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Author SHA1 Message Date
Emmanuele Bassi
79acb088e7 Remove mentions of the FSF address
Since using addresses that might change is something that finally
the FSF acknowledge as a plausible scenario (after changing address
twice), the license blurb in the source files should use the URI
for getting the license in case the library did not come with it.

Not that URIs cannot possibly change, but at least it's easier to
set up a redirection at the same place.

As a side note: this commit closes the oldes bug in Clutter's bug
report tool.

http://bugzilla.openedhand.com/show_bug.cgi?id=521
2010-03-01 12:56:10 +00:00
Emmanuele Bassi
9c8f881878 analysis: ClutterTimeline
Remove an unused variable.
2010-02-12 14:57:50 +00:00
Emmanuele Bassi
9dc012c07d [timeline] Account for clock roll backs between frames
If the system clock rolls back between two frames then we need
to account for the change, to avoid stopping the timeline.

The best option, since a roll back can be any arbitrary amount
of milliseconds, is to skip a frame.

Fixes bug:

  http://bugzilla.moblin.org/show_bug.cgi?id=3839
2009-09-16 11:57:57 +01:00
Emmanuele Bassi
a79d6228aa Remove the last few fixed-point entry points
The last fixed-point entry points are just a few, and trivial. The
end user is expected to do the conversion using the CoglFixed type
and macros.
2009-06-19 16:38:35 +01:00
Neil Roberts
f1000db3ca [timelines] Improve marker hit check and don't fudge the delta
Markers added at the start of the timeline need to be special cased
because we effectively check whether the marker time is greater than
the old frame time or less than or equal to the new frame time but we
never actually emit a frame for the start of the timeline.

If the timeline is looping then it adjusts the position to interpolate
a wrapped around position. However we do not emit a new frame after
setting this position so we need to check for markers again there.

clutter_timeline_get_delta should return the actual wall clock time
between emissions of the new-frame signal - even if the elapsed time
has been fudged at the end of the timeline. To make this work it no
longer directly manipulates priv->msecs_delta but instead passes a
delta value to check_markers.
2009-06-11 12:14:53 +01:00
Neil Roberts
9021aa2909 Revert "[timeline] Don't clamp the elapsed time when a looping tl reaches the end"
This reverts commit 9c5663d671.

The patch was causing problems for applications that expect the
elapsed_time to be at either end of the timeline when the completed
signal is fired. For example test-behave swaps the direction of the
timeline in the completed handler but if the time has overflowed the
end then the timeline would only take a short time to get back the
beginning. This caused the animation to just vibrate around the
beginning.
2009-06-11 11:46:41 +01:00
Neil Roberts
9c5663d671 [timeline] Don't clamp the elapsed time when a looping tl reaches the end
The new-frame signal of a timeline was previously guaranteed to be
emitted with the elapsed_time set to the end before it emits the
completed signal. This doesn't necessarily make sense for looping
timelines because it would cause the elapsed time to be clamped to a
slightly off value whenever the timeline restarts. This patch makes it
perform the wrap around before emitting the new-frame signal so that
the elapsed time always corresponds to the time elapsed since the
timeline was started.

Additionally it no longer fudges the msecs_delta property to make the
marker check work so clutter_timeline_get_delta will always return the
wall clock time since the last frame.
2009-06-10 17:47:33 +01:00
Owen W. Taylor
6705ce6c6a Move elapsed-time calculations into ClutterTimeline
Instead of calculating a delta in the master clock, and passing that
into each timeline, make each timeline individually responsible for
remembering the last time and computing the delta.

This:

 - Fixes a problem where we could spin infinitely processing
   timeline-only frames with < 1msec differences.
 - Makes timelines consistently start timing on the first frame;
   instead of doing different things for the first started timeline
   and other timelines.
 - Improves accuracy of elapsed time computations by avoiding
   accumulating microsecond => millisecond truncation errors.

http://bugzilla.openedhand.com/show_bug.cgi?id=1637

Signed-off-by: Emmanuele Bassi <ebassi@linux.intel.com>
2009-06-09 15:03:56 +01:00
Owen W. Taylor
ebaec9798e Simplify timeout list handling for the master clock
Instead of keeping a list of all timelines, and connecting to
signals and weak notifies, simply keep a list of running timelines;
this greatly simplifies both the book-keeping, and also determining
if there are any running timelines.

http://bugzilla.openedhand.com/show_bug.cgi?id=1637

Signed-off-by: Emmanuele Bassi <ebassi@linux.intel.com>
2009-06-09 15:03:55 +01:00
Emmanuele Bassi
19c2e66398 [docs] Various gtk-docs fixes 2009-06-09 14:47:36 +01:00
Owen W. Taylor
fd0a490ced Properly adjust msecs_delta when clamping elapsed time
When we complete a timeline, we clamp the elapsed_time variable
to the range of the timeline. We need to adjust msecs_delta so that
when we check for hit markers we have the correct interval.

http://bugzilla.openedhand.com/show_bug.cgi?id=1641

Signed-off-by: Emmanuele Bassi <ebassi@linux.intel.com>
2009-06-08 15:03:16 +01:00
Owen W. Taylor
276952d6f9 Fix stopping a timeline
Correctly apply De Morgan's laws to the short-circuit test in
clutter_timeline_pause(); it was short-circuiting always and
never actually pausing.

http://bugzilla.openedhand.com/show_bug.cgi?id=1629

Signed-off-by: Emmanuele Bassi <ebassi@linux.intel.com>
2009-06-06 13:01:17 +01:00
Neil Roberts
9c7afe0c5b [timeline] Remove the concept of frames from timelines
Timelines no longer work in terms of a frame rate and a number of
frames but instead just have a duration in milliseconds. This better
matches the working of the master clock where if any timelines are
running it will redraw as fast as possible rather than limiting to the
lowest rated timeline.

Most applications will just create animations and expect them to
finish in a certain amount of time without caring about how many
frames are drawn. If a frame is going to be drawn it might as well
update all of the animations to some fraction of the total animation
rather than rounding to the nearest whole frame.

The 'frame_num' parameter of the new-frame signal is now 'msecs' which
is a number of milliseconds progressed along the
timeline. Applications should use clutter_timeline_get_progress
instead of the frame number.

Markers can now only be attached at a time value. The position is
stored in milliseconds rather than at a frame number.

test-timeline-smoothness and test-timeline-dup-frames have been
removed because they no longer make sense.
2009-06-04 13:21:57 +01:00
Emmanuele Bassi
181ba67114 Revert commit 762873e7
The commit 762873e79e is completely
and utterly wrong and I should have never pushed it.

Serves me well for trying to work on three different branches and
on three different things.
2009-06-03 14:05:05 +01:00
Emmanuele Bassi
762873e79e [master clock] Avoid excessive redraws
Currently, the clock source spins a redraw every time there is at
least a timeline running. If the timelines were not advanced in
the previous frame, though, because their interval is larger than
the vblanking interval then this will lead to excessive redraws of
the scenegraph even if nothing has changed.

To avoid this a simple guard should be set by the MasterClock::advance
method in case no timeline was effectively advanced, and checked
before dispatching the stage redraws.
2009-06-03 12:02:56 +01:00
Emmanuele Bassi
7afdfb080b [docs] Document the destructor for Timeline
The rest of the API reference lists the destructor for the class
inside the constructor's return value -- except Timeline.
2009-05-06 16:42:57 +01:00
Neil Roberts
fa9efe4828 Accumulate small deltas
The clutter frame source tries to average out the frame deltas so that
if one frame takes 1 interval plus a little bit of extra time then the
next frame will be 1 interval minus that little bit of extra
time. Therefore the deltas can sometimes be less than the frame
interval. ClutterTimeline should accumulate these small differences
otherwise it will end up missing out frames so the total duration of
the timeline will be a lot longer.

For example this was causing test-actors to appear to run very slow.
2009-05-01 15:12:08 +01:00
Emmanuele Bassi
5be29cf9bc [timeline] Expose the msec advancement
The method of ClutterTimeline that advances the timeline by a
delta (in millisecond) is going to be useful for testing the
timeline's behaviour -- and unbreak the timeline test suite that
was broken by the MasterClock merge.
2009-05-01 15:05:51 +01:00
Emmanuele Bassi
678f99677f Use a single master "clock" to drive timelines
Currently, all timelines install a timeout inside the TimeoutPool
they share. Every time the main loop spins, all the timeouts are
updated. This, in turn, will usually lead to redraws being queued
on the stages.

This behaviour leads to the potential starvation of timelines and
to excessive redraws.

One lesson learned from the games developers is that the scenegraph
should be prepared in its entirety before the GL paint sequence is
initiated. This means making sure that every ::new-frame signal
handler is called before clutter_redraw() is invoked.

In order to do so a TimeoutPool is not enough: we need a master
clock. The clock will be responsible for advancing all the active
timelines created inside a scene, but only when the stage is
being redrawn.

The sequence is:

  + queue_redraw() is invoked on an actor and bubbles up
    to the stage

  + if no redraw() has already been scheduled, install an
    idle handler with a known priority

  + inside the idle handler:

    - advance the master clock, which will in turn advance
      every playing timeline by the amount of milliseconds
      elapsed since the last redraw; this will make every
      playing timeline emit the ::new-frame signal

    - queue a relayout

    - call the redraw() method of the backend

This way we trade multiple timeouts with a single frame source
that only runs if a timeline is playing and queues redraws on
the various stages.
2009-04-24 15:28:15 +01:00
Chris Lord
cc21a4aa5f [ClutterTimeline] Fix clutter_timeline_set_delay
When setting a delay, timeout_add was being used with msecs. timeout_add
takes fps since the fix to bug #1495. Delay now uses g_timeout_add
instead.
2009-03-26 20:29:23 +00:00
Emmanuele Bassi
ccca24ab76 Remove usage of the grave accent as quotation mark
See:

  http://www.cl.cam.ac.uk/~mgk25/ucs/quotes.html

This should make Thomas happy.
2009-03-17 14:13:31 +00:00
Neil Roberts
a93a93d007 Count timeline frames using the FPS instead of an integer interval
Bug 1495 - Timelines run 4% short

Previously the timelines were timed by calculating the interval
between each frame stored as an integer number of milliseconds so some
precision is lost. For example, requesting 60 frames per second gets
converted to 16 ms per frame which is actually 62.5 frames per
second. This makes the timeline shorter by 4%.

This patch merges the common code for timing from the timeout pools
and frame sources into an internal clutter-timeout-interval file. This
stores the interval directly as the FPS and counts the number of
frames that have been reached instead of the elapsed time.
2009-03-16 15:40:18 +00:00
Emmanuele Bassi
720341b301 Move ClutterTimeline to CoglFixed
The ClutterTimeline::get_progressx() method should return a
CoglFixed, now that ClutterFixed is being deprecated.
2009-03-10 12:38:03 +00:00
Owen W. Taylor
c5afd98416 Add gobject-introspection annotations
Add annotations such as (transfer-none) (out) (element-type ClutterActor),
and so forth to the doc comments as appropriate.

The annotations added here are a combination of the annotations previously
in gir-repository for Clutter and annotations found in a review of all
return values with that were being parsed with a transfer of "full".

http://bugzilla.openedhand.com/show_bug.cgi?id=1452

Signed-off-by: Emmanuele Bassi <ebassi@linux.intel.com>
2009-02-20 12:09:07 +00:00
Emmanuele Bassi
1816106047 [timeline] Set the n_markers out paramater
Bug 1464 - clutter_timeline_list_markers should set n_markers=0 when
           there are no markers

If no markers are registered and we bail out we should also set the
n_markers out parameter to 0 so that code checking the number of
markers will still work.
2009-02-20 11:47:14 +00:00
Emmanuele Bassi
2138b1cbb2 Bug 1388 - Clarify signal emission for advance_to_marker()
Like clutter_timeline_advance(), calling advance_to_marker() will
not emit ::new-frame for the frame where the marker is set on; it
will also not emit ::marker-reached for the marker we are advancing
the timeline to.
2009-01-27 11:25:06 +00:00
Emmanuele Bassi
8608d103f8 Bug 1387 - Clarify new-frame signal emission with advance()
When calling clutter_timeline_advance(), a timeline will not emit
the ::new-frame signal for the frame we are advancing to, as this
would break the invariants of the timeline behaviour.

The documentation should make this clear.
2009-01-27 11:18:09 +00:00
Emmanuele Bassi
43bd4e5d3f [timeline] Check the fps property range in the ctor
The clutter_timeline_new() constructor is not checking the full
range of the passed :fps property. The ParamSpec of the property
and the setter method perform this check, so the ctor should as
well.
2009-01-27 10:35:50 +00:00
Emmanuele Bassi
f753847851 [timeline] Move a complex condition into its own function
The "is-timeline-complete" condition is pretty long, spanning
four lines and four logical sub-conditions. It is possible to
neatly move it into an is_complete() function and make the
code more readable.
2009-01-27 10:33:44 +00:00
Emmanuele Bassi
092db1098c [timeline] Intern signal names
The signal names are static string and thus should be interned
so that Glib can do a simple pointer comparison whenever needed,
instead of a strcmp().
2009-01-27 10:32:15 +00:00
Emmanuele Bassi
7863ca4a55 [timeline] Whitespace fixes 2009-01-27 10:31:53 +00:00
Emmanuele Bassi
2be9cdc267 [timeline] Documentation and comment fixes
The long description of the ClutterTimeline class is very C
developer-oriented. Since many language bindings will refer to
the C API reference we should probably be more verbose and
language agnostic -- at least in the class description.

The methods documentation also requires a little pass to increase
the consistency of the terminology, the grammar and the syntax.

Finally, comments never killed anyone.
2009-01-27 10:27:33 +00:00
Emmanuele Bassi
763de185e9 [timeline] Create markers hash tables on demand
Since not every timeline will have markers it's unfair to make
all of them crete two empty hash tables (with a preallocated
fixed size).

This commit moves the responsibility of creating the hash tables
to the marker API itself, and adds the relative checks.
2009-01-27 09:51:45 +00:00
Emmanuele Bassi
1e071ed859 [timeline] Limit timelines to 1000 frames per second
Since we are using milliseconds granularity to integrate timelines
with the GLib main loop, we cannot allow values of the :fps
property bigger than 1000. This means validating the fps value both
in the GParamSpec and the clutter_timeline_set_speed() accessor
function.

This should also fix floating point exceptions when trying to
perform "n_frames = milliseconds / (1000 / fps)".

See bug 1354:

  http://bugzilla.openedhand.com/show_bug.cgi?id=1354
2009-01-27 09:51:45 +00:00
Neil Roberts
4d7caa4bd5 [clutter-timeline] Remove the code for backwards timelines in get_progress
The special check to invert the progress when the timeline direction
is backwards is not necessary because the actual frame number will be
decreasing in that case. Inverting just makes it progress forwards
again.

This is more apparent since the float-alpha-value branch merge because
the clutter_linear function directly returns the value from
get_progress. For example in test-depth, the animations loop instead
of oscillating back and forth.
2009-01-23 22:57:36 +00:00
Robert Bragg
e82f656590 [Automatic fixed-to-float.sh change] Applies all scripted changes
This is the result of running a number of sed and perl scripts over the code to
do 90% of the work in converting from 16.16 fixed to single precision floating
point.

Note: A pristine cogl-fixed.c has been maintained as a standalone utility API
      so that applications may still take advantage of fixed point if they
      desire for certain optimisations where lower precision may be acceptable.

Note: no API changes were made in Clutter, only in Cogl.

Overview of changes:
- Within clutter/* all usage of the COGL_FIXED_ macros have been changed to use
the CLUTTER_FIXED_ macros.

- Within cogl/* all usage of the COGL_FIXED_ macros have been completly stripped
and expanded into code that works with single precision floats instead.

- Uses of cogl_fixed_* have been replaced with single precision math.h
alternatives.

- Uses of COGL_ANGLE_* and cogl_angle_* have been replaced so we use a float for
angles and math.h replacements.
2009-01-20 16:20:54 +00:00
Emmanuele Bassi
2410f74e29 2008-12-05 Emmanuele Bassi <ebassi@linux.intel.com>
Bug 1309 - clutter_timeline_new and clutter_timeline_set_speed
	have two standard of the fps limitation

	* clutter/clutter-timeline.c:
	(clutter_timeline_class_init): Set the maximum value of the
	:fps property to be G_MAXUINT. (Zhang Wei)
2008-12-05 17:44:12 +00:00
Neil Roberts
74ba6fd8c4 * clutter/clutter-timeline.c:
* clutter/clutter-texture.c:
	* clutter/clutter-stage.c:
	* clutter/clutter-label.c:
	* clutter/clutter-behaviour-path.c:
	* clutter/clutter-actor.c: Fix the 'Since' annotation in the
	gtk-doc.
2008-12-05 14:08:06 +00:00
Neil Roberts
fc8c2c5d9b Bug 1207 - Timelines sometime miss markers
* clutter/clutter-timeline.c (timeline_timeout_func): Move the
	code for firing the new-frame and marker-reached signals into a
	separate static function so that it can also be called when the
	last frame is reached. Also fix an issue where the frame numbers
	were changed in the wrong direction when detecting missed markers
	in a reversed timeline. Based on a patch by Michael Boccara.

	* tests/test-timeline.c: Now tries to automatically verify whether
	the test worked by keeping track of all the signal emissions. The
	timelines are run a second time with an extra timeout that causes
	delays to simulate skipped frames.
2008-11-03 12:42:17 +00:00
Emmanuele Bassi
911b395c8a 2008-10-30 Emmanuele Bassi <ebassi@linux.intel.com>
Bug 1209 - Move fixed point API in COGL

	* clutter/cogl/cogl-fixed.h:
	* clutter/cogl/cogl.h.in:
	* clutter/cogl/common/Makefile.am:
	* clutter/cogl/common/cogl-fixed.c: Add fixed point API, modelled
	after the ClutterFixed. The CoglFixed API supercedes the ClutterFixed
	one and avoids the dependency of COGL on Clutter's own API.

	* clutter/cogl/common/cogl-clip-stack.c:
	* clutter/cogl/common/cogl-primitives.c:
	* clutter/cogl/common/cogl-primitives.h: Update internal usage of
	ClutterFixed to CoglFixed.

	* clutter/cogl/gl/Makefile.am:
	* clutter/cogl/gl/cogl-primitives.c:
	* clutter/cogl/gl/cogl-texture.c:
	* clutter/cogl/gl/cogl.c: Ditto, in the GL implementation of the
	COGL API.

	* clutter/cogl/gles/Makefile.am:
	* clutter/cogl/gles/cogl-fbo.c:
	* clutter/cogl/gles/cogl-gles2-wrapper.c:
	* clutter/cogl/gles/cogl-primitives.c:
	* clutter/cogl/gles/cogl-texture.c:
	* clutter/cogl/gles/cogl.c: Ditto, in the GLES implementation of
	the COGL API.

	* clutter/pango/pangoclutter-glyph-cache.c:
	* clutter/pango/pangoclutter-glyph-cache.h: Ditto, in the Pango
	renderer glyphs cache.

	* clutter/clutter-fixed.c:
	* clutter/clutter-fixed.h: ClutterFixed and related API becomes
	a simple transition API for bindings and public Clutter API.

	* clutter/clutter-actor.c:
	* clutter/clutter-alpha.c:
	* clutter/clutter-backend.c:
	* clutter/clutter-behaviour-depth.c:
	* clutter/clutter-behaviour-ellipse.c:
	* clutter/clutter-behaviour-path.c:
	* clutter/clutter-behaviour-rotate.c:
	* clutter/clutter-behaviour-scale.c:
	* clutter/clutter-clone-texture.c:
	* clutter/clutter-color.c:
	* clutter/clutter-entry.c:
	* clutter/clutter-stage.c:
	* clutter/clutter-texture.c:
	* clutter/clutter-timeline.c:
	* clutter/clutter-units.h: Move from the internal usage of
	ClutterFixed to CoglFixed.

	* doc/reference/clutter/clutter-sections.txt:
	* doc/reference/cogl/cogl-docs.sgml:
	* doc/reference/cogl/cogl-sections.txt: Update the documentation.

	* tests/test-cogl-tex-tile.c:
	* tests/test-project.c: Fix tests after the API change

	* README: Add release notes.
2008-10-30 16:37:55 +00:00
Neil Roberts
fc73b84002 Bug 1071 - clutter_timeline_get_duration doesn't always work
* clutter/clutter-timeline.c: Calculate the 'duration' property
	on-demand instead of storing it as a member variable. Notify
	duration property changes whenever the fps or num_frames changes.
2008-08-01 11:09:43 +00:00
Neil Roberts
7df15542e4 * clutter/clutter-timeline.c (clutter_timeline_list_markers): When
requesting the list of markers it was returning the marker data as
	a string instead of the name so it was copying garbage.
2008-07-26 14:00:32 +00:00
Emmanuele Bassi
dd185940c0 2008-06-25 Emmanuele Bassi <ebassi@openedhand.com>
* clutter/clutter-main.h: Make the priority constants public.

	* clutter/clutter-stage.c: Use CLUTTER_PRIORITY_REDRAW.

	* clutter/clutter-timeline.c: Use CLUTTER_PRIORITY_TIMELINE.
2008-06-25 16:46:42 +00:00
Emmanuele Bassi
8996406189 2008-06-15 Emmanuele Bassi <ebassi@openedhand.com>
Bug #967 - Mismatch of Timeline::marker-reached signal signature

	* clutter/clutter-marshal.list:
	* clutter/clutter-timeline.c:
	(clutter_timeline_class_init): Fix the type of the frame_num
	argument in the ::marker-reached signal creation to match the
	signal class handler. (Armin Burgmeier)
2008-06-15 12:50:05 +00:00
Emmanuele Bassi
8ff6cec829 2008-06-12 Emmanuele Bassi <ebassi@openedhand.com>
* clutter/clutter-actor.[ch]: Documentation fixes.

	* clutter/clutter-backend.c: Documentation fixes.

	* clutter/clutter-container.h: Documentation fixes.

	* clutter/clutter-fixed.c (clutter_qdivx): Fix the return
	value to be after the description.

	* clutter/clutter-texture.[ch]: Documentation fixes.

	* clutter/clutter-timeline.c: Documentation fixes.
2008-06-12 11:43:25 +00:00
Tommi Komulainen
863837baec 7 small miscellaneous fixes
Bug#959 - Multiple minor improvements

	* configure.ac: pick up GDKPIXBUF_PREFIX from gdk-pixbuf-2.0
	module, not pango

	* clutter/clutter-keysyms-table.h: cosmetic fix for ifdef guard
	name in the comment (leftover from earlier commit)

	* tests/test-textures.c: don't depend on GdkPixbuf as we're not
	using any actual features from it, just plain pixel buffer
	manipulation

	* clutter/clutter-timeline.c
	* clutter/clutter-timeline.h (clutter_timeline_list_markers): Use
	gsize* to return number of items, not guint*
	* tests/test-paint-wrapper.c: use correct type (guint*) in call
	to clutter_actor_get_size()

	* tests/test-depth.c (janus_group): properly take height2 into
	account when calculating needed height for the rectangle

	* tests/test-cogl-tex-getset.c: use rowstride, not width*4, when
	calculating pixel offsets

	* tests/test-cogl-tex-getset.c: Don't assume/force RGBA format,
	also support ARGB format (needed with quartz imageloader.)
2008-06-10 06:37:46 +00:00
Robert Bragg
c76e576141 2008-05-12 Robert Bragg <bob@openedhand.com>
* clutter/clutter-timeline.c:
	Adds clutter-timeline documentation RE: r2337, explaining
	the current timeline semantics.
2008-05-12 15:18:38 +00:00
Neil Roberts
e97cba0162 * clutter/clutter-timeline.c (clutter_timeline_get_progressx):
Changed to use clutter_qdiv instead of CLUTTER_FIXED_DIV otherwise
	it can't cope with timelines with more than 255 frames.
2008-04-18 13:51:16 +00:00
Neil Roberts
827c26757e Applied patch from bug #881
* clutter/clutter-frame-source.h: 
	* clutter/clutter-frame-source.c:
	New files that contain a replacement for g_timeout that try to
	cope with system delays.

	* clutter/Makefile.am: Added clutter-frame-source.{c,h}

	* clutter/clutter-timeline.c (timeout_add): Use a frame source
	instead of a g_timeout.

	* clutter/clutter-main.c (clutter_threads_add_frame_source_full)
	(clutter_threads_add_frame_source): New public functions to wrap a
	frame source and grab the Clutter mutex.

	* clutter/clutter-timeout-pool.c: Now calculates the timeout
	expiration times in the same way as a frame source does so that it
	counts time in frame intervals instead of setting the next
	expiration time as an offset from the current time.
2008-04-17 16:50:23 +00:00
Neil Roberts
f7b53e6004 Bug #853
* clutter/clutter-timeline.c (clutter_timeline_get_progressx): Fix
	arithmetic for calculating the reverse progress when the timeline
	is backward. (Should subtract from one instead of taking the
	reciprocal).
2008-04-14 11:07:34 +00:00