History log of /external/skia/src/pathops/SkOpSpan.h
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c3cc5fa6de0a8237d9241dbf3e6c0786a9040069 07-Mar-2017 Herb Derby <herb@google.com> Move from SkChunkAlloc to SkArenaAlloc for PathOps

Attempt two. Remove ~SkOpContour because it is handled by the SkArenaAlloc.

Change-Id: Id3049db97aebcc1009d403a031f2fac219f58f2f
Reviewed-on: https://skia-review.googlesource.com/9381
Reviewed-by: Derek Sollenberger <djsollen@google.com>
Commit-Queue: Herb Derby <herb@google.com>
/external/skia/src/pathops/SkOpSpan.h
c0a4c4f969464ec9854d726836a430262351d63d 07-Mar-2017 Derek Sollenberger <djsollen@google.com> Revert "Move from SkChunkAlloc to SkArenaAlloc for PathOps"

This reverts commit 38c60180241e335e368fdadbf7856aff114ff668.

Reason for revert: breaking ASAN run in TAP build

Original change's description:
> Move from SkChunkAlloc to SkArenaAlloc for PathOps
>
> Change-Id: Iab111a4ebcae4e896b1fdfe285def9ef0ae2ab6b
> Reviewed-on: https://skia-review.googlesource.com/7314
> Reviewed-by: Cary Clark <caryclark@google.com>
> Commit-Queue: Herb Derby <herb@google.com>
>

TBR=herb@google.com,caryclark@google.com,reviews@skia.org
NOPRESUBMIT=true
NOTREECHECKS=true
NOTRY=true

Change-Id: I6364254571bb1617a9f45ed08f2af4a59f9d5841
Reviewed-on: https://skia-review.googlesource.com/9335
Reviewed-by: Derek Sollenberger <djsollen@google.com>
Commit-Queue: Derek Sollenberger <djsollen@google.com>
/external/skia/src/pathops/SkOpSpan.h
38c60180241e335e368fdadbf7856aff114ff668 01-Mar-2017 Herb Derby <herb@google.com> Move from SkChunkAlloc to SkArenaAlloc for PathOps

Change-Id: Iab111a4ebcae4e896b1fdfe285def9ef0ae2ab6b
Reviewed-on: https://skia-review.googlesource.com/7314
Reviewed-by: Cary Clark <caryclark@google.com>
Commit-Queue: Herb Derby <herb@google.com>
/external/skia/src/pathops/SkOpSpan.h
595ac28c3990ea89ee40ec14117dc1667acfc126 24-Oct-2016 caryclark <caryclark@google.com> fix a few more fuzzes

Minor changes to fix some fuzz conditions.
A couple of ignored asserts when the data
is fuzzy, and one fail condition when the
underlying data has already been deleted.

TBR=reed@google.com
GOLD_TRYBOT_URL= https://gold.skia.org/search?issue=2443243002

Review-Url: https://codereview.chromium.org/2443243002
/external/skia/src/pathops/SkOpSpan.h
e47ae2998c1cf944db5743a416583dd0f042b6d9 05-Oct-2016 Cary Clark <caryclark@google.com> remove dead code

Use code coverage and a new '-c' flag to find
and remove unneeded code.

TBR=reed@google.com

GOLD_TRYBOT_URL= https://gold.skia.org/search?issue=2397593002

patch from issue 2397593002 at patchset 1 (http://crrev.com/2397593002#ps1)

Change-Id: I741a82de9191146c10457d4c0b9cb9605dff2069
Reviewed-on: https://skia-review.googlesource.com/2983
Reviewed-by: Cary Clark <caryclark@google.com>
/external/skia/src/pathops/SkOpSpan.h
ab87d7abf1df007c90bef2e916294ca325d81c81 04-Oct-2016 Cary Clark <caryclark@google.com> coin debugging runs all tests in extended

This extends path ops concidence debugging
to find unused algorithms and determine the extent
of loops.

This verifies that all 140M tests run without error
in release and debug.

TBR=reed@google.com
BUG=skia:
GOLD_TRYBOT_URL= https://gold.skia.org/search?issue=2391733002

patch from issue 2391733002 at patchset 1 (http://crrev.com/2391733002#ps1)

Change-Id: I02ca29764405c5ac3e7ca3b2621fba28dbaaffc2
Reviewed-on: https://skia-review.googlesource.com/2923
Reviewed-by: Cary Clark <caryclark@google.com>
/external/skia/src/pathops/SkOpSpan.h
81a478ca6c36aac3e53ce0373a281ac8940f4780 09-Sep-2016 caryclark <caryclark@google.com> Skip adding coincident edges found
during curve intersection if their
ends are nearly the same.

Loosen conic/line intersection point
check.

Detect when coincident points are
unordered. This means that points
a/b/c on one curve may appear in
b/c/a order on the opposite curve.

Restructure addMissing to return
success and return if a coincidence
was added as a parameter.

With this, tiger part a works.
Tiger part b exposes bugs around
tight quads that are nearly coincident
with themselves, and are coincident
with something else.

The greedy coicident matcher
may cause the point order to be
out of sync.

Still working out what to do in
this case.

TBR=reed@google.com
GOLD_TRYBOT_URL= https://gold.skia.org/search?issue=2321773002

Review-Url: https://codereview.chromium.org/2321773002
/external/skia/src/pathops/SkOpSpan.h
8016b264ceec2b11d2acbeb77a9fbe66e48368b9 06-Sep-2016 caryclark <caryclark@google.com> interpolation of coincidence must be local to a single span

Pathops makes up intersections that it doesn't detect directly,
but do exist. For instance, if a is coincident with b, and
b is coincident with c, then for where they overlap
a is coincident with c.

The intersections are made up in different ways. In a few
places, the t values that are detected are interpolated to
guess the t values that represent invented intersections.

The interpolated t is not necessarily linear, but a linear
guess is good enough if the invented t lies between known
t values.

Additionally, improve debugging.

This passes the extended release test suite and additionally
passes the first 17 levels in the tiger test suite;
previously, path ops passed 7 levels.

The tiger suite is composed of 37 levels in increasing
complexity, described by about 300K tests.

TBR=reed@google.com
BUG=skia:5131
GOLD_TRYBOT_URL= https://gold.skia.org/search?issue=2300203002

Review-Url: https://codereview.chromium.org/2300203002
/external/skia/src/pathops/SkOpSpan.h
30b9fdd6a1d607bde20c793af65b5e2e8a1737ca 31-Aug-2016 caryclark <caryclark@google.com> pathops coincident work

This is working towards fixing all bugs around simplifying the tiger.

This installment simplifies the point-t intersection list as it is built rather than doing the analysis once the intersections are complete. This avoids getting the list in an inconsistent state and makes coincident checks faster and more stable.

GOLD_TRYBOT_URL= https://gold.skia.org/search?issue=2237223002

TBR=reed@google.com
BUG=skia:5131

Review-Url: https://codereview.chromium.org/2237223002
/external/skia/src/pathops/SkOpSpan.h
29b2563afb1677515739f1d24fb27733626eca92 25-Aug-2016 caryclark <caryclark@google.com> path ops stream-lining

The addT() function is a workhorse of pathops.
Make it simpler, removing branches and parameters.

Separate addOpp() into const and modify parts.

Add more debugging that asserts if the function
fails and the data is not extreme (e.g., fuzzer
generated).

TBR=reed@google.com
GOLD_TRYBOT_URL= https://gold.skia.org/search?issue=2273293004

Review-Url: https://codereview.chromium.org/2273293004
/external/skia/src/pathops/SkOpSpan.h
025b11ecde8733d9b3eee54e132cc50a5ce8eb78 25-Aug-2016 caryclark <caryclark@google.com> add pathops debugging

Pathops has many points of failure, most of which
are triggered by extreme data generated by fuzzers.
It's difficult to figure out which failure point
was triggered when the operation gives up.

Add instrumentation so that the failure can
be debugged when the data is well-behaved.

Also, add a check that looks for a sequence of
coincident points on multiple edges that are out
of order when compared to each other.

TBR=reed@google.com
GOLD_TRYBOT_URL= https://gold.skia.org/search?issue=2274803003

Review-Url: https://codereview.chromium.org/2274803003
/external/skia/src/pathops/SkOpSpan.h
ef4f32ac858825dc443cfe4739ea878fb0bf550f 24-Aug-2016 caryclark <caryclark@google.com> remove point aliases

This removes the notion of keeping track of every different t value
that resolves to the same or a similar point. Other fixes make
this concept unnecessary, and removing it simplifies the code.

This removes an allocation, and speeds up paths with many
overlapping curves.

As a bonus, four fuzzer tests that failed before now succeed.

TBR=reed@google.com
GOLD_TRYBOT_URL= https://gold.skia.org/search?issue=2275703003

Review-Url: https://codereview.chromium.org/2275703003
/external/skia/src/pathops/SkOpSpan.h
fc560e09b3f777bb32dccb9f52d715383a10a620 27-Jul-2016 caryclark <caryclark@google.com> fuzz wednesday

Add debug 'skip assert' access to SkCoincidentSpans.
That permits suppressing asserts to make it easier
to detect when this fuzz data generates unparsable
data.

TBR=reed@google.com
BUG=631564, 631992
GOLD_TRYBOT_URL= https://gold.skia.org/search?issue=2186973002

Review-Url: https://codereview.chromium.org/2186973002
/external/skia/src/pathops/SkOpSpan.h
55888e44171ffd48b591d19256884a969fe4da17 18-Jul-2016 caryclark <caryclark@google.com> pathops coincidence and security rewrite

Most changes stem from working on an examples bracketed
by #if DEBUG_UNDER_DEVELOPMENT // tiger
These exposed many problems with coincident curves,
as well as errors throughout the code.

Fixing these errors also fixed a number of fuzzer-inspired
bug reports.

* Line/Curve Intersections
Check to see if the end of the line nearly intersects
the curve. This was a FIXME in the old code.

* Performance
Use a central chunk allocator.
Plumb the allocator into the global variable state
so that it can be shared. (Note that 'SkGlobalState'
is allocated on the stack and is visible to children
functions but not other threads.)

* Refactor
Let SkOpAngle grow up from a structure to a class.
Let SkCoincidentSpans grow up from a structure to a class.
Rename enum Alias to AliasMatch.

* Coincidence Rewrite
Add more debugging to coincidence detection.
Parallel debugging routines have read-only logic to report
the current coincidence state so that steps through the
logic can expose whether things got better or worse.

More functions can error-out and cause the pathops
engine to non-destructively exit.

* Accuracy
Remove code that adjusted point locations. Instead,
offset the curve part so that sorted curves all use
the same origin.
Reduce the size (and influence) of magic numbers.

* Testing
The debug suite with verify and the full release suite
./out/Debug/pathops_unittest -v -V
./out/Release/pathops_unittest -v -V -x
expose one error. That error is captured as cubics_d3.
This error exists in the checked in code as well.

BUG=skia:
GOLD_TRYBOT_URL= https://gold.skia.org/search?issue=2128633003

BUG=skia:
GOLD_TRYBOT_URL= https://gold.skia.org/search?issue=2128633003

Review-Url: https://codereview.chromium.org/2128633003
/external/skia/src/pathops/SkOpSpan.h
18300a3aa7cb6eb55d21bb0450dffa58b6fc062c 16-Mar-2016 mtklein <mtklein@chromium.org> detach -> release

The C++ standard library uses the name "release" for the operation we call "detach".

Rewriting each "detach(" to "release(" brings us a step closer to using standard library types directly (e.g. std::unique_ptr instead of SkAutoTDelete).

This was a fairly blind transformation. There may have been unintentional conversions in here, but it's probably for the best to have everything uniformly say "release".

BUG=skia:
GOLD_TRYBOT_URL= https://gold.skia.org/search2?unt=true&query=source_type%3Dgm&master=false&issue=1809733002

Review URL: https://codereview.chromium.org/1809733002
/external/skia/src/pathops/SkOpSpan.h
ef784fb7f58c9c021172045a8e0b396c81fdc425 30-Oct-2015 caryclark <caryclark@google.com> More conic-specific tests revealed a few conic-specific bugs. Because javascript / canvas make visualizing conics tricky, new native tools are required.

The utility SubsetPath removes parts of a potentially very large path to isolate a minimal test case. SubsetPath is very useful for debugging path ops, but is not path ops specific.

PathOpsBuilderConicTest compares the output of the Path Ops Builder, sequential calls to Simplify, and SkRegions for some number of rotated ovals.

Some tests caused path ops to hang. It was caught adding a loop of curves because the head was not found by the tail. Even though the root cause has been fixed, SkSegment::addCurveTo callers now abort the path op if the same curve was added twice.

The subdivided conic weight was been computed anew. Fortunately, it's a simpler computation that the one it replaces.

Some Simplify() subroutines returned false to signal that the results needed assembling. Change these to abort the current operation instead.

Coincident curve intersection triggered two small bugs; one where no perpendicular could be found for coincident curves, and one where no coincident curves remain after looping.

The SixtyOvals test can be run through multiple processes instead of multiple threads. This strategy allows a 48 core machine to saturate all cores at 100%.

The DEBUG_VISUALIZE_CONICS code in PathOpsConicIntersectionTest acknowleges that it is easier to visualize conics with Skia than with script and html canvas. This test also verifies that path ops subdivision matches geometry chopping.

TBR=reed@google.com

Review URL: https://codereview.chromium.org/1405383004
/external/skia/src/pathops/SkOpSpan.h
26ad22ab61539e3d3b6bc5e0da8dcebbd52a53de 16-Oct-2015 caryclark <caryclark@google.com> Enabling clip stack flattening exercises path ops.
Iterating through the 903K skps that represent the
imagable 1M top web pages triggers a number of
bugs, some of which are addressed here.

Some web pages trigger intersecting cubic
representations of arc with their conic
counterparts. This exposed a flaw in coincident
detection that caused an infinite loop. The loop
alternatively extended the coincident section and,
determining the that the bounds of the curve pairs
did not overlap, deleted the extension.

Track the number of times the coincident detection
is called, and if it exceeds an empirically found
limit, assume that the curves are coincident and
force it to be so.

The loop count limit can be determined by enabling
DEBUG_T_SECT_LOOP_COUNT and running all tests. The
largest count is reported on completion.

Another class of bugs was caused by concident
detection duplicating nearly identical points that
had been merged earlier. To track these bugs, the
'handle coincidence' code was duplicated as a
const debug variety that reported if one of a
dozen or so irregularities are present; then it is
easier to see when a block of code that fixes one
irregularity regresses another.

Creating the debug const code version exposed some
non-debug code that could be const, and some that
was experimental and could be removed. Set
DEBUG_COINCIDENCE to track coincidence health and
handling.

For running on Chrome, DEBUG_VERIFY checks the
result of pathops against the same operation
using SkRegion to verify that the results are
nearly the same.

When visualizing the pathops work using
tools/pathops_visualizer.htm, set
DEBUG_DUMP_ALIGNMENT to see the curves after
they've been aligned for coincidence.

Other bugs fixed include detecting when a
section of a pair of curves have devolved into
lines and are coincident.

TBR=reed@google.com

Review URL: https://codereview.chromium.org/1394503003
/external/skia/src/pathops/SkOpSpan.h
96fcdcc219d2a0d3579719b84b28bede76efba64 27-Aug-2015 halcanary <halcanary@google.com> Style Change: NULL->nullptr
DOCS_PREVIEW= https://skia.org/?cl=1316233002

Review URL: https://codereview.chromium.org/1316233002
/external/skia/src/pathops/SkOpSpan.h
d4349723fac9c0fd4dcf8c275fb7c756bdfdff7b 23-Jul-2015 caryclark <caryclark@google.com> fix path ops fuzz buster

Mark collapsed segments as done and remove collapsed
segment references from the coincidence array.

Also add test names to global debugging.

R=fmalita@chromium.org
BUG=512592

Review URL: https://codereview.chromium.org/1250293002
/external/skia/src/pathops/SkOpSpan.h
27c8eb8ffd7e221693d840c2b9279d53fe6f03d4 06-Jul-2015 caryclark <caryclark@google.com> When three or more edges are coincident, the logic needs
to compute the overlapping ranges and combine the winding
into a single destination.

This computes coincidence more rigorously, fixing the
edge cases exposed by this bug.

Also, add the ability to debug and dump pathop structures
from the coincident context.

TBR=reed@google.com
BUG=skia:3651

Review URL: https://codereview.chromium.org/1182493015
/external/skia/src/pathops/SkOpSpan.h
bca19f77479adfd8ba2171753382bc8bf4c2b4ca 13-May-2015 caryclark <caryclark@google.com> deal more consistently with unsortable edges

Improve line/curve coincident detection and resolution. This fixed the remaining simple failures.

When an edge is unsortable, use the ray intersection to determine the angles' winding.

Deal with degenerate segments.

TBR=reed@google.com
BUG=skia:3588,skia:3762

Review URL: https://codereview.chromium.org/1140813002
/external/skia/src/pathops/SkOpSpan.h
624637cc8ec22c000409704d0b403ac1b81ad4b0 11-May-2015 caryclark <caryclark@google.com> Path ops formerly found the topmost unprocessed edge and determined its angle sort order to initialize the winding. This never worked correctly with cubics and was flaky with paths consisting mostly of vertical edges.

This replacement shoots axis-aligned rays through all intersecting edges to find the outermost one either horizontally or vertically. The resulting code is smaller and twice as fast.

To support this, most of the horizontal / vertical intersection code was rewritten and standardized, and old code supporting the top-directed winding was deleted.

Contours were pointed to by an SkTDArray. Instead, put them in a linked list, and designate the list head with its own class to ensure that methods that take lists of contours start at the top. This change removed a large percentage of memory allocations used by path ops.

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

Review URL: https://codereview.chromium.org/1111333002
/external/skia/src/pathops/SkOpSpan.h
08bc8488fa2ea2d2a17efb1443f0ec6579d5a3c8 24-Apr-2015 caryclark <caryclark@google.com> 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
/external/skia/src/pathops/SkOpSpan.h
1049f1246e7be4ccb68001361efceb8933e6f81c 20-Apr-2015 caryclark <caryclark@google.com> 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
/external/skia/src/pathops/SkOpSpan.h
54359294a7c9dc54802d512a5d891a35c1663392 26-Mar-2015 caryclark <caryclark@google.com> 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
/external/skia/src/pathops/SkOpSpan.h
0dc4dd6dda9a7912f696b46d9c02155ec1d1ba5f 24-Mar-2015 reed <reed@google.com> 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
/external/skia/src/pathops/SkOpSpan.h
ccec0f958ffc71a9986d236bc2eb335cb2111119 24-Mar-2015 caryclark <caryclark@google.com> 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
/external/skia/src/pathops/SkOpSpan.h
dac1d17027dcaa5596885a9f333979418b35001c 17-Jun-2014 caryclark <caryclark@google.com> 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
/external/skia/src/pathops/SkOpSpan.h
8cb1daaa1e4343eb60a7c4f21c12e33de30dad64 25-Apr-2014 commit-bot@chromium.org <commit-bot@chromium.org@2bbb7eff-a529-9590-31e7-b0007b416f81> 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
/external/skia/src/pathops/SkOpSpan.h
4431e7757cfcb8cfa99535eed0e9f156dabf95c2 14-Apr-2014 commit-bot@chromium.org <commit-bot@chromium.org@2bbb7eff-a529-9590-31e7-b0007b416f81> 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
/external/skia/src/pathops/SkOpSpan.h
866f4e34a943c115ac372c22123a1520aa5f9b06 21-Nov-2013 commit-bot@chromium.org <commit-bot@chromium.org@2bbb7eff-a529-9590-31e7-b0007b416f81> optimize pathops coverage

Remove unused code from SkOpSegment.cpp and friends.
Add new tests exposed by coverage.
Fix a bug exposed by coverage -- removing the need to detect points that are nearby when intersecting.
Add gyp rule for building coverage flavor on Mac.

R=mtklein@google.com

Author: caryclark@google.com

Review URL: https://codereview.chromium.org/75453003

git-svn-id: http://skia.googlecode.com/svn/trunk@12344 2bbb7eff-a529-9590-31e7-b0007b416f81
/external/skia/src/pathops/SkOpSpan.h
570863f2e22b8ea7d7c504bd15e4f766af097df2 16-Sep-2013 caryclark@google.com <caryclark@google.com@2bbb7eff-a529-9590-31e7-b0007b416f81> 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
/external/skia/src/pathops/SkOpSpan.h
07393cab57ce74a4aae89a31fae9aaa9780fc19d 08-Apr-2013 caryclark@google.com <caryclark@google.com@2bbb7eff-a529-9590-31e7-b0007b416f81> Add base types for path ops

Paths contain lines, quads, and cubics, which are
collectively curves.

To work with path intersections, intermediary curves
are constructed. For now, those intermediates use
doubles to guarantee sufficient precision.

The DVector, DPoint, DLine, DQuad, and DCubic
structs encapsulate these intermediate curves.

The DRect and DTriangle structs are created to
describe intersectable areas of interest.

The Bounds struct inherits from SkRect to create
a SkScalar-based rectangle that intersects shared
edges.

This also includes common math equalities and
debugging that the remainder of path ops builds on,
as well as a temporary top-level interface in
include/pathops/SkPathOps.h.
Review URL: https://codereview.chromium.org/12827020

git-svn-id: http://skia.googlecode.com/svn/trunk@8551 2bbb7eff-a529-9590-31e7-b0007b416f81
/external/skia/src/pathops/SkOpSpan.h