Commit Graph

615 Commits

Author SHA1 Message Date
Andrew Tridgell dbf337e1b3 AP_Math: move closest_point to cpp 2019-06-11 13:13:22 +09:00
Andrew Tridgell bfc28dfde9 AP_Math: move normalize, reflect, project and perpendicular to cpp 2019-06-11 13:13:22 +09:00
Andrew Tridgell 01e541b7d1 AP_Math: minor formatting changes to length method 2019-06-11 13:13:22 +09:00
Andrew Tridgell 4c4de1f021 AP_Math: vector2f::length_squared always returns float 2019-06-11 13:13:22 +09:00
Andrew Tridgell 46617e6c72 AP_Math: remove unused include from Vector2 2019-06-11 13:13:22 +09:00
Andrew Tridgell 69781cda42 AP_Math: add Vector2::angle 2019-06-11 13:13:22 +09:00
Peter Hall ea4ecebfc4 AP_Math: add speed unit converstion defs 2019-06-03 10:48:19 +09:00
Peter Barker e4de5a17d1 AP_Math: add pitch-7 to rotation tests 2019-05-29 17:12:32 +10:00
Andrew Tridgell e2eda63d2c AP_Math: added new rotation for PITCH_7 2019-05-29 17:12:32 +10:00
Peter Barker 977fe09276 AP_Math: add a more complex polygon for Polygon_outside tests 2019-05-29 15:34:02 +10:00
Peter Barker d3971c18fa AP_Math: more tests for closed-vs-open polygons 2019-05-29 15:34:02 +10:00
Peter Barker d74e6db12e AP_Math: add more tests for Polygon_outside 2019-05-29 15:34:02 +10:00
Peter Barker 36fe9a18a0 AP_Math: make Polygon_outside cope with being passed unclosed polygons 2019-05-29 15:34:02 +10:00
Peter Barker 64aafb2af2 AP_Math: add Polygon_outside tests for long template instantiation 2019-05-28 09:08:07 +10:00
Peter Barker 51a0401383 AP_Math: correct Polygon_outside floating point instatiation
This routine was entemplatificated from the integer version, which was
designed to be perfect across representable ranges of points.  The
floating point version suffered from a rounding problem.
2019-05-28 09:08:07 +10:00
Peter Barker b35b65eed1 AP_Math: add GTEST suite for Polygon_outside 2019-05-28 09:08:07 +10:00
Peter Barker f09efe0908 AP_Math: correct URL for Polygon_outside algorithm 2019-05-24 13:17:43 +10:00
Francisco Ferreira 6e95a144ef AP_Math: add macro for m/s to knots convertion 2019-05-21 09:41:15 +10:00
murata c6bcb1d54c AP_Math: Collect CRC16 into CRC file
AP_Math: Collect CRC16 into CRC file
2019-05-21 09:19:19 +10:00
Andrew Tridgell 85ce10adfd AP_Math: fixed test build 2019-05-15 15:33:48 +10:00
murata 7f42be5d3e AP_Math: Commonize the CRC4 method 2019-04-24 08:44:11 -07:00
Mark Whitehorn b515431008 AP_Math: add expo and throttle_curve functions 2019-04-23 09:46:38 +10:00
Peter Barker b22d3a0103 AP_Math: avoid casting floats to int32's for temporary variables
Note the use of 64-bit integer arithmetic further down, however
2019-04-23 09:36:17 +10:00
Pierre Kancir ff4587a33a AP_Math: move location define to Location class 2019-04-23 09:20:43 +10:00
Pierre Kancir 1854681e09 AP_Math: use past_interval_finish_line and line_path_proportion from Location 2019-04-23 09:20:43 +10:00
Pierre Kancir 4f31c3dcd5 AP_Math: move line_path_proportion to Location 2019-04-23 09:20:43 +10:00
Pierre Kancir e06d7dbbf7 AP_Math: move location_passed_point to Location and rename 2019-04-23 09:20:43 +10:00
Peter Barker 11dcdc58e0 AP_Math: clean up includes a little 2019-04-16 10:00:29 +10:00
Pierre Kancir 121e5d0abf AP_Math: move location_3d_diff_NED to Location and rename 2019-04-09 20:59:48 +10:00
Peter Barker 381bb41a5e AP_Math: make constraining NaNs an internal error 2019-04-09 10:18:43 +10:00
Pierre Kancir e787922ab0 AP_Math: move check_latlng to Location 2019-04-08 12:56:01 -07:00
Pierre Kancir b10e75f4e1 AP_Math: move locations_are_same to Location and rename to same_latlon_as 2019-04-08 08:05:05 -07:00
Pierre Kancir 058cade92c AP_Math: use get_distance_NE instead of location_diff 2019-04-08 08:00:52 -07:00
Pierre Kancir 00fa07ef33 AP_Math: move location_diff to Location and rename 2019-04-08 08:00:52 -07:00
Peter Barker ce53ae63ae AP_Math: use /2 in place of *0.5f
MdB says:

dividing by 2 is actually optimal. It's type correct for all usage, and the compiler generates the multiplication if it's float, and sticks with divide for integers

Godbolt indicates on any optimization level (O1-O3, and Os) that the compiler will correctly optimize the / 2 into a float multiplication if using a float, but if using integer types in the template it will stick with the / 2 which is faster then doing the conversions to/from float.
2019-04-05 23:04:17 -07:00
Peter Barker 39ae285a7f AP_Math: add floating point constant designators 2019-04-05 23:04:17 -07:00
Pierre Kancir b31e5bf055 AP_Math: move location_update to Location and rename to offset_bearing 2019-04-06 09:10:28 +11:00
Pierre Kancir 88b29ff18c AP_Math: move get_bearing_cd to Location and rename to get_bearing_to 2019-04-06 09:10:28 +11:00
Pierre Kancir f6941beeb9 AP_Math: fix circulary inclusion error 2019-04-02 19:00:02 +11:00
Pierre Kancir d47e9c8514 AP_Math: add missing include on matrix3 2019-04-02 19:00:02 +11:00
Peter Barker e6a8e337c7 AP_Math: move sanitize to be a method on location 2019-04-02 10:19:38 +11:00
Peter Barker 431bd77d7e AP_Math: move print_latlon into sole caller 2019-04-02 10:19:38 +11:00
Peter Barker 499cc45ac0 AP_Math: move longitude_scale into Location class 2019-03-12 10:11:12 +11:00
Dr.-Ing. Amilcar do Carmo Lucas 65ccef04b9 AP_Math: replace location_offset() and get_distance() C function calls with Location object member (C++) function calls
This allows removing duplicated code in the AP_Math/location.cpp file
2019-02-28 11:44:09 +11:00
Andrew Tridgell ecbe67a0fe AP_Math: fixed inefficient sq() function 2019-02-23 21:04:00 +11:00
Randy Mackay 07f7d793df AP_Math: add quaternion::angular_difference 2019-02-22 13:00:07 +09:00
Peter Barker 81ddeef1bd AP_Math: remove keywords.txt 2019-02-17 00:29:38 -08:00
Pierre Kancir 695073db49 AP_Math: correct crc_xmodem definition 2019-02-06 23:20:07 +11:00
Pierre Kancir 9e927d1376 AP_Math: correct copyright, add pragma-once 2019-02-06 23:20:07 +11:00
Pierre Kancir 97ce39bf0c AP_Math: use direct assignment for rotate() 2019-02-06 21:41:30 +11:00
Pierre Kancir dd0283d537 AP_Math: reduce variable scope in crc_crc8 2019-02-06 21:41:30 +11:00
Peter Barker 2fa0b61f8b AP_Math: update example/test for Location_Class merge 2019-01-16 11:45:29 +11:00
Peter Barker 31fa9e582e AP_Math: adjust for Location_Class and Location unification 2019-01-16 11:45:29 +11:00
Peter Barker ce37c9f69b AP_Math: adjust for location flags being moved out of union 2019-01-16 11:45:29 +11:00
Pierre Kancir 85b83ed6af AP_Math: remove non-ascii caracter 2018-12-22 08:39:23 +09:00
Pierre Kancir f1270b4b22 AP_Math: const correctness 2018-12-22 08:39:06 +09:00
Michael du Breuil 48610ea0a0 AP_Math: Remove an unneeded safe_sqrtf, leverage is_zero 2018-11-07 10:43:28 +11:00
Peter Barker 154d771e6c AP_Math: correct compilation when running MATH_CHECK_INDEXES 2018-10-19 08:46:43 +11:00
Peter Barker dc14d7bce4 AP_Math: add another test for wrap_360_cd 2018-10-16 10:29:24 +11:00
Lucas De Marchi 5521fce676 AP_Math: add non-uniform Vector3f scaling 2018-10-15 14:41:09 -07:00
Andrew Tridgell d4eaf09baf AP_Math: added rotation_equal() 2018-10-01 14:26:56 +09:00
Michael du Breuil 9cd1be1d6f AP_Math: Speed up location calculations slightly 2018-09-19 14:40:48 +10:00
Peter Barker 43f3d611b2 AP_Math: pragma away the float-equal test for the maths tests
There are legitimate reasons for doing direct equivalence in these files
2018-08-28 09:54:47 +10:00
Peter Barker 8fee27937a AP_Math: eliminate SITL float-equals issues 2018-08-28 09:54:47 +10:00
Peter Barker fa5757f618 AP_Math: fix float-equals warnings 2018-08-15 12:16:49 +10:00
Andrew Tridgell c3cf8f5435 AP_Math: fixed a bug in segment_intersection()
we could get an intercept point beyond the end of the segment
2018-08-14 19:41:45 +10:00
Peter Barker 626467db14 AP_Math: add tests for line intersection 2018-08-14 19:41:45 +10:00
Michael du Breuil d568767164 AP_Math: Add conversion between inches of water to pascals 2018-08-08 09:07:17 +10:00
Michael du Breuil 46355e3de9 AP_Math: Add a warning to rotations to indicate that it is expected to
match the MAVLink definitions
2018-07-26 12:58:14 +09:00
Andrew Tridgell 8170fbcf80 AP_Math: added a comment on conventions for to_euler() 2018-07-18 16:07:19 +10:00
Peter Barker 20d22f3629 AP_Math: quaternion requires isnan, so include math.h to get it 2018-07-02 09:31:11 +10:00
Peter Barker 6af0dcfed0 AP_Math: create a constrain_int64
The template system doesn't work across 32/64 bit builds (SITL
vs fmuv4), probably because int is typedef'd to int64
2018-06-15 08:01:22 +10:00
Tom Pittenger 3653ba61d7 AP_Math: add is_valid_octal helper function.
returns true if valid
2018-05-23 14:02:45 -07:00
Patrick José Pereira 1ca6647b2e AP_Math: Create Standard Sea Level variables
Signed-off-by: Patrick José Pereira <patrickelectric@gmail.com>
2018-05-23 02:36:43 +01:00
Andrew Tridgell d4d7d1f734 AP_Math: avoid double maths when not needed 2018-05-07 11:43:23 +10:00
Andrew Tridgell 61c8dfac31 AP_Math: split out double precision location functions
this allows ALLOW_DOUBLE_MATH_FUNCTIONS to be used
2018-05-07 11:43:23 +10:00
Andrew Tridgell 3b8ec3a2a0 AP_Math: allow double precision maths where needed 2018-05-07 11:43:23 +10:00
Jacob Walser f97ac4af30 AP_Math: add custom rotation option 2018-04-24 13:04:37 +01:00
Jacob Walser 4f02f709a2 AP_Math: fix typo 2018-04-24 13:04:37 +01:00
Jacob Walser e738f33770 AP_Math: Add ROTATION_PITCH_315 and ROTATION_ROLL_90_PITCH_315 2018-04-24 13:04:37 +01:00
Andrew Tridgell a6e05cbf5a AP_Math: added crc32 for IOMCU bootloader protocol 2018-04-17 08:44:44 +10:00
Andrew Tridgell 17f2f40b11 AP_Math: added xmodem CRC
used by blheli 4-way ESC protocol
2018-04-07 09:10:29 +10:00
Peter Barker febcdd766b AP_Math: narrow enumeration to uint8_t to avoid narrowing-warnings
/home/pbarker/rc/ardupilot/libraries/DataFlash/LogFile.cpp:361:25:
error: non-constant-expression cannot be narrowed from type 'enum
Rotation' to 'uint8_t' (aka 'unsigned char') in initializer list
[-Wc++11-narrowing]
        orient1       : s0 ? s0->orientation() : ROTATION_NONE,
2018-04-02 14:12:09 +09:00
Peter Barker c343a286c5 AP_Math: quaternion: add contructor from float[4] 2018-03-27 20:13:03 +09:00
bnsgeyer 600e0dac92 AP_Math: added support for cubic spline interpolation 2018-03-27 09:07:03 +11:00
Randy Mackay c28cfcdc27 AP_Math: add Vector2f::circle_segment_intersection 2018-01-22 17:18:41 +09:00
Randy Mackay a655c36159 AP_Math: add Vector2f::segment_intersection 2018-01-22 17:18:41 +09:00
Andrew Tridgell ee1fea55ce AP_Math: moved constants from AP_Baro 2018-01-16 07:14:20 +11:00
Andrew Tridgell 4ce696a520 AP_Math: fixed example build on ChibiOS 2018-01-15 11:46:02 +11:00
Andrew Tridgell f5b24a3838 AP_Math: fixed build of Sub with ChibiOS 2018-01-15 11:46:02 +11:00
Andrew Tridgell 3d2c4ffa79 AP_Math: allow write to indexed vector2 2018-01-15 11:46:02 +11:00
Andrew Tridgell f088c3de23 AP_Math: added long templates 2018-01-15 11:46:02 +11:00
Dr.-Ing. Amilcar Do Carmo Lucas e13281ab2d AP_Math: add overloaded functions get_horizontal_distance_cm() and get_bearing_cd() (NFC) 2017-12-05 08:54:49 +09:00
Dr.-Ing. Amilcar Do Carmo Lucas ec1790dad9 AP_Math: Use DEGX100 define instead of hardcoded value (NFC) 2017-12-05 08:54:49 +09:00
Andrew Tridgell 9660973975 AP_Math: make crc_crc8 const 2017-11-27 10:15:07 +09:00
Andrew Tridgell 3f226cd2b9 AP_Math: added from_rotation() method to Matrix3
this is used to get a rotation matrix from a rotation enum
2017-11-23 14:26:11 +11:00
Peter Barker 1ca76173a5 AP_Math: set radians(...) and degrees(...) as constexpr 2017-10-27 16:33:45 +11:00
Randy Mackay 2aa1f3f100 AP_Math: replace divide with multiply in distance_to_segment 2017-09-09 14:05:41 +09:00
Randy Mackay e892bbbac0 AP_Math: add Vector3f::distance_to_segment 2017-09-09 14:05:41 +09:00
Randy Mackay e6328c350d AP_Math: add Vector3f::distance_squared 2017-09-09 14:05:41 +09:00
khancyr 15398f8b0e AP_Math: correct variable init and remove define in polygon 2017-07-31 17:35:08 +09:00
Miguel Arroyo 7cea21afa2 AP_Math: Moves rand_vec3f from SITL_State. 2017-06-29 09:22:08 +10:00
Francisco Ferreira da5060964b AP_Math: uniformize template type parameter keyword
Use typename everywhere instead of class
2017-06-21 18:19:31 +09:00
Francisco Ferreira 1ffe12008c AP_Math: adapt test for new norm method API 2017-06-21 18:19:31 +09:00
Francisco Ferreira 7b98f41947 AP_Math: correct norm to need two arguments
Correctly use sqrtf instead of the double version
Stop casting to float since sq already returns one
2017-06-21 18:19:31 +09:00
Randy Mackay db45442de2 AP_Math: remove unused angle method 2017-06-09 15:21:58 +09:00
Michael du Breuil 2cd6ff6dd5 AP_Math: Accept float epsilon in is_positive is_negative as a valid result 2017-05-27 10:46:59 -07:00
Michael du Breuil 5a15413513 AP_Math: Add is_negative and is_positive helpers 2017-05-24 15:22:27 -07:00
Andrew Tridgell 607220d12b AP_Math: rename macros to avoid conflicts
these macros were also defined in NuttX in clock.h
2017-05-06 15:21:14 +10:00
Andrew Tridgell 2fcecaa7c5 AP_Math: added rand_float() 2017-05-03 20:12:04 +10:00
Pierre Kancir f2812c1efd AP_Math: example fix travis warning
missing function declaration
implicit cast
some style fix
2017-04-13 19:56:16 +01:00
Tom Pittenger 1abeb03d2b AP_Math: remove HAL_CPU_CLASS_16 2017-04-12 17:25:30 -07:00
Andrey Kolobov a1fa2a9de3 AP_Math: added matrixN for soaring controller 2017-03-14 08:35:44 +11:00
Francisco Ferreira 7afcbf51ec
AP_Math: also fix SEC_PER_WEEK 2017-03-13 02:57:30 +00:00
murata 1982285e23 AP_Math: update MSEC_PER_SEC definition to fix GPS time calcs 2017-03-13 11:50:33 +09:00
Michael du Breuil c5c94949bf AP_Math: Extend vector2::angle(vector2) to distinguish parallel and antiparallel vectors
There are a number of use cases where distingusihing antiparallel from parallel vectors is important
2017-03-02 00:50:44 +00:00
Michael du Breuil 97c57764c4 AP_Math: Add a 3D location difference, returning NED 2017-02-13 09:23:14 +11:00
murata 30151c8253 Global: Define MSEC_PER_SEC, MSEC_PER_WEEK, SEC_PER_WEEK and UNIX_OFFSET. 2017-02-11 01:34:09 -08:00
Lucas De Marchi 2b9478f430 AP_Math: tests: make both arguments double
libraries/AP_Math/tests/test_math.cpp.3.o: In function `MathTest_IsEqual_Test::TestBody()':
test_math.cpp:(.text._ZN21MathTest_IsEqual_Test8TestBodyEv+0x1a0): undefined reference to `std::enable_if<std::is_floating_point<std::common_type<float, double>::type>::value, bool>::type is_equal<float, double>(float, double)'
collect2: error: ld returned 1 exit status
2017-02-06 09:27:22 -08:00
Lucas De Marchi 008ac0a2a8 AP_Math: remove unused double instantiation 2017-02-06 09:27:22 -08:00
Lucas De Marchi 87038d8ef1 AP_Math: add casts to consider literals as doubles
Since we pass -fsingle-precision-constant to the compiler, add casts to
make literals real doubles.
2017-02-06 09:27:22 -08:00
Lucas De Marchi 48d94db259 AP_Math: double constants need a type
We can't use define since we use -fsingle-precision-constant and they
would be interpreted as float.
2017-02-06 09:27:22 -08:00
Lucas De Marchi a500aced3c AP_Math: remove unused double constants 2017-02-06 09:27:22 -08:00
Lucas De Marchi 87c82ce0c6 AP_Math: add some more tests for constrain_value() 2017-01-27 12:15:20 -08:00
Lucas De Marchi 82d210144b AP_Math: remove warnings from constrain_value()
Return type is T which can be an integral type, float or double. By
dividing by 2 we avoid float operation on the first case and do the
right thing on the second and third.
2017-01-27 12:15:19 -08:00
Lucas De Marchi 2605c7265b AP_Math: remove warnings from safe_asin()
Return type is float, so operate on float types everywhere.
Fixes this warning while building for PX4:

../../libraries/AP_Math/AP_Math.cpp: In instantiation of 'float safe_asin(T) [with T = double]':
../../libraries/AP_Math/AP_Math.cpp:56:48:   required from here
../../libraries/AP_Math/AP_Math.cpp:44:11: warning: implicit conversion from 'float' to 'double' to match other operand of binary expression [-Wdouble-promotion]
     if (v >= 1.0f) {
           ^
../../libraries/AP_Math/AP_Math.cpp:47:11: warning: implicit conversion from 'float' to 'double' to match other operand of binary expression [-Wdouble-promotion]
     if (v <= -1.0f) {
           ^
2017-01-27 12:15:19 -08:00
Lucas De Marchi 69a9cd3625 AP_Math: add tests to is_equal()
Contemplate the use of double values.
2017-01-27 12:15:19 -08:00
Lucas De Marchi 4f8d2059f8 AP_Math: use right epsilon for is_equal()
We are calling fabsf(), which returns a float. We should use the epsilon
from float type, not from the argument type passed to fabsf().

On the other hand when the double version is instantiated we do want to
use the std::numeric_limits<double>::epsilon() value.

This adds a branch to the function, but it's removed when the function
is intantiated by the compiler since the type is known at compile-time.

Fixes this warning when building for PX4:
../../libraries/AP_Math/AP_Math.cpp: In instantiation of 'typename std::enable_if<std::is_floating_point<typename std::common_type<_Tp, _Up>::type>::value, bool>::type is_equal(Arithmetic1, Arithmetic2) [with Arithmetic1 = double; Arithmetic2 = double; typename std::enable_if<std::is_floating_point<typename std::common_type<_Tp, _Up>::type>::value, bool>::type = bool]':
../../libraries/AP_Math/AP_Math.cpp:23:66:   required from here
../../libraries/AP_Math/AP_Math.cpp:17:29: warning: implicit conversion from 'float' to 'double' to match other operand of binary expression [-Wdouble-promotion]
     return fabsf(v_1 - v_2) < std::numeric_limits<decltype(v_1 - v_2)>::epsilon();
                             ^
2017-01-27 12:15:19 -08:00
murata ec4cce15a1 AP_Math: Unify from print or println to printf. 2017-01-27 18:20:22 +11:00
Andrew Tridgell 67a2441b12 AP_Math: started a set of crc functions
these functions are often common between drivers
2017-01-27 18:11:29 +11:00
murata e903cb9945 AP_Math: Change mask value to hexadecimal number. 2017-01-17 10:20:15 -08:00
Pierre Kancir 47f1a754c5 AP_Math: add some test for vector2 equality test 2016-12-20 14:09:04 +00:00
Pierre Kancir eae093cd2a AP_Math: add test for is_equal for int 2016-12-20 14:09:04 +00:00
Pierre Kancir da49149d19 AP_Math: is_equal correct comparison for integer as epsilon doesn't exist.
Credit to Kwikius for the right solution
2016-12-20 14:09:04 +00:00
Pierre Kancir ce734b5f7b AP_Math: Remove unecessary check 2016-12-19 14:36:03 +00:00
Pierre Kancir 556993d7f0 AP_Math: Vector2 add == operator for int 2016-12-06 09:31:21 -08:00
Pierre Kancir 6bf1322633 AP_Math: polygon.cpp correct float comparison 2016-12-06 09:31:21 -08:00
Pierre Kancir 79a9e8dfad AP_Math: Matrix_alg fix implicite cast from bool to float 2016-12-05 12:39:31 -08:00
Pierre Kancir fb7a00799f AP_Math: quaternion fix missing return 2016-12-05 10:33:41 -08:00
Andrew Tridgell a8d10e8c2c AP_Math: added get_random16() 2016-12-02 09:49:38 +11:00
murata f9add59b58 Global: Aggregate the same definitions.
Global: Aggregate the same definitions.
2016-11-09 11:46:55 -03:00
Andrew Tridgell b00fd95725 AP_Math: define Vector3l for += op 2016-11-09 17:08:13 +11:00
murata c808ee2f49 Global: To nullptr from NULL.
RC_Channel: To nullptr from NULL.

AC_Fence: To nullptr from NULL.

AC_Avoidance: To nullptr from NULL.

AC_PrecLand: To nullptr from NULL.

DataFlash: To nullptr from NULL.

SITL: To nullptr from NULL.

GCS_MAVLink: To nullptr from NULL.

DataFlash: To nullptr from NULL.

AP_Compass: To nullptr from NULL.

Global: To nullptr from NULL.

Global: To nullptr from NULL.
2016-11-02 16:04:47 -02:00
Mathieu OTHACEHE 152edf7189 Global: remove mode line from headers
Using a global .dir-locals.el file is a better alternative than
reincluding the same emacs header in every file of the project.
2016-10-24 09:42:01 -02:00
Jonathan Challinger 80d9092993 AP_Math: remove rotateXY and rotateXYinv 2016-10-13 10:02:14 +11:00
Lucas De Marchi ae53920e5b build: don't build examples with old build system
We currently check examples are buildable with waf which doesn't need
the libraries to be specified in a make.inc file.  Having the makefiles
there is misleading since people try to build and realize the build is
broken.
2016-10-11 13:03:08 +11:00
Lucas De Marchi 0d4caa3ccc AP_Math: remove declaration of not implemented functions 2016-08-03 00:16:35 -03:00
Murilo Belluzzo 70942472d3 AP_Math: Matrix: Change deallocator to match allocator used 2016-08-03 00:09:11 -03:00
Lucas De Marchi 7b7e73680f AP_Math: add USEC_PER_MSEC 2016-07-30 00:55:28 -03:00
Peter Barker 2047d53470 Math: move closest_point in from AC_Avoid 2016-07-25 20:24:37 +09:00