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Tempo ramps - minor optimisation and comment clarification.

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This commit is contained in:
nick_m
2016-02-26 07:01:37 +11:00
parent 28127b1768
commit 895bbbba11
2 changed files with 22 additions and 24 deletions
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3
libs/ardour/ardour/tempo.h
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@@ -190,8 +190,7 @@ class LIBARDOUR_API TempoSection : public MetricSection, public Tempo {
double beat_at_frame (framepos_t frame, framecnt_t frame_rate) const;
framepos_t frame_at_beat (double beat, framecnt_t frame_rate) const;
framecnt_t ramp_duration_from_tempo_and_beat (double end_tpm, double end_beat, framecnt_t frame_rate);
void set_c_func_from_tempo_and_beat (double end_bpm, double end_beat, framecnt_t frame_rate);
double compute_c_func (double end_bpm, framepos_t end_frame, framecnt_t frame_rate) const;
double get_c_func () const { return _c_func; }
void set_c_func (double c_func) { _c_func = c_func; }

43
libs/ardour/tempo.cc
View File

@@ -264,7 +264,7 @@ TempoSection::frame_at_beat (double beat, framecnt_t frame_rate) const
/*
Ramp Overview
| *
Tempo | *
Tt----|-----------------*|
Ta----|--------------|* |
@@ -272,7 +272,7 @@ Ta----|--------------|* |
| * | |
| * | |
T0----|* | |
| | |
* | | |
_______________|___|_____
time a t (next tempo)
[ c ] defines c
@@ -286,21 +286,21 @@ c = log(Ta/T0)/a
and
a = log(Ta/T0)/c
We define c for a tempo ramp by placing a new tempo at some distance t away from our existing one.
Given the function constant, the beat function (duration in beats at some time t) is:
Given the function constant, the integral of the Tempo function (the beat function, which is the duration in beats at some time t) is:
b(t) = T0(e^(ct) - 1) / c
To find the time t at any beat b on the curve, we use the inverse function of the beat function:
To find the time t at any beat b, we use the inverse function of the beat function (the time function) which can be shown to be :
t(b) = log((cb / T0) + 1) / c
When we add or move the next tempo section, we change the function constant. We take advantage of t being equal to a here.
We define c for a tempo ramp by placing a new tempo at some distance t away from our existing one.
The problem is that we usually don't know t.
We do know the beat duration until the next tempo section.
Substituting t = a into the beat function allows us to find a in terms of beat duration b and the two relevant tempos:
We do know the duration in beats where the next tempo section lies.
Where t = a (when we define c), we can solve a in terms of beat duration b and the two relevant tempos using the beat function:
a = b log (Ta / T0) / (T0 (e^(log (Ta / T0)) - 1))
We then use a to set the function constant c (above).
Solving a and setting c in one operation allows us to further reduce the problem to:
c = T0 (e^(log (Ta / T0)) - 1) / b
Most of this stuff is taken from this paper:
WHERE’S THE BEAT?
@@ -312,12 +312,12 @@ https://www.zhdk.ch/fileadmin/data_subsites/data_icst/Downloads/Timegrid/ICST_Te
*/
/* compute the duration of this tempo section givan the end tempo and duration in beats of some later tempo section*/
framecnt_t
TempoSection::ramp_duration_from_tempo_and_beat (double end_bpm, double end_beat, framecnt_t frame_rate)
/* set this ramp's function constant using the end tempo and duration in beats of some later tempo section*/
void
TempoSection::set_c_func_from_tempo_and_beat (double end_bpm, double end_beat, framecnt_t frame_rate)
{
double const log_tempo_ratio = log ((end_bpm * BBT_Time::ticks_per_beat) / ticks_per_minute());
return minute_to_frame (((end_beat * BBT_Time::ticks_per_beat) * log_tempo_ratio) / (ticks_per_minute() * (exp (log_tempo_ratio) - 1)), frame_rate);
_c_func = ticks_per_minute() * (exp (log_tempo_ratio) - 1) / (end_beat * BBT_Time::ticks_per_beat);
}
/* compute the function constant from some later tempo section, given tempo (beats/min.) and distance (in frames) from this tempo section */
@@ -1124,17 +1124,16 @@ TempoMap::recompute_map (bool reassign_tempo_bbt, framepos_t end)
if ((t = dynamic_cast<TempoSection*> (*i)) != 0) {
if (prev_ts) {
double const ticks_relative_to_prev = (t->beat() - prev_ts->beat()) * BBT_Time::ticks_per_beat;
framecnt_t duration;
if (prev_ts->type() == TempoSection::Ramp) {
duration = prev_ts->ramp_duration_from_tempo_and_beat (t->beats_per_minute(), t->beat() - prev_ts->beat(), _frame_rate);
prev_ts->set_c_func_from_tempo_and_beat (t->beats_per_minute(), t->beat() - prev_ts->beat(), _frame_rate);
t->set_frame (prev_ts->frame_at_tempo (t->beats_per_minute(), _frame_rate) + prev_ts->frame());
} else {
duration = (framecnt_t) floor (ticks_relative_to_prev * prev_ts->frames_per_beat (_frame_rate) * BBT_Time::ticks_per_beat);
double const ticks_relative_to_prev = (t->beat() - prev_ts->beat()) * BBT_Time::ticks_per_beat;
framecnt_t const duration = (framecnt_t) floor (ticks_relative_to_prev * prev_ts->frames_per_beat (_frame_rate)
* BBT_Time::ticks_per_beat);
prev_ts->set_c_func (0.0);
t->set_frame (duration + prev_ts->frame());
}
prev_ts->set_c_func (prev_ts->compute_c_func (t->beats_per_minute(), duration, _frame_rate));
t->set_frame (duration + prev_ts->frame());
}
prev_ts = t;
}
@@ -1144,7 +1143,7 @@ TempoMap::recompute_map (bool reassign_tempo_bbt, framepos_t end)
MeterSection* meter = 0;
for (mi = metrics.begin(); mi != metrics.end(); ++mi) {
/* we can do this beacuse we have the tempo section frames set */
/* We now have the tempo map set. use it to set meter positions.*/
if ((meter = dynamic_cast<MeterSection*> (*mi)) != 0) {
meter->set_frame (frame_at_tick (meter->beat() * BBT_Time::ticks_per_beat));
}