Commit Graph

45 Commits

Author SHA1 Message Date
caryclark
aec2510125 minor fixes to cubics code and overall alignment of how bounds and tops are computed for all curve types
All but 17 extended tests work.

A helper function is privately added to SkPath.h to permit a test to modify a given point in a path.

BUG=skia:3588

Review URL: https://codereview.chromium.org/1107353004
2015-04-29 08:28:30 -07:00
caryclark
08bc8488fa fix multiple intersection logic
When three or more curves intersect at the same point, ensure that
each curve records the intersections of the others. This fixes a
number of cubic tests.

TBR=reed@google.com
BUG=skia:3588

Review URL: https://codereview.chromium.org/1105943002
2015-04-24 09:08:57 -07:00
caryclark
03b03cad01 working on initial winding for cubics
Path ops works well for all tests except for cubics.
Isolate failures caused by cubics, and do a better job of computing
the initial winding for cubics.

TBR=reed@google.com
BUG=skia:3588

Review URL: https://codereview.chromium.org/1096923003
2015-04-23 09:13:37 -07:00
caryclark
1049f1246e Now, path ops natively intersect conics, quads, and cubics in any combination. There are still a class of cubic tests that fail and a handful of undiagnosed failures from skps and fuzz tests, but things are much better overall.
Extended tests (150M+) run to completion in release in about 6 minutes; the standard test suite exceeds 100K and finishes in a few seconds on desktops.

TBR=reed
BUG=skia:3588

Review URL: https://codereview.chromium.org/1037953004
2015-04-20 08:31:59 -07:00
caryclark
54359294a7 cumulative pathops patch
Replace the implicit curve intersection with a geometric curve intersection. The implicit intersection proved mathematically unstable and took a long time to zero in on an answer.

Use pointers instead of indices to refer to parts of curves. Indices required awkward renumbering.

Unify t and point values so that small intervals can be eliminated in one pass.

Break cubics up front to eliminate loops and cusps.

Make the Simplify and Op code more regular and eliminate arbitrary differences.

Add a builder that takes an array of paths and operators.

Delete unused code.

BUG=skia:3588
R=reed@google.com

Review URL: https://codereview.chromium.org/1037573004
2015-03-26 07:52:43 -07:00
reed
0dc4dd6dda Revert of pathops version two (patchset #16 id:150001 of https://codereview.chromium.org/1002693002/)
Reason for revert:
ASAN investigation

Original issue's description:
> pathops version two
>
> R=reed@google.com
>
> marked 'no commit' to attempt to get trybots to run
>
> TBR=reed@google.com
>
> Committed: https://skia.googlesource.com/skia/+/ccec0f958ffc71a9986d236bc2eb335cb2111119

TBR=caryclark@google.com
NOPRESUBMIT=true
NOTREECHECKS=true
NOTRY=true

Review URL: https://codereview.chromium.org/1029993002
2015-03-24 13:55:33 -07:00
caryclark
ccec0f958f pathops version two
R=reed@google.com

marked 'no commit' to attempt to get trybots to run

TBR=reed@google.com

Review URL: https://codereview.chromium.org/1002693002
2015-03-24 07:28:17 -07:00
kkinnunen
297aaf97a3 Avoid wrong memory access due to double substitution and %%
Use the form SkDebugf("%s", arbitraryString) instead of
SkDebugf(arbitraryString).

Fixes the case where SkString::appendf-ing a string with "%%" and then
printing the string with SkDebugf would cause uninitialized read and
corrupted debug print.

ninja -C out/Debug tools && valgrind --leak-check=full
./out/Debug/render_pictures --config gpu  -w q -r ...

...

==7307== Conditional jump or move depends on uninitialised value(s)
==7307==    at 0x6908475: __printf_fp (printf_fp.c:1180)
==7307==    by 0x6904267: vfprintf (vfprintf.c:1629)
==7307==    by 0x6906E53: buffered_vfprintf (vfprintf.c:2313)
==7307==    by 0x690188D: vfprintf (vfprintf.c:1316)
==7307==    by 0x67E8F5: SkDebugf(char const*, ...) (SkDebug_stdio.cpp:18)
==7307==    by 0x7983F1: GrContext::printCacheStats() const (GrTest.cpp:54)
==7307==    by 0x408ECF: tool_main(int, char**) (render_pictures_main.cpp:480)
==7307==    by 0x40913E: main (render_pictures_main.cpp:511)
==7307==
Budget: 2048 items 100663296 bytes
		Entry Count: current 652 (651 budgeted, 0 wrapped, 297 locked, 638 scratch 32 0.000000ull), high 652
		Entry Bytes: current 51087658 (budgeted 49826658, 49 0.000000ull, 1261000 unbudgeted) high 51087658

(observe "ull" instead of "% full")

(from mtklein)
This CL is not editing public API.
TBR=reed@google.com

Review URL: https://codereview.chromium.org/943453002
2015-02-19 06:32:12 -08:00
caryclark
65f553182a These tests stress pathops by describing the union of circle-like paths that have tiny line segments embedded and double back to create near-coincident conditions.
The fixes include
- detect when finding the active top loops between two possible answers
- preflight chasing winding to ensure answer is consistent
- binary search more often when quadratic intersection fails
- add more failure paths when an intersect is missed

While this fixes the chrome bug, reenabling path ops in svg should be deferred until additional fixes are landed.

TBR=
BUG=421132

Committed: https://skia.googlesource.com/skia/+/6f726addf3178b01949bb389ef83cf14a1d7b6b2

Review URL: https://codereview.chromium.org/633393002
2014-11-13 06:58:52 -08:00
hcm
27c46a08a9 Revert of harden pathops for pathological test (patchset #19 id:410001 of https://codereview.chromium.org/633393002/)
Reason for revert:
Compile errors on bots

Original issue's description:
> These tests stress pathops by describing the union of circle-like paths that have tiny line segments embedded and double back to create near-coincident conditions.
>
> The fixes include
> - detect when finding the active top loops between two possible answers
> - preflight chasing winding to ensure answer is consistent
> - binary search more often when quadratic intersection fails
> - add more failure paths when an intersect is missed
>
> While this fixes the chrome bug, reenabling path ops in svg should be deferred until additional fixes are landed.
>
> TBR=
> BUG=421132
>
> Committed: https://skia.googlesource.com/skia/+/6f726addf3178b01949bb389ef83cf14a1d7b6b2

TBR=caryclark@google.com
NOTREECHECKS=true
NOTRY=true
BUG=421132

Review URL: https://codereview.chromium.org/686843002
2014-10-28 10:55:54 -07:00
caryclark
6f726addf3 These tests stress pathops by describing the union of circle-like paths that have tiny line segments embedded and double back to create near-coincident conditions.
The fixes include
- detect when finding the active top loops between two possible answers
- preflight chasing winding to ensure answer is consistent
- binary search more often when quadratic intersection fails
- add more failure paths when an intersect is missed

While this fixes the chrome bug, reenabling path ops in svg should be deferred until additional fixes are landed.

TBR=
BUG=421132

Review URL: https://codereview.chromium.org/633393002
2014-10-28 10:33:09 -07:00
caryclark
65b427cff9 fix battlefield website by disallowing very small coordinates
also add and remove comments to document other attempts to fix this that had drawbacks

R=fmalita@chromium.org
BUG=414409

Author: caryclark@google.com

Review URL: https://codereview.chromium.org/575553003
2014-09-18 10:32:57 -07:00
mtklein
406654be7a SkThreadPool ~~> SkTaskGroup
SkTaskGroup is like SkThreadPool except the threads stay in
one global pool.  Each SkTaskGroup itself is tiny (4 bytes)
and its wait() method applies only to tasks add()ed to that
instance, not the whole thread pool.

This means we don't need to bring up new thread pools when
tests themselves want to use multithreading (e.g. pathops,
quilt).  We just create a new SkTaskGroup and wait for that
to complete.  This should be more efficient, and allow us
to expand where we use threads to really latency sensitive
places.  E.g. we can probably now use these in nanobench
for CPU .skp rendering.

Now that all threads are sharing the same pool, I think we
can remove most of the custom mechanism pathops tests use
to control threading.  They'll just ride on the global pool
with all other tests now.

This (temporarily?) removes the GPU multithreading feature
from DM, which we don't use.

On my desktop, DM runs a little faster (57s -> 55s) in
Debug, and a lot faster in Release (36s -> 24s).  The bots
show speedups of similar proportions, cutting more than a
minute off the N4/Release and Win7/Debug runtimes.

BUG=skia:

Committed: https://skia.googlesource.com/skia/+/9c7207b5dc71dc5a96a2eb107d401133333d5b6f

R=caryclark@google.com, bsalomon@google.com, bungeman@google.com, mtklein@google.com, reed@google.com

Author: mtklein@chromium.org

Review URL: https://codereview.chromium.org/531653002
2014-09-03 15:34:37 -07:00
mtklein
2460bbdfbb Revert of SkThreadPool ~~> SkTaskGroup (patchset #4 id:60001 of https://codereview.chromium.org/531653002/)
Reason for revert:
Leaks, leaks, leaks.

Original issue's description:
> SkThreadPool ~~> SkTaskGroup
>
> SkTaskGroup is like SkThreadPool except the threads stay in
> one global pool.  Each SkTaskGroup itself is tiny (4 bytes)
> and its wait() method applies only to tasks add()ed to that
> instance, not the whole thread pool.
>
> This means we don't need to bring up new thread pools when
> tests themselves want to use multithreading (e.g. pathops,
> quilt).  We just create a new SkTaskGroup and wait for that
> to complete.  This should be more efficient, and allow us
> to expand where we use threads to really latency sensitive
> places.  E.g. we can probably now use these in nanobench
> for CPU .skp rendering.
>
> Now that all threads are sharing the same pool, I think we
> can remove most of the custom mechanism pathops tests use
> to control threading.  They'll just ride on the global pool
> with all other tests now.
>
> This (temporarily?) removes the GPU multithreading feature
> from DM, which we don't use.
>
> On my desktop, DM runs a little faster (57s -> 55s) in
> Debug, and a lot faster in Release (36s -> 24s).  The bots
> show speedups of similar proportions, cutting more than a
> minute off the N4/Release and Win7/Debug runtimes.
>
> BUG=skia:
>
> Committed: https://skia.googlesource.com/skia/+/9c7207b5dc71dc5a96a2eb107d401133333d5b6f

R=caryclark@google.com, bsalomon@google.com, bungeman@google.com, reed@google.com, mtklein@chromium.org
TBR=bsalomon@google.com, bungeman@google.com, caryclark@google.com, mtklein@chromium.org, reed@google.com
NOTREECHECKS=true
NOTRY=true
BUG=skia:

Author: mtklein@google.com

Review URL: https://codereview.chromium.org/533393002
2014-09-03 14:17:48 -07:00
mtklein
9c7207b5dc SkThreadPool ~~> SkTaskGroup
SkTaskGroup is like SkThreadPool except the threads stay in
one global pool.  Each SkTaskGroup itself is tiny (4 bytes)
and its wait() method applies only to tasks add()ed to that
instance, not the whole thread pool.

This means we don't need to bring up new thread pools when
tests themselves want to use multithreading (e.g. pathops,
quilt).  We just create a new SkTaskGroup and wait for that
to complete.  This should be more efficient, and allow us
to expand where we use threads to really latency sensitive
places.  E.g. we can probably now use these in nanobench
for CPU .skp rendering.

Now that all threads are sharing the same pool, I think we
can remove most of the custom mechanism pathops tests use
to control threading.  They'll just ride on the global pool
with all other tests now.

This (temporarily?) removes the GPU multithreading feature
from DM, which we don't use.

On my desktop, DM runs a little faster (57s -> 55s) in
Debug, and a lot faster in Release (36s -> 24s).  The bots
show speedups of similar proportions, cutting more than a
minute off the N4/Release and Win7/Debug runtimes.

BUG=skia:
R=caryclark@google.com, bsalomon@google.com, bungeman@google.com, mtklein@google.com, reed@google.com

Author: mtklein@chromium.org

Review URL: https://codereview.chromium.org/531653002
2014-09-03 14:06:48 -07:00
bungeman
d6aeb6dc8f Fix thread unsafe mutex initialization.
BUG=skia:2779
R=robertphillips@google.com, mtklein@google.com, reed@android.com, bsalomon@google.com

Author: bungeman@google.com

Review URL: https://codereview.chromium.org/419113002
2014-07-25 11:52:48 -07:00
caryclark
19eb3b2f0a update pathops core and tests
split out skpclip (the test of 1M pictures) into its own project

TBR=reed

Author: caryclark@google.com

Review URL: https://codereview.chromium.org/400033002
2014-07-18 05:08:14 -07:00
caryclark
dac1d17027 Enabling the canvas bit to turn the clip stack into a flat replace exposed around 100 failures when testing the 800K skp set generated from the top 1M web sites.
This fixes all but one of those failures.

Major changes include:
- Replace angle indices with angle pointers. This was motivated by the need to add angles later but not renumber existing angles.
- Aggressive segment chase. When the winding is known on a segment, more aggressively passing that winding to adjacent segments allows fragmented data sets to succeed.
- Line segments with ends nearly the same are treated as coincident first.
- Transfer partial coincidence by observing that if segment A is partially coincident to B and C then B and C may be partially coincident.

TBR=reed

Author: caryclark@google.com

Review URL: https://codereview.chromium.org/272153002
2014-06-17 05:15:38 -07:00
commit-bot@chromium.org
91fc81c972 fix cubic/line intersection; add skp tests
BUG=skia:2488
TBR=reed

Author: caryclark@google.com

Review URL: https://codereview.chromium.org/252243003

git-svn-id: http://skia.googlecode.com/svn/trunk@14458 2bbb7eff-a529-9590-31e7-b0007b416f81
2014-04-30 13:37:48 +00:00
skia.committer@gmail.com
e02c5dabbb Sanitizing source files in Housekeeper-Nightly
git-svn-id: http://skia.googlecode.com/svn/trunk@14387 2bbb7eff-a529-9590-31e7-b0007b416f81
2014-04-26 03:04:35 +00:00
commit-bot@chromium.org
8cb1daaa1e fix minor skp-found bugs
remove globals from pathops_unittest

BUG=skia:2460
TBR=mtklein

Author: caryclark@google.com

Review URL: https://codereview.chromium.org/239563004

git-svn-id: http://skia.googlecode.com/svn/trunk@14378 2bbb7eff-a529-9590-31e7-b0007b416f81
2014-04-25 12:59:11 +00:00
commit-bot@chromium.org
4431e7757c Mike R: please sanity check SkPostConfig.h
Mike K: please sanity check Test.cpp and skia_test.cpp

Feel free to look at the rest, but I don't expect any in depth review of path ops innards.

Path Ops first iteration used QuickSort to order segments radiating from an intersection to compute the winding rule.

This revision uses a circular sort instead. Breaking out the circular sort into its own long-lived structure (SkOpAngle) allows doing less work and provides a home for caching additional sorting data.

The circle sort is more stable than the former sort, has a robust ordering and fewer exceptions. It finds unsortable ordering less often. It is less reliant on the initial curve  tangent, using convex hulls instead whenever it can.

Additional debug validation makes sure that the computed structures are self-consistent. A new visualization tool helps verify that the angle ordering is correct.

The 70+M tests pass with this change on Windows, Mac, Linux 32 and Linux 64 in debug and release.

R=mtklein@google.com, reed@google.com

Author: caryclark@google.com

Review URL: https://codereview.chromium.org/131103009

git-svn-id: http://skia.googlecode.com/svn/trunk@14183 2bbb7eff-a529-9590-31e7-b0007b416f81
2014-04-14 17:08:59 +00:00
mike@reedtribe.org
deee496cd3 replace setConfig+allocPixels with single call
BUG=skia:

Review URL: https://codereview.chromium.org/162643002

git-svn-id: http://skia.googlecode.com/svn/trunk@13426 2bbb7eff-a529-9590-31e7-b0007b416f81
2014-02-13 14:41:43 +00:00
reed@google.com
e1ca705cac deprecate SkScalarRound (and its ilk), use SkScalarRound[ToInt,ToScalar]. #define SK_SUPPORT_DEPRECATED_SCALARROUND for legacy clients
BUG=
R=robertphillips@google.com

Review URL: https://codereview.chromium.org/111353003

git-svn-id: http://skia.googlecode.com/svn/trunk@12719 2bbb7eff-a529-9590-31e7-b0007b416f81
2013-12-17 19:22:07 +00:00
caryclark@google.com
a2bbc6e19d pathops work in progress
BUG=

Review URL: https://codereview.chromium.org/52653002

git-svn-id: http://skia.googlecode.com/svn/trunk@12089 2bbb7eff-a529-9590-31e7-b0007b416f81
2013-11-01 17:36:03 +00:00
commit-bot@chromium.org
409774e8ac Sadly TSAN still reports this as a race, even when we're obviously writing the
same values.  Initializing with the declaration should quiet it down.

BUG=
R=caryclark@google.com

Author: mtklein@google.com

Review URL: https://codereview.chromium.org/25713004

git-svn-id: http://skia.googlecode.com/svn/trunk@11574 2bbb7eff-a529-9590-31e7-b0007b416f81
2013-10-02 16:15:44 +00:00
caryclark@google.com
7eaa53d8f7 path ops work in progress
make more skps work

remove edit files

BUG=

Review URL: https://codereview.chromium.org/23542056

git-svn-id: http://skia.googlecode.com/svn/trunk@11570 2bbb7eff-a529-9590-31e7-b0007b416f81
2013-10-02 14:49:34 +00:00
commit-bot@chromium.org
57f035ecae Writing to testName and reading its size isn't thread safe, TSAN reminds us.
Guarding it into a no-op makes it safe.  Looks like this is only used for debugging, presumably singlethreaded?

BUG=
R=caryclark@google.com

Author: mtklein@google.com

Review URL: https://codereview.chromium.org/25366002

git-svn-id: http://skia.googlecode.com/svn/trunk@11562 2bbb7eff-a529-9590-31e7-b0007b416f81
2013-10-01 18:44:04 +00:00
caryclark@google.com
570863f2e2 path ops work in progress
path ops work in progress

BUG=

Review URL: https://codereview.chromium.org/21359002

git-svn-id: http://skia.googlecode.com/svn/trunk@11291 2bbb7eff-a529-9590-31e7-b0007b416f81
2013-09-16 15:55:01 +00:00
caryclark@google.com
8d0a524a48 harden and speed up path op unit tests
PathOps tests internal routines direcctly. Check to make sure that
test points, lines, quads, curves, triangles, and bounds read from
arrays are valid (i.e., don't contain NaN) before calling the
test function.

Repurpose the test flags.
- make 'v' verbose test region output against path output
- make 'z' single threaded (before it made it multithreaded)

The latter change speeds up tests run by the buildbot by 2x to 3x.

BUG=

Review URL: https://codereview.chromium.org/19374003

git-svn-id: http://skia.googlecode.com/svn/trunk@10107 2bbb7eff-a529-9590-31e7-b0007b416f81
2013-07-16 16:11:16 +00:00
caryclark@google.com
fa2aeee27a path ops near exact
Modify line intersections to first
- match exact ends
- compute intersections
- match near ends
where the exact ends are preferred, then near matches, then
computed matches. This pulls matches towards existing end points
when possible, and keeps intersection distances consistent with
different line/line line/quad and line/cubic computations.

BUG=

Review URL: https://codereview.chromium.org/19183003

git-svn-id: http://skia.googlecode.com/svn/trunk@10073 2bbb7eff-a529-9590-31e7-b0007b416f81
2013-07-15 13:29:13 +00:00
caryclark@google.com
07e97fccd2 path ops work in progress
BUG=

Review URL: https://codereview.chromium.org/18058007

git-svn-id: http://skia.googlecode.com/svn/trunk@9908 2bbb7eff-a529-9590-31e7-b0007b416f81
2013-07-08 17:17:02 +00:00
caryclark@google.com
cffbcc3b96 path ops -- rewrite angle sort
This is a major change resulting from a minor
tweak. In the old code, the intersection point
of two curves was shared between them, but the
intersection points and end points of sorted edges was
computed directly from the intersection T value.

In this CL, both intersection points and sorted points
are the same, and intermediate control points are computed
to preserve their slope.

The sort itself has been completely rewritten to be more
robust and remove 'magic' checks, conditions that empirically
worked but couldn't be rationalized.

This CL was triggered by errors generated computing the clips
of SKP files. At this point, all 73M standard tests work and
at least the first troublesome SKPs work.

Review URL: https://codereview.chromium.org/15338003

git-svn-id: http://skia.googlecode.com/svn/trunk@9432 2bbb7eff-a529-9590-31e7-b0007b416f81
2013-06-04 17:59:42 +00:00
caryclark@google.com
a5e55925ea path ops -- fix skp bugs
This fixes a series of bugs discovered by running
the small set of Skia skp files through pathops
to flatten the clips.
Review URL: https://codereview.chromium.org/14798004

git-svn-id: http://skia.googlecode.com/svn/trunk@9042 2bbb7eff-a529-9590-31e7-b0007b416f81
2013-05-07 18:51:31 +00:00
caryclark@google.com
66560ca776 path ops -- handle non-finite numbers
Op() and Simplify() do nothing if the input
is non-finite. Add code and tests.
Review URL: https://codereview.chromium.org/14407006

git-svn-id: http://skia.googlecode.com/svn/trunk@8882 2bbb7eff-a529-9590-31e7-b0007b416f81
2013-04-26 19:51:16 +00:00
caryclark@google.com
6dc7df69ae path ops : fix empty-diff bug, op-in-place
add some debugging around reverse diff, inverse
Review URL: https://codereview.chromium.org/13851015

git-svn-id: http://skia.googlecode.com/svn/trunk@8852 2bbb7eff-a529-9590-31e7-b0007b416f81
2013-04-25 11:51:54 +00:00
commit-bot@chromium.org
44c661ff15 Add thread-per-core setting to SkThreadPool.
BUG=
R=scroggo@google.com, caryclark@google.com

Author: mtklein@google.com

Review URL: https://chromiumcodereview.appspot.com/13855009

git-svn-id: http://skia.googlecode.com/svn/trunk@8802 2bbb7eff-a529-9590-31e7-b0007b416f81
2013-04-22 15:23:14 +00:00
caryclark@google.com
16cfe40276 allow tests to optionally use multiple threads
modify threaded path ops tests to check

Background: this CL came out of a conversation with Eric where I learned that 10s of machines host 100s of bots. Since the bot hosting tests may be shared with many other tasks, it seems unwise for path ops to launch multiple test threads.

The change here is to make launching multiple threads "opt-in" and by default, bots can run path ops in a single thread.
Review URL: https://codereview.chromium.org/14002007

git-svn-id: http://skia.googlecode.com/svn/trunk@8750 2bbb7eff-a529-9590-31e7-b0007b416f81
2013-04-18 18:47:37 +00:00
caryclark@google.com
0361032c0b path ops work in progress
fix bugs in tests on 32 bit release

Most changes revolve around pinning computed t values
very close to zero and one.

git-svn-id: http://skia.googlecode.com/svn/trunk@8745 2bbb7eff-a529-9590-31e7-b0007b416f81
2013-04-18 15:58:21 +00:00
caryclark@google.com
ad65a3e5fb path ops work in progress
standardize tests
use SK_ARRAY_COUNT everywhere
debug why x87 differs from SIMD 64
various platform specific fixes

git-svn-id: http://skia.googlecode.com/svn/trunk@8689 2bbb7eff-a529-9590-31e7-b0007b416f81
2013-04-15 19:13:59 +00:00
skia.committer@gmail.com
391ca66276 Sanitizing source files in Skia_Periodic_House_Keeping
git-svn-id: http://skia.googlecode.com/svn/trunk@8608 2bbb7eff-a529-9590-31e7-b0007b416f81
2013-04-11 07:01:45 +00:00
caryclark@google.com
e942bc329a fix a few pathops test bugs exposed on Mac and Linux
git-svn-id: http://skia.googlecode.com/svn/trunk@8601 2bbb7eff-a529-9590-31e7-b0007b416f81
2013-04-10 18:53:01 +00:00
caryclark@google.com
66089e4ec4 Make parallel unit testing work on windows
Review URL: https://codereview.chromium.org/14072002

git-svn-id: http://skia.googlecode.com/svn/trunk@8594 2bbb7eff-a529-9590-31e7-b0007b416f81
2013-04-10 15:55:37 +00:00
skia.committer@gmail.com
3284017a60 Sanitizing source files in Skia_Periodic_House_Keeping
git-svn-id: http://skia.googlecode.com/svn/trunk@8568 2bbb7eff-a529-9590-31e7-b0007b416f81
2013-04-09 07:01:27 +00:00
caryclark@google.com
818b0cc1b8 Add implementation of path ops
This CL depends on
https://codereview.chromium.org/12880016/
"Add intersections for path ops"

Given a path, iterate through its contour, and
construct an array of segments containing its curves.

Intersect each curve with every other curve, and for
cubics, with itself.

Given the set of intersections, find one with the 
smallest y and sort the curves eminating from the
intersection. Assign each curve a winding value.

Operate on the curves, keeping and discarding them
according to the current operation and the sum of
the winding values.

Assemble the kept curves into an output path.
Review URL: https://codereview.chromium.org/13094010

git-svn-id: http://skia.googlecode.com/svn/trunk@8553 2bbb7eff-a529-9590-31e7-b0007b416f81
2013-04-08 11:50:46 +00:00