt );
if ( ! BreakpointUtils::isNonNull( bp1 ) )
{
// if bp1 is null, just compute a new phase,
// no need to match it.
bp1.setPhase( wrapPi( bp0.phase() + travel ) );
}
else if ( ! BreakpointUtils::isNonNull( bp0 ) )
{
// if bp0 is null, and bp1 is not, then bp0
// should be a phase reset Breakpoint during
// rendering, so compute a new phase for
// bp0 that achieves bp1's phase.
bp0.setPhase( wrapPi( bp1.phase() - travel ) ) ;
}
else
{
// invariant:
// neither bp0 nor bp1 is null
//
// modify frequecies to match phases as nearly as possible
double err = wrapPi( bp1.phase() - ( bp0.phase() + travel ) );
// The most common kinds of errors are local (or burst) errors in
// frequency and phase. These errors are best corrected by correcting
// less than half the detected error at any time. Correcting more
// than that will produce frequency oscillations for the remainder of
// the Partial, in the case of a single bad frequency (as is common
// at the onset of a tone). Any damping factor less then one will
// converge eventually, .5 or less will converge without oscillating.
// #define DAMPING .5
travel += damping * err;
double f0 = bp0.frequency();
double ftgt = ( travel / ( Pi * dt ) ) - f0;
#ifdef Loris_Debug
debugger << "matchPhaseFwd: correcting " << bp1.frequency() << " to " << ftgt
<< " (phase " << wrapPi( bp1.phase() ) << "), ";
#endif
// If the target is not a null breakpoint, may need to
// clamp the amount of frequency modification.
//
// Actually, should probably always clamp the amount
// of modulation, should never have arbitrarily large
// frequency adjustments.
//
// Really, should never call this function if bp1
// is a null Breakpoint, because we don't care about
// those phases in Loris.
if ( true ) // bp1.amplitude() != 0. )
{
if ( ftgt > bp1.frequency() * ( 1 + (maxFixPct*.01) ) )
{
ftgt = bp1.frequency() * ( 1 + (maxFixPct*.01) );
}
else if ( ftgt < bp1.frequency() * ( 1 - (maxFixPct*.01) ) )
{
ftgt = bp1.frequency() * ( 1 - (maxFixPct*.01) );
}
}
bp1.setFrequency( ftgt );
// Recompute the phase according to the new frequency.
double phi = wrapPi( bp0.phase() + phaseTravel( bp0, bp1, dt ) );
bp1.setPhase( phi );
#ifdef Loris_Debug
debugger << "achieved " << ftgt << " (phase " << phi << ")" << endl;
#endif
}
}
// ---------------------------------------------------------------------------
// fixPhaseBetween
//
//! Fix the phase travel between two Breakpoints by adjusting the
//! frequency and phase of Breakpoints between those two.
//!
//! This algorithm assumes that there is nothing interesting about the
//! phases of the intervening Breakpoints, and modifies their frequencies
//! as little as possible to achieve the correct amount of phase travel
//! such that the frequencies and phases at the specified times
//! match the stored values. The phases of all the Breakpoints between
//! the specified times are recomputed.
//!
//! Null Breakpoints are treated the same as non-null Breakpoints.
//!
//! \pre b and e are iterators on the same Partials, and
//! e must not preceed b in that Partial.
//! \pre There must be at least one Breakpoint in the
//! Partial between b and e.
//! \post The phases and frequencies of the Breakpoints in the
//! range have been recomputed such that an oscillator
//! initialized to the parameters of the first Breakpoint
//! will arrive at the parameters of the last Breakpoint,
//! and all the intervening Breakpoints will be matched.
//! \param b The phases and frequencies of Breakpoints later than
//! this one may be modified.
//! \param e The phases and frequencies of Breakpoints earlier than
//! this one may be modified.
//
void fixPhaseBetween( Partial::iterator b, Partial::iterator e )
{
if ( 1 < std::distance( b, e ) )
{
// Accumulate the actual phase travel over the Breakpoint
// span, and count the envelope segments.
double travel = 0;
Partial::iterator next = b;
do
{
Partial::iterator prev = next++;
travel += phaseTravel( prev, next );
} while( next != e );
// Compute the desired amount of phase travel:
double deviation = wrapPi( e.breakpoint().phase() - ( b.breakpoint().phase() + travel ) );
double desired = travel + deviation;
/*
debugger << "---------- fixing breakpoint frequencies over time ( "
<< b.time() << " , " << e.time() << " )" << endl;
debugger << "desired travel: " << desired << endl;
debugger << "actual travel: " << travel << endl;
*/
// Compute the amount by which to perturb the frequencies of
// all the null Breakpoints between b and e.
//
// The accumulated phase travel is the sum of the average frequency
// (in radians) of each segment times the duration of each segment
// (the actual phase travel is computed this way). If this sum is
// computed with each Breakpoint frequency perturbed (additively)
// by delta, and set equal to the desired phase travel, then it
// can be simplified to:
// delta = 2 * ( phase error ) / ( tN + tN-1 - t1 - t0 )
// where tN is the time of e, tN-1 is the time of its predecessor,
// t0 is the time of b, and t1 is the time of b's successor.
//
Partial::iterator iter = b;
double t0 = iter.time();
++iter;
double t1 = iter.time();
iter = e;
double tN = iter.time();
--iter;
double tNm1 = iter.time();
Assert( t1 < tN ); // else there were no Breakpoints in between
double delta = ( 2 * ( desired - travel ) / ( tN + tNm1 - t1 - t0 ) ) / ( 2 * Pi );
// Perturb the Breakpoint frequencies.
double DEBUGtravel = 0;
next = b;
Partial::iterator prev = next++;
while ( next != e )
{
//debugger << "changing frequency from " << next.breakpoint().frequency();
next.breakpoint().setFrequency( next.breakpoint().frequency() + delta );
//debugger << " to " << next.breakpoint().frequency() << endl;
double newtravel = phaseTravel( prev, next );
DEBUGtravel += newtravel;
//debugger << "changing phase from " << wrapPi( next.breakpoint().phase() );
next.breakpoint().setPhase( wrapPi( prev.breakpoint().phase() + newtravel ) );
//debugger << " to " << next.breakpoint().phase() << endl;
prev = next++;
}
DEBUGtravel += phaseTravel( prev, next );
/*
debugger << "travel: " << DEBUGtravel << endl;
debugger << "desired: " << e.breakpoint().phase() << endl;
debugger << "got: " << wrapPi( prev.breakpoint().phase() + phaseTravel( prev, next ) ) << endl;
debugger << "---------- done." << endl;
*/
}
else
{
// Preconditions not met, cannot fix the phase travel.
// Should raise exception?
debugger << "cannot fix phase between " << b.time() << " and " << e.time()
<< ", there are no Breakpoints between those times" << endl;
}
}