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Timeline: now able to increase to maximum pixel count

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There is a built-in limitation, which now is even
lowered to 100000 pixels horizontally.

With the techniques introduced in this changeset, it seems possible
to support more -- yet this would be a case of unnecessary genricity;
handling such large numbers will drive more computations into the
danger zone, and doing so incurs cost in terms of testing and debugging.

Placing that into context, contemporary displays are not even 4K on
average, and it does not look likely even for cinema display to go
way beyond 8k -- so yes, I want display hardware with 100000 pixels!!


The key takeaway of this changeset:
 - can calculate px = trunc(zoomFactor * duration) step wise,
   even when the direct calculation would lead to wrap-around
 - can safely adjust and fix the zoomFactor using Newton approximation
This commit is contained in:
Fischlurch 2022-12-09 19:37:35 +01:00
parent 068549dace
commit ce3713d872
3 changed files with 386 additions and 20 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

69
src/stage/model/zoom-window.hpp
View file

@ -175,7 +175,7 @@ namespace model {
namespace {// initial values (rather arbitrary)
const FSecs DEFAULT_CANVAS{23};
const Rat DEFAULT_METRIC{25};
const uint MAX_PX_WIDTH{1000000};
const uint MAX_PX_WIDTH{100000};
const FSecs MAX_TIMESPAN{_FSecs(Duration::MAX)};
const FSecs MICRO_TICK{1_r/Time::SCALE};
@ -259,7 +259,7 @@ namespace model {
pxWidth() const
{
REQUIRE (startWin_ < afterWin_);
return rational_cast<uint> (px_per_sec() * FSecs(afterWin_-startWin_));
return calcPixelsForDurationAtScale (px_per_sec(), afterWin_-startWin_);
}
@ -677,6 +677,53 @@ namespace model {
: start + Time{DEFAULT_CANVAS};
}
/** Assertion helper: resulting pxWidth matches expectations */
static void
__assertMatchesExpectedPixWidth (Rat zoomFactor, FSecs duration, uint pxWidth)
{
auto sizeAtRequestedScale = calcPixelsForDurationAtScale (zoomFactor, duration);
ENSURE (abs(pxWidth - sizeAtRequestedScale) <= 1
,"ZoomWindow: established size or metric misses expectation "
"by more than 1px. %upx != %1.6f expected pixel."
, pxWidth, sizeAtRequestedScale);
}
static void
__assertMetricConforms2pxWidth (Rat zoomFactor, FSecs duration, uint pxWidth)
{
if (util::can_represent_Product(zoomFactor, duration))
{
ENSURE (pxWidth == rational_cast<uint> (zoomFactor*duration)
,"ZoomWindow: established zoom factor misses expected "
"width in pixels: %upx != %upx (resulting)"
, pxWidth, rational_cast<uint> (zoomFactor*duration));
}
else
{
auto sizeAtRequestedScale = approx(zoomFactor) * approx(duration);
ENSURE (pxWidth == uint(sizeAtRequestedScale + 0.5)
,"ZoomWindow: established zoom factor misses expected "
"width in pixels: %upx != %1.8f px (resulting)"
, pxWidth, sizeAtRequestedScale);
}
}
/** @remark indirect calculation path to avoid overflow on large durations */
static int64_t
calcPixelsForDurationAtScale (Rat zoomFactor, FSecs duration)
{// calculate rational_cast<uint> (zoomFactor * duration)
auto zn = zoomFactor.numerator();
auto zd = zoomFactor.denominator();
auto dn = duration.numerator();
auto dd = duration.denominator();
auto [secs,r] = util::iDiv (dn, dd); // split duration in full seconds and rest
auto [px1,r1] = util::iDiv (secs*zn, zd); // calc pixels required for full seconds
auto [px2,r2] = util::iDiv (r*zn, dd*zd); // calc pixels required for rest duration
auto pxr = (r1*dd +r2) /(dd*zd); // and calculate integer div for combined remainders
ENSURE (0 <= px1 and 0 <= px2 and 0<= pxr);
return px1 + px2 + pxr;
}
/** window size beyond that limit would yield
* numerically dangerous zoom factors */
static FSecs
@ -706,7 +753,20 @@ namespace model {
REQUIRE (afterWin_> startWin_);
FSecs dur{afterWin_-startWin_};
Rat adjMetric = detox (Rat(pxWidth) / dur);
ENSURE (pxWidth == rational_cast<uint> (adjMetric*dur));
// check if new metric reproduces expected pxWidth...
for (uint resPx
;pxWidth != (resPx = calcPixelsForDurationAtScale (adjMetric, dur)) // calculate trunc {adjMetric*dur}
; // but calculate cleverly to avoid numeric wrap
) // Problem: detox() introduced too much error
{ // need to adjust metric to match expected pxWidth
// Using Newton-Raphson; can't just calculate fix due to numeric-wraparound
auto delta = double(resPx) - pxWidth; // note: approximation calculated in double
int64_t mn{adjMetric.numerator()}, dn{dur.numerator()},
md{adjMetric.denominator()}, dd{dur.denominator()};
//assuming: f(xₙ) ≔ Δₙ = resPx-pxWidth = trunc{ xₙ * dn/(md*dd) } - pxWidth
mn -= int64_t(delta * md*dd / dn); // xₙ₁ ≔ xₙ - f(xₙ)/f'(xₙ)
adjMetric = Rat{mn, md};
}
return adjMetric;
}
@ -731,8 +791,7 @@ namespace model {
// re-check metric to maintain precise pxWidth
px_per_sec_ = conformMetricToWindow (pxWidth);
ENSURE (_FSecs(afterWin_-startWin_) < MAX_TIMESPAN);
auto sizeAtRequestedScale = approx(changedMetric)*approx(dur);
ENSURE (abs(pxWidth - sizeAtRequestedScale) <= 1);
__assertMatchesExpectedPixWidth (changedMetric, dur, pxWidth);
}
/**

25
tests/stage/model/zoom-window-test.cpp
View file

@ -680,6 +680,7 @@ namespace test {
void
safeguard_extremeZoomOut()
{
/*--Test-1-----------*/
ZoomWindow win{3, TimeSpan{_t(-1,2), _t(1,2)}}; // setup ZoomWindow to very small pixel size (3px)
CHECK (win.overallSpan().duration() == _t(1));
CHECK (win.px_per_sec() == 3_r/1);
@ -690,6 +691,7 @@ namespace test {
CHECK (win.px_per_sec() == 3_r/1);
CHECK (win.pxWidth() == 3);
/*--Test-2-----------*/
Rat bruteZoom{3_r/(int64_t{1}<<60)};
win.setMetric (bruteZoom); // zoom out beyond what is possible and to a toxic factor
@ -705,11 +707,13 @@ namespace test {
CHECK (win.px_per_sec() == 3 / _FSecs(win.visible().duration())); // and this value also conforms with the pixel size and window duration
CHECK (win.pxWidth() == 3);
/*--Test-3-----------*/
win.setMetric (5_r/std::numeric_limits<int64_t>::max()); // same limiting applies to even more nasty values
CHECK (_raw(win.visible().duration()) == 3298534883328); // still unchanged at limit
CHECK (win.px_per_sec() == 15625_r/17179869184);
CHECK (win.pxWidth() == 3);
/*--Test-4-----------*/
win.setMetric (1000001_r/LIM_HAZARD); // but zooming in more than that limit will be honored
CHECK (_raw(win.visible().duration()) == 3298531584796); // ...window now slightly reduced in size
CHECK (_raw(win.visible().duration()) < 3 * LIM_HAZARD);
@ -718,6 +722,27 @@ namespace test {
CHECK (win.px_per_sec() > 1000001_r/LIM_HAZARD); // (this is what was requested)
CHECK (win.px_per_sec() < 1000002_r/LIM_HAZARD); // (thus result was slightly adjusted upwards)
CHECK (win.pxWidth() == 3);
/*--Test-5-----------*/
win.calibrateExtension (1'000'000'000); // implicit drastic zoom-out by increasing the number of pixels
CHECK (win.pxWidth() < 1'000'000'000); // however: this number is capped at a fixed maximum
CHECK (win.pxWidth() == MAX_PX_WIDTH); // (which „should be enough“ for the time being...)
CHECK (win.px_per_sec() == 508631_r/559239974093); // the zoom metric has been adapted, but to a sanitised value
CHECK (_raw(win.overallSpan().duration()) == 614891469123651720); // overall canvas duration not changed
CHECK (_raw(win.visible().duration()) == 109951052826533333); // window duration now drastically increased
CHECK (win.overallSpan().end() == TimeValue{307445734561825860}); // window is somewhere within canvas
CHECK (win.visible().end() == TimeValue{109949403560740935}); // but was expanded to the right,
CHECK (win.visible().start() == TimeValue{ -1649265792398}); // ... retaining the start value
// Note: these parameters build up to really »poisonous« values....
CHECK (MAX_PX_WIDTH / _FSecs(win.visible().duration()) == 100000000000_r/109951052826533333);
CHECK (win.px_per_sec() * _FSecs(win.visible().duration()) < 0); // we can't even calculate the resulting pxWidth() naively
CHECK (rational_cast<float>(win.px_per_sec()) // ...while effectively these values are still correct
* rational_cast<float>(_FSecs(win.visible().duration())) == 100000.914f);
CHECK (rational_cast<float>(100000000000_r/109951052826533333) == 9.09495611e-07f); // theoretical value
CHECK (rational_cast<float>(win.px_per_sec()) == 9.09503967e-07f); // value actually chosen
CHECK (win.px_per_sec() == 508631_r/559239974093);
}

312
wiki/thinkPad.ichthyo.mm
View file

@ -39597,11 +39597,43 @@
<icon BUILTIN="messagebox_warning"/>
</node>
<node CREATED="1668263422928" ID="ID_1049514706" MODIFIED="1668263422928" TEXT="setVisiblePos (double percentage)"/>
<node COLOR="#435e98" CREATED="1670608837155" ID="ID_1810196404" MODIFIED="1670608847785" TEXT="pxWidth()">
<icon BUILTIN="messagebox_warning"/>
<node COLOR="#435e98" CREATED="1670608849328" ID="ID_1135224410" MODIFIED="1670608880268" TEXT="kann bei maximal zul&#xe4;ssigen Parametern bereits in numeric-wrap laufen">
<icon BUILTIN="broken-line"/>
</node>
<node COLOR="#338800" CREATED="1670608881221" ID="ID_617148644" LINK="#ID_1459847631" MODIFIED="1670609042831">
<richcontent TYPE="NODE"><html>
<head>
</head>
<body>
<p>
gel&#246;st durch geschickte schrittweise Berechnung:
</p>
<p>
<font face="Monospaced" color="#403786">calcPixelsForDurationAtScale (Rat zoomFactor, FSecs duration)</font>
</p>
</body>
</html></richcontent>
<richcontent TYPE="NOTE"><html>
<head>
</head>
<body>
<p>
Wir nutzen explizit aus, da&#223; das Ergebnis durch truncating quantisiert wird (Integer-Division). Daher k&#246;nnen wir erst den ersten Dividenden (die Zeitspanne) aufteilen, und zwar erst mal in den Sekunden-Anteil, dann den Rest, und dann den Rest vom Rest
</p>
</body>
</html></richcontent>
<icon BUILTIN="button_ok"/>
</node>
</node>
</node>
<node CREATED="1668263441959" ID="ID_1366157126" MODIFIED="1668263454322" TEXT="2.Layer &#x2014; privat">
<node BACKGROUND_COLOR="#eee5c3" COLOR="#990000" CREATED="1668263464370" ID="ID_452384864" MODIFIED="1668269820128" TEXT="establishMetric (uint pxWidth, Time startWin, Time afterWin)">
<node COLOR="#435e98" CREATED="1668263464370" ID="ID_452384864" MODIFIED="1670608807787" TEXT="establishMetric (uint pxWidth, Time startWin, Time afterWin)">
<icon BUILTIN="messagebox_warning"/>
<node BACKGROUND_COLOR="#eee5c3" COLOR="#990000" CREATED="1668269822171" ID="ID_1581625515" MODIFIED="1668269880707" TEXT="Resultat sollte &quot;ungiftig&quot; sein">
<node COLOR="#435e98" CREATED="1668269822171" ID="ID_1581625515" MODIFIED="1670608805543" TEXT="Resultat sollte &quot;ungiftig&quot; sein">
<richcontent TYPE="NOTE"><html>
<head>
@ -39614,16 +39646,21 @@
</html></richcontent>
<icon BUILTIN="yes"/>
</node>
<node BACKGROUND_COLOR="#f0d5c5" COLOR="#990033" CREATED="1668269838609" ID="ID_982888658" MODIFIED="1668269848857" TEXT="geeignet normieren oder kappen?">
<node COLOR="#435e98" CREATED="1668269838609" ID="ID_982888658" MODIFIED="1670608801375" TEXT="geeignet normieren oder kappen?">
<icon BUILTIN="help"/>
<node CREATED="1670608693763" ID="ID_1403342865" MODIFIED="1670608757928" TEXT="genauere Betrachtung zeigt: hier keine Gefahr">
<arrowlink COLOR="#7bb8a2" DESTINATION="ID_1497381497" ENDARROW="Default" ENDINCLINATION="-341;0;" ID="Arrow_ID_301661313" STARTARROW="None" STARTINCLINATION="584;36;"/>
</node>
<node CREATED="1670608703396" ID="ID_1449271152" MODIFIED="1670608722973" TEXT="Duration wird errechnet und ist daher ggfs. sehr gro&#xdf;, aber nicht giftig"/>
<node CREATED="1670608782329" ID="ID_1737555624" MODIFIED="1670608799171" TEXT="Pixel-Zahl wird grade hier explizit gekappt"/>
</node>
</node>
<node BACKGROUND_COLOR="#eee5c3" COLOR="#990000" CREATED="1668263473958" ID="ID_1175951405" MODIFIED="1668703238535" TEXT="conformWindowToMetric (Rat changedMetric)">
<node COLOR="#338800" CREATED="1668263473958" ID="ID_1175951405" MODIFIED="1670608663663" TEXT="conformWindowToMetric (Rat changedMetric)">
<arrowlink COLOR="#bf0f5b" DESTINATION="ID_1671513743" ENDARROW="Default" ENDINCLINATION="297;-23;" ID="Arrow_ID_389982782" STARTARROW="None" STARTINCLINATION="-323;20;"/>
<arrowlink COLOR="#856e9e" DESTINATION="ID_773636992" ENDARROW="Default" ENDINCLINATION="138;-8;" ID="Arrow_ID_976571904" STARTARROW="None" STARTINCLINATION="219;13;"/>
<arrowlink COLOR="#65253d" DESTINATION="ID_1915595988" ENDARROW="Default" ENDINCLINATION="9;-40;" ID="Arrow_ID_382076752" STARTARROW="None" STARTINCLINATION="-11;29;"/>
<linktarget COLOR="#965e8b" DESTINATION="ID_1175951405" ENDARROW="Default" ENDINCLINATION="253;-8;" ID="Arrow_ID_354964355" SOURCE="ID_909162669" STARTARROW="None" STARTINCLINATION="302;-12;"/>
<icon BUILTIN="flag-yellow"/>
<icon BUILTIN="button_ok"/>
<node BACKGROUND_COLOR="#fefc4e" COLOR="#351d75" CREATED="1668555596031" HGAP="151" ID="ID_1196389964" MODIFIED="1668555795593" TEXT="&#xd83e;&#xdc46; die zentrale Gelenkstelle" VSHIFT="4">
<edge COLOR="#fdf7a5" STYLE="linear"/>
<font BOLD="true" NAME="SansSerif" SIZE="12"/>
@ -39659,10 +39696,10 @@
</node>
</node>
</node>
<node BACKGROUND_COLOR="#eee5c3" COLOR="#990000" CREATED="1668703200176" ID="ID_1915595988" MODIFIED="1669479310199" TEXT="conformMetricToWindow()">
<node COLOR="#338800" CREATED="1668703200176" ID="ID_1915595988" MODIFIED="1670608657540" TEXT="conformMetricToWindow()">
<linktarget COLOR="#65253d" DESTINATION="ID_1915595988" ENDARROW="Default" ENDINCLINATION="9;-40;" ID="Arrow_ID_382076752" SOURCE="ID_1175951405" STARTARROW="None" STARTINCLINATION="-11;29;"/>
<linktarget COLOR="#6a6a92" DESTINATION="ID_1915595988" ENDARROW="Default" ENDINCLINATION="37;170;" ID="Arrow_ID_1959668732" SOURCE="ID_4317582" STARTARROW="None" STARTINCLINATION="-243;-9;"/>
<icon BUILTIN="flag-yellow"/>
<icon BUILTIN="button_ok"/>
<node BACKGROUND_COLOR="#fdfdcf" COLOR="#ff0000" CREATED="1668703282413" ID="ID_1976673029" MODIFIED="1669473783896" TEXT="Output mu&#xdf; entgiftet werden">
<edge COLOR="#f74141" STYLE="linear"/>
<icon BUILTIN="clanbomber"/>
@ -39765,14 +39802,35 @@
</node>
</node>
</node>
<node BACKGROUND_COLOR="#eee5c3" COLOR="#990000" CREATED="1668784031268" ID="ID_1513611206" MODIFIED="1668784041478" TEXT="die bestehende Duration k&#xf6;nnte sehr gro&#xdf; sein">
<icon BUILTIN="flag-yellow"/>
<node CREATED="1668784196906" ID="ID_1074723893" MODIFIED="1668784217911" TEXT="mit dem Nenner des changeFactor bereis &#xdc;berlauf m&#xf6;glich"/>
<node CREATED="1668784229969" ID="ID_1956828761" MODIFIED="1668784257285" TEXT="neu errechnete Duration k&#xf6;nnte toxisch sein"/>
<node COLOR="#435e98" CREATED="1668784031268" ID="ID_1513611206" MODIFIED="1670608646043" TEXT="die bestehende Duration k&#xf6;nnte sehr gro&#xdf; sein">
<icon BUILTIN="messagebox_warning"/>
<node COLOR="#435e98" CREATED="1668784196906" ID="ID_1074723893" MODIFIED="1670608369272" TEXT="mit dem Nenner des changeFactor bereis &#xdc;berlauf m&#xf6;glich">
<icon BUILTIN="messagebox_warning"/>
<node COLOR="#338800" CREATED="1670608372852" ID="ID_110351902" MODIFIED="1670608389199" TEXT="diese Gefahr nun durch Konvention gebannt">
<icon BUILTIN="yes"/>
</node>
<node CREATED="1670608390801" ID="ID_1235208681" MODIFIED="1670608405664" TEXT="die changedMetric wird entgiftet"/>
<node CREATED="1670608406491" ID="ID_839442543" MODIFIED="1670608429101" TEXT="die etablierte Metrik wird stets in der Berechnung entgiftet"/>
<node CREATED="1670608433666" ID="ID_1742946325" MODIFIED="1670608454073" TEXT="die Pixel-Zahl ist auch beschr&#xe4;nkt, damit sind auch die Z&#xe4;hler beschr&#xe4;nkt"/>
<node CREATED="1670608484281" ID="ID_368230032" MODIFIED="1670608495227" TEXT="au&#xdf;derdem ist die Metrik nun nach oben wie nach unten limitiert"/>
</node>
<node COLOR="#435e98" CREATED="1668784229969" ID="ID_1956828761" MODIFIED="1670608513302" TEXT="neu errechnete Duration k&#xf6;nnte toxisch sein">
<icon BUILTIN="messagebox_warning"/>
<node CREATED="1668784295985" ID="ID_1396219141" MODIFIED="1668784307787" TEXT="Rechnung in mutateDuration() k&#xf6;nnte entgleisen"/>
<node CREATED="1668784318075" ID="ID_901869945" MODIFIED="1668784338191" TEXT="wird alles zwar in conformWindowToMetric(changed) aufgefangen..."/>
<node CREATED="1668784339323" ID="ID_1591426559" MODIFIED="1668784345302" TEXT="..is aber trotzdem falsch"/>
</node>
<node COLOR="#338800" CREATED="1670608539818" ID="ID_196272847" MODIFIED="1670608638949" TEXT="Duration wird aus Time-Values berechnet">
<icon BUILTIN="button_ok"/>
<node CREATED="1670608554153" ID="ID_1497381497" MODIFIED="1670608748968" TEXT="Konsequenz: der Nenner ist limitiert (kleiner Time::SCALE) und nicht toxisch">
<linktarget COLOR="#7bb8a2" DESTINATION="ID_1497381497" ENDARROW="Default" ENDINCLINATION="-341;0;" ID="Arrow_ID_301661313" SOURCE="ID_1403342865" STARTARROW="None" STARTINCLINATION="584;36;"/>
</node>
<node CREATED="1670608581444" ID="ID_1656731502" MODIFIED="1670608593486" TEXT="daher kann Rat(px) / duration nicht entgleisen"/>
<node COLOR="#338800" CREATED="1670608611402" ID="ID_1320558101" MODIFIED="1670608633024" TEXT="confirmWindowToMetric und conformMetricToWindow sind abgesichert">
<icon BUILTIN="button_ok"/>
</node>
</node>
</node>
</node>
<node COLOR="#435e98" CREATED="1668263638141" ID="ID_909162669" MODIFIED="1669477898780" TEXT="mutateDuration (FSecs duration, uint px =0)">
<arrowlink COLOR="#965e8b" DESTINATION="ID_1175951405" ENDARROW="Default" ENDINCLINATION="253;-8;" ID="Arrow_ID_354964355" STARTARROW="None" STARTINCLINATION="302;-12;"/>
@ -39824,8 +39882,8 @@
</node>
</node>
<node CREATED="1668267393360" ID="ID_1700728412" MODIFIED="1668267398176" TEXT="giftige Br&#xfc;che">
<node COLOR="#435e98" CREATED="1669508070174" ID="ID_171647736" MODIFIED="1670016138169" TEXT="Aua: so ziemlich alles kann hier giftig sein">
<linktarget COLOR="#8c2958" DESTINATION="ID_171647736" ENDARROW="Default" ENDINCLINATION="8;76;" ID="Arrow_ID_1341085031" SOURCE="ID_196873456" STARTARROW="None" STARTINCLINATION="577;-36;"/>
<node COLOR="#435e98" CREATED="1669508070174" ID="ID_171647736" MODIFIED="1670549465314" TEXT="Aua: so ziemlich alles kann hier giftig sein">
<linktarget COLOR="#8c2958" DESTINATION="ID_171647736" ENDARROW="Default" ENDINCLINATION="103;88;" ID="Arrow_ID_1341085031" SOURCE="ID_196873456" STARTARROW="None" STARTINCLINATION="351;-26;"/>
<icon BUILTIN="broken-line"/>
<node CREATED="1669508081900" ID="ID_1740115162" MODIFIED="1669508382889" TEXT="zwar kann das Ergebnis nicht grob entgleisen">
<icon BUILTIN="button_ok"/>
@ -40122,12 +40180,208 @@
<icon BUILTIN="button_ok"/>
</node>
</node>
<node BACKGROUND_COLOR="#eef0c5" COLOR="#990000" CREATED="1670520735802" ID="ID_208606753" MODIFIED="1670608124573" TEXT="Pixel-Zahl dann extrem vergr&#xf6;&#xdf;ern">
<icon BUILTIN="pencil"/>
<node COLOR="#338800" CREATED="1670520761346" ID="ID_159180995" MODIFIED="1670608116400" TEXT="bereits sehr gro&#xdf;es Fenster">
<icon BUILTIN="button_ok"/>
</node>
<node COLOR="#338800" CREATED="1670520772342" ID="ID_139525815" MODIFIED="1670608119171" TEXT="sollte erweitert werden">
<icon BUILTIN="button_ok"/>
<node COLOR="#435e98" CREATED="1670528324475" ID="ID_681633951" MODIFIED="1670608109444" TEXT="entgleist bereits hier">
<icon BUILTIN="broken-line"/>
<node CREATED="1670528706677" ID="ID_511512599" MODIFIED="1670528730642" TEXT="zoomFactor * duration">
<icon BUILTIN="messagebox_warning"/>
<node CREATED="1670528736693" ID="ID_692399777" MODIFIED="1670528752135" TEXT="duration kann im Z&#xe4;hler eine sehr gro&#xdf;e Zahl haben"/>
<node CREATED="1670528767251" ID="ID_718316208" MODIFIED="1670528801175" TEXT="zoomFactor ist zwar limitiert..."/>
<node CREATED="1670528801884" ID="ID_1318256555" MODIFIED="1670528842450" TEXT="aber der Z&#xe4;hler kann MAX_PX_WIDTH haben"/>
</node>
<node CREATED="1670529398909" ID="ID_1760275990" MODIFIED="1670529444484" TEXT="kann nicht durch weitere Beschr&#xe4;nkungen gel&#xf6;st werden">
<richcontent TYPE="NOTE"><html>
<head>
</head>
<body>
<p>
sofern wir &#252;berhaupt relevant gro&#223;e Zeitspannen zulassen wollen
</p>
</body>
</html></richcontent>
<icon BUILTIN="yes"/>
</node>
<node COLOR="#338800" CREATED="1670529488664" ID="ID_1459847631" MODIFIED="1670608100497" TEXT="Aufgabe: pxWidth zuverl&#xe4;ssig berechnen">
<linktarget COLOR="#984981" DESTINATION="ID_1459847631" ENDARROW="Default" ENDINCLINATION="37;46;" ID="Arrow_ID_1118525297" SOURCE="ID_1603322916" STARTARROW="None" STARTINCLINATION="-82;-3;"/>
<icon BUILTIN="button_ok"/>
<node CREATED="1670529520436" ID="ID_1589666141" MODIFIED="1670529556855" TEXT="Beobachtung: Ergebnis ist quantisiert">
<icon BUILTIN="idea"/>
</node>
<node CREATED="1670530578527" ID="ID_106780218" MODIFIED="1670530592241" TEXT="aufteilen in Pixel f&#xfc;r die ganzen Sekunden + den Rest"/>
<node CREATED="1670533665256" ID="ID_1624584888" MODIFIED="1670533684900" TEXT="letztlich nur Bruchrechnen"/>
<node BACKGROUND_COLOR="#e0ceaa" COLOR="#690f14" CREATED="1670533759294" ID="ID_1337555507" MODIFIED="1670533795730">
<richcontent TYPE="NODE"><html>
<head>
</head>
<body>
<p>
<u>latente Gefahr</u>: Rest bei <i>giftiger Duration</i>
</p>
</body>
</html></richcontent>
<icon BUILTIN="clanbomber"/>
<node CREATED="1670533870555" ID="ID_649716018" MODIFIED="1670533882170" TEXT="nach meinem Verst&#xe4;ndnis ist aber die Duration stets berechnet"/>
<node CREATED="1670533882974" ID="ID_1544775451" MODIFIED="1670533906598" TEXT="und daher kann der Z&#xe4;hler nicht &gt; LIM_HAZARD sein"/>
</node>
</node>
</node>
<node CREATED="1670533969244" ID="ID_509879073" MODIFIED="1670534000608" TEXT="Problem: detox verf&#xe4;lscht die pxWidth">
<icon BUILTIN="messagebox_warning"/>
<node CREATED="1670534010893" ID="ID_719080732" MODIFIED="1670534023047" TEXT="in conformMetricToWindow(pxWidth)"/>
<node CREATED="1670534028996" ID="ID_218226232" MODIFIED="1670534040364" TEXT="detox(metric) ist unverzichtbar"/>
<node COLOR="#338800" CREATED="1670534041313" ID="ID_1590617796" MODIFIED="1670608092950" TEXT="mu&#xdf; dann aber korrigieren">
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<node CREATED="1670535342258" ID="ID_1603322916" MODIFIED="1670535392115" TEXT="kann nun erst mal ein Delta (zuverl&#xe4;ssig) ausrechnen">
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<icon BUILTIN="info"/>
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<node CREATED="1670535410497" ID="ID_1208592840" MODIFIED="1670535642174" TEXT="pixel = metric * duration"/>
<node CREATED="1670535643825" ID="ID_1568387866" MODIFIED="1670535934094" TEXT="Ansatz : px + &#x394; = (mn + &#x3b4;)/md * dur">
<icon BUILTIN="idea"/>
<node CREATED="1670535754235" ID="ID_1587392333" MODIFIED="1670535810351" TEXT="mn/md*dur + &#x394; = md/md*dur + &#x3b4;/md*dur"/>
<node CREATED="1670535823465" ID="ID_250829706" MODIFIED="1670607989952" STYLE="bubble" TEXT="&#x27f9; &#x394; = &#x3b4;/md*dur &#x27fa; &#x3b4; = &#x394;*md/dur"/>
<node BACKGROUND_COLOR="#e0ceaa" COLOR="#690f14" CREATED="1670608025807" ID="ID_303221939" MODIFIED="1670608049361" TEXT="ist aber nicht genau">
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</node>
<node BACKGROUND_COLOR="#e0ceaa" COLOR="#690f14" CREATED="1670536172779" ID="ID_118806151" MODIFIED="1670608043975" TEXT="Vorsicht Divisionsrest!">
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<node COLOR="#d10909" CREATED="1670607546820" ID="ID_1768315854" MODIFIED="1670607657973" TEXT="habe naiv eingesetzt px = mn/md * dn/dd">
<richcontent TYPE="NOTE"><html>
<head>
</head>
<body>
<p>
das unterschl&#228;gt den Divisionsrest. Oder anders gesagt, die Integer-Division ist keine lineare Funktion, die man einfach so umkehren kann
</p>
</body>
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<icon BUILTIN="stop-sign"/>
</node>
<node CREATED="1670536172779" ID="ID_1511677021" MODIFIED="1670539160426" TEXT="Divisionsrest: px + r &#x2254; mn/md*dur">
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<node CREATED="1670535823465" ID="ID_1442936314" MODIFIED="1670539218793" TEXT="&#x27f9; &#x394;+r = &#x3b4;/md*dur">
<node CREATED="1670539261437" ID="ID_1632113284" MODIFIED="1670539263858" TEXT="r &lt; 1"/>
</node>
<node CREATED="1670539193095" ID="ID_393314988" MODIFIED="1670539228949" TEXT=" &#x27fa; &#x3b4; = &#x394;*md/dur + r*md/dur"/>
</node>
<node CREATED="1670547897187" ID="ID_567199472" MODIFIED="1670547982037" TEXT="wobei px = trunc(mn/md*dur)"/>
<node BACKGROUND_COLOR="#fdfdcf" COLOR="#ff0000" CREATED="1670550198610" ID="ID_108770284" MODIFIED="1670550213350" TEXT="Berechnung wrappt">
<icon BUILTIN="stop-sign"/>
<node CREATED="1670607729254" ID="ID_236985538" MODIFIED="1670607748664" TEXT="kann weder direkt die (an sich linerare) Beziehung umkehren"/>
<node CREATED="1670607749430" ID="ID_44338618" MODIFIED="1670607760342" TEXT="noch kann ich den modulus berechnen">
<node CREATED="1670607771857" ID="ID_432964800" MODIFIED="1670607787595" TEXT="mod = (mn*dn) % (md*dd)"/>
<node CREATED="1670607788343" ID="ID_1369221920" MODIFIED="1670607952820" TEXT="vor allem der erste Faktor k&#xf6;nnte wrappen">
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<node CREATED="1670607798845" ID="ID_1832446179" MODIFIED="1670607935324" TEXT="es gibt hier keine Garantien">
<richcontent TYPE="NOTE"><html>
<head>
</head>
<body>
<p>
anders im Nenner;&#160;&#160;md * dd ist garantiert berechenbar, sofern die Duration selber aus einem time::Duration gebildet wurde (und md ist durch das detox() limitiert worden)
</p>
</body>
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</node>
</node>
</node>
<node CREATED="1670550618233" ID="ID_717977520" MODIFIED="1670550628155" TEXT="hngra">
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<node COLOR="#435e98" CREATED="1670598462329" ID="ID_1937499858" MODIFIED="1670608058331" TEXT="Einsicht: Problem liegt bei der Umkehrung">
<richcontent TYPE="NOTE"><html>
<head>
</head>
<body>
<p>
Der Rechenweg ist hier eine &#187;Einbahnstra&#223;e&#171; : durch einen Kniff ist es gelungen die Quatisierung zu berechnen Metrik &#10236; pxWidth. Aber die Umkehrfunktion k&#246;nnen wir nicht berechnen, weil es in der Berechnung zu einem &#220;berlauf kommt. Daher k&#246;nnen wir die Fehler-Korrektur nicht einfach ausrechnen, weil wir nicht einfach von einen Pixel-&#916; auf ein Metrik-&#916; zur&#252;ckrechnen k&#246;nnen
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<icon BUILTIN="idea"/>
<node COLOR="#435e98" CREATED="1670598658291" ID="ID_215061275" MODIFIED="1670608011680" TEXT="Newton-Iteration k&#xf6;nnte ein eleganter L&#xf6;sungsweg sein">
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<icon BUILTIN="idea"/>
<node CREATED="1648160051303" ID="ID_1360701786" MODIFIED="1670600088741" TEXT="setze x&#x2099; &#x2254; mn und f(x&#x2099;) &#x2254; trunc{ x&#x2099; * dn/(md*dd) } - sollPx"/>
<node CREATED="1648160051303" ID="ID_1815070178" MODIFIED="1670600102106" TEXT="x&#x2099; &#x2254; x&#x2099; - f(x&#x2099;)/f&apos;(x&#x2099;)">
<node CREATED="1670600262299" ID="ID_200772347" MODIFIED="1670600289470" TEXT="trunc{&#x2022;} ist nicht differenzierbar">
<icon BUILTIN="messagebox_warning"/>
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<node CREATED="1670600297357" ID="ID_1661748842" MODIFIED="1670600371342" TEXT="berechne ersatzweise die nicht-Quantisierte lineare Beziehung">
<richcontent TYPE="NOTE"><html>
<head>
</head>
<body>
<p>
...das mag unsinnig erscheinen, aber der Punkt ist, wir k&#246;nnen diese lineare Beziehung nur eingeschr&#228;nkt numerisch berechnen
</p>
</body>
</html></richcontent>
</node>
<node CREATED="1670601331854" ID="ID_1987937364" MODIFIED="1670601421702" TEXT="aber: f(x&#x2099;) &#x2254; &#x394;&#x2099; = istPx-sollPx = trunc{ x&#x2099; * dn/(md*dd) } - sollPx"/>
<node CREATED="1670600125528" ID="ID_44998069" MODIFIED="1670600375236" TEXT="&#x27f9; f&apos;(x&#x2099;) = dn/(md*dd)">
<node CREATED="1670600381136" ID="ID_1737301130" MODIFIED="1670600391140" TEXT="Faktor md*dd ist zu gro&#xdf;"/>
<node CREATED="1670600392117" ID="ID_972774071" MODIFIED="1670600415383" TEXT="&#x27f9; Konsequenz: N&#xe4;herung per floating-point rechnen"/>
</node>
<node CREATED="1670600444488" ID="ID_1680948621" MODIFIED="1670608003557" STYLE="bubble" TEXT="Schritt: mn&#x2099;&#x2081; &#x2254; mn&#x2099; - &#x394;&#x2099; * md*dd / dn"/>
</node>
</node>
<node CREATED="1670600703979" ID="ID_1488808337" MODIFIED="1670600728131" TEXT="effektiv war die erste naive Rechnung ein Newtion-Iterationsschritt"/>
<node COLOR="#338800" CREATED="1670600731863" ID="ID_186434159" MODIFIED="1670608063458" TEXT="Implementierung">
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<node COLOR="#338800" CREATED="1670600737086" ID="ID_844920706" MODIFIED="1670608065992" TEXT="Ziel-Test in while-Schleife einbauen">
<icon BUILTIN="button_ok"/>
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<node COLOR="#338800" CREATED="1670602664659" ID="ID_1968097363" MODIFIED="1670608071566" TEXT="Delta und Schritt-Berechnung in floating-point">
<icon BUILTIN="button_ok"/>
</node>
<node COLOR="#435e98" CREATED="1670608072601" ID="ID_693088307" MODIFIED="1670608085799" TEXT="Berechnung damit sicher, elegant (und funktioniert auch)"/>
</node>
</node>
</node>
</node>
</node>
<node BACKGROUND_COLOR="#eef0c5" COLOR="#990000" CREATED="1670520779106" ID="ID_442688956" MODIFIED="1670608133729" TEXT="dann nochmal giftigen maximal-Zoom-out">
<icon BUILTIN="pencil"/>
</node>
</node>
</node>
<node BACKGROUND_COLOR="#eee5c3" COLOR="#990000" CREATED="1668555072594" ID="ID_742229180" MODIFIED="1669473993488" TEXT="Ansteuern exterm gro&#xdf;er Zeit-Positionen">
<icon BUILTIN="flag-yellow"/>
<node CREATED="1669475536331" ID="ID_486161883" MODIFIED="1669475548565" TEXT="setVisiblePos mit extremer Time"/>
<node CREATED="1669475549345" ID="ID_234786683" MODIFIED="1669475556499" TEXT="setVisiblePos mit extremem Faktor"/>
<node CREATED="1669479474484" ID="ID_1657847338" MODIFIED="1669479489366" TEXT="alle Mutatoren, die conformWindowToMetric() verwenden"/>
<node CREATED="1669479474484" ID="ID_1657847338" MODIFIED="1669479489366" TEXT="alle Mutatoren, die conformWindowToMetric() verwenden">
<node CREATED="1670520100834" ID="ID_636101408" MODIFIED="1670520114018" TEXT="das sind nicht viele (&#xfc;berraschenderweise)">
<node CREATED="1670520136501" ID="ID_1373384288" MODIFIED="1670520142854" TEXT="mutateDuration(FSecs)"/>
<node CREATED="1670520143698" ID="ID_113302808" MODIFIED="1670520150597" TEXT="und ensureInvariants()"/>
</node>
<node CREATED="1670520153513" ID="ID_574049062" MODIFIED="1670520170810" TEXT="wozu? weil dort das Window anteilig neu positioniert wird"/>
<node CREATED="1670520176781" ID="ID_171252675" MODIFIED="1670520196129" TEXT="&#x27f9; gef&#xe4;hrlich wenn die bestehende Window-Pos gef&#xe4;hrlich ist"/>
<node CREATED="1670520232861" ID="ID_1248431637" MODIFIED="1670520238057" TEXT="Szenario">
<node CREATED="1670520238693" ID="ID_1734279608" MODIFIED="1670520244664" TEXT="sehr kleines Fenster"/>
<node CREATED="1670520245444" ID="ID_428615363" MODIFIED="1670520257330" TEXT="fast aber nicht ganz an Time::MIN"/>
<node CREATED="1670520259018" ID="ID_591142628" MODIFIED="1670520301032" TEXT="vergr&#xf6;&#xdf;ern auf MutatDuration - aWeng"/>
</node>
</node>
</node>
<node BACKGROUND_COLOR="#eee5c3" COLOR="#990000" CREATED="1668555157385" ID="ID_1157546672" MODIFIED="1669473993486" TEXT="Time-wrap nach extremem Offset">
<icon BUILTIN="flag-yellow"/>
@ -40141,7 +40395,7 @@
<icon BUILTIN="button_ok"/>
</node>
<node COLOR="#338800" CREATED="1669479930775" ID="ID_196873456" MODIFIED="1670016092876" TEXT="Fall-3 : setVisiblePos mit giftigem faktor">
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<icon BUILTIN="button_ok"/>
<node COLOR="#435e98" CREATED="1669682888293" HGAP="67" ID="ID_1431682003" MODIFIED="1670016089041" TEXT="erweist sich als ziemlich schwer unter Kontrolle zu bekommen" VSHIFT="-1">
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@ -62758,6 +63012,34 @@
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<node CREATED="1512923647255" ID="ID_1800845122" MODIFIED="1557498707237" TEXT="Plug-in"/>
</node>
<node COLOR="#435e98" CREATED="1670599468591" HGAP="175" ID="ID_1144378342" MODIFIED="1670599561156" POSITION="left" TEXT="Methoden" VSHIFT="-32">
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<node CREATED="1648160042105" ID="ID_681739014" MODIFIED="1648160050003" TEXT="finde Nullstelle einer Funktion"/>
<node CREATED="1648160051303" ID="ID_1883017382" MODIFIED="1648160167185" TEXT="x&#x2099; &#x2254; x&#x2099; - f(x&#x2099;)/f&apos;(x&#x2099;)"/>
<node CREATED="1648160182198" ID="ID_286076492" MODIFIED="1648160199375" TEXT="oft gen&#xfc;gt guter Startwert + ein/zwei Iterationen"/>
<node CREATED="1670599038025" ID="ID_1741473977" MODIFIED="1670599307446" TEXT="Konvergenz nur gut f&#xfc;r Startwert nahe an der L&#xf6;sung">
<richcontent TYPE="NOTE"><html>
<head>
</head>
<body>
<p>
Die Methode steht und f&#228;llt damit, da&#223; die Tangente n&#228;her zur L&#246;sung zeigt, als der aktuelle (Start)Wert. Sonst kann die Iteration in weite Oszillationen m&#252;nden und sich ggfs sogar in einem neben-Minimum festbei&#223;en. Die Newton-Methode spielt daher ihr Potential einer senationell schnellen Konvergenz nur aus, wenn man <i>anderweitig schon eine sehr gute N&#228;herung als Startwert hat.</i>
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