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implement DubinsPath planning based on C++ Dubins-Curves
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The MIT License | ||
|
||
Copyright (c) 2024 dohyeunglee | ||
|
||
Permission is hereby granted, free of charge, to any person obtaining a copy | ||
of this software and associated documentation files (the "Software"), to deal | ||
in the Software without restriction, including without limitation the rights | ||
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell | ||
copies of the Software, and to permit persons to whom the Software is | ||
furnished to do so, subject to the following conditions: | ||
|
||
The above copyright notice and this permission notice shall be included in | ||
all copies or substantial portions of the Software. | ||
|
||
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR | ||
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, | ||
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE | ||
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER | ||
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, | ||
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN | ||
THE SOFTWARE. |
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# dubins | ||
> Pure Golang implementation of Dubins Path, based on C++ [Dubins-Curves](https://github.com/AndrewWalker/Dubins-Curves) | ||
WIP | ||
## Installation | ||
```bash | ||
go get github.com/dohyeunglee/dubins | ||
``` | ||
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## API | ||
Visit https://pkg.go.dev/github.com/dohyeunglee/dubins | ||
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## Example | ||
An example is available in [example/main.go](example/main.go) | ||
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## Demo | ||
A demo with plot is available in [demo](demo/README.md) | ||
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## Test | ||
```bash | ||
go test | ||
``` | ||
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## Benchmark | ||
```bash | ||
go test -bench . | ||
``` | ||
### Result | ||
Run on M1 Macbook Pro | ||
```bash | ||
BenchmarkMinLengthPath-8 1000000 1126 ns/op | ||
``` | ||
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## Note | ||
If you want ReedsSheppPath, check https://github.com/dohyeunglee/reedsshepp. | ||
|
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package dubins | ||
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import ( | ||
"math" | ||
) | ||
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const ( | ||
twoPi = 2 * math.Pi | ||
) | ||
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type pathTypeFunc func(pathParams) (Path, bool) | ||
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var ( | ||
pathTypeFuncMap = map[PathType]pathTypeFunc{ | ||
LSL: lsl, | ||
LSR: lsr, | ||
RSL: rsl, | ||
RSR: rsr, | ||
RLR: rlr, | ||
LRL: lrl, | ||
} | ||
pathTypeCourseTypesMap = map[PathType][3]PathCourseType{ | ||
LSL: {CourseTypeLeft, CourseTypeStraight, CourseTypeLeft}, | ||
LSR: {CourseTypeLeft, CourseTypeStraight, CourseTypeRight}, | ||
RSL: {CourseTypeRight, CourseTypeStraight, CourseTypeLeft}, | ||
RSR: {CourseTypeRight, CourseTypeStraight, CourseTypeRight}, | ||
RLR: {CourseTypeRight, CourseTypeLeft, CourseTypeRight}, | ||
LRL: {CourseTypeLeft, CourseTypeRight, CourseTypeLeft}, | ||
} | ||
) | ||
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type pathParams struct { | ||
alpha float64 | ||
beta float64 | ||
d float64 | ||
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sinAlpha float64 | ||
sinBeta float64 | ||
cosAlpha float64 | ||
cosBeta float64 | ||
cosAlphaMinusBeta float64 | ||
dSquare float64 | ||
} | ||
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func lsl(pp pathParams) (Path, bool) { | ||
pSquare := 2 + pp.dSquare - 2*pp.cosAlphaMinusBeta + 2*pp.d*(pp.sinAlpha-pp.sinBeta) | ||
if pSquare < 0 { | ||
return Path{}, false | ||
} | ||
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tmp := math.Atan2(pp.cosBeta-pp.cosAlpha, pp.d+pp.sinAlpha-pp.sinBeta) | ||
return Path{ | ||
t: mod2pi(tmp - pp.alpha), | ||
p: math.Sqrt(pSquare), | ||
q: mod2pi(pp.beta - tmp), | ||
pathType: LSL, | ||
}, true | ||
} | ||
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func rsr(pp pathParams) (Path, bool) { | ||
pSquare := 2 + pp.dSquare - 2*pp.cosAlphaMinusBeta + 2*pp.d*(pp.sinBeta-pp.sinAlpha) | ||
if pSquare < 0 { | ||
return Path{}, false | ||
} | ||
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tmp := math.Atan2(pp.cosAlpha-pp.cosBeta, pp.d-pp.sinAlpha+pp.sinBeta) | ||
return Path{ | ||
t: mod2pi(pp.alpha - tmp), | ||
p: math.Sqrt(pSquare), | ||
q: mod2pi(tmp - pp.beta), | ||
pathType: RSR, | ||
}, true | ||
} | ||
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func lsr(pp pathParams) (Path, bool) { | ||
pSquare := -2 + pp.dSquare + 2*pp.cosAlphaMinusBeta + 2*pp.d*(pp.sinAlpha+pp.sinBeta) | ||
if pSquare < 0 { | ||
return Path{}, false | ||
} | ||
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p := math.Sqrt(pSquare) | ||
tmp := math.Atan2(-pp.cosAlpha-pp.cosBeta, pp.d+pp.sinAlpha+pp.sinBeta) - math.Atan2(-2, p) | ||
t := mod2pi(tmp - pp.alpha) | ||
q := mod2pi(tmp - mod2pi(pp.beta)) | ||
return Path{ | ||
t: t, | ||
p: p, | ||
q: q, | ||
pathType: LSR, | ||
}, true | ||
} | ||
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func rsl(pp pathParams) (Path, bool) { | ||
pSquare := -2 + pp.dSquare + 2*pp.cosAlphaMinusBeta - 2*pp.d*(pp.sinAlpha+pp.sinBeta) | ||
if pSquare < 0 { | ||
return Path{}, false | ||
} | ||
p := math.Sqrt(pSquare) | ||
tmp := math.Atan2(pp.cosAlpha+pp.cosBeta, pp.d-pp.sinAlpha-pp.sinBeta) - math.Atan2(2, p) | ||
t := mod2pi(pp.alpha - tmp) | ||
q := mod2pi(pp.beta - tmp) | ||
return Path{ | ||
t: t, | ||
p: p, | ||
q: q, | ||
pathType: RSL, | ||
}, true | ||
} | ||
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func rlr(pp pathParams) (Path, bool) { | ||
tmp := (6 - pp.dSquare + 2*pp.cosAlphaMinusBeta + 2*pp.d*(pp.sinAlpha-pp.sinBeta)) / 8 | ||
if math.Abs(tmp) > 1 { | ||
return Path{}, false | ||
} | ||
phi := math.Atan2(pp.cosAlpha-pp.cosBeta, pp.d-pp.sinAlpha+pp.sinBeta) | ||
p := mod2pi(twoPi - math.Acos(tmp)) | ||
t := mod2pi(pp.alpha - phi + mod2pi(p/2)) | ||
q := mod2pi(pp.alpha - pp.beta - t + mod2pi(p)) | ||
return Path{ | ||
t: t, | ||
p: p, | ||
q: q, | ||
pathType: RLR, | ||
}, true | ||
} | ||
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func lrl(pp pathParams) (Path, bool) { | ||
tmp := (6 - pp.dSquare + 2*pp.cosAlphaMinusBeta + 2*pp.d*(pp.sinBeta-pp.sinAlpha)) / 8 | ||
if math.Abs(tmp) > 1 { | ||
return Path{}, false | ||
} | ||
phi := math.Atan2(pp.cosAlpha-pp.cosBeta, pp.d+pp.sinAlpha-pp.sinBeta) | ||
p := mod2pi(twoPi - math.Acos(tmp)) | ||
t := mod2pi(-pp.alpha - phi + p/2) | ||
q := mod2pi(mod2pi(pp.beta) - pp.alpha - t + mod2pi(p)) | ||
return Path{ | ||
t: t, | ||
p: p, | ||
q: q, | ||
pathType: LRL, | ||
}, true | ||
} | ||
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func fmodr(x float64, y float64) float64 { | ||
return x - y*math.Floor(x/y) | ||
} | ||
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func mod2pi(theta float64) float64 { | ||
return fmodr(theta, twoPi) | ||
} |
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The MIT License | ||
|
||
Copyright (c) 2024 dohyeunglee | ||
|
||
Permission is hereby granted, free of charge, to any person obtaining a copy | ||
of this software and associated documentation files (the "Software"), to deal | ||
in the Software without restriction, including without limitation the rights | ||
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell | ||
copies of the Software, and to permit persons to whom the Software is | ||
furnished to do so, subject to the following conditions: | ||
|
||
The above copyright notice and this permission notice shall be included in | ||
all copies or substantial portions of the Software. | ||
|
||
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR | ||
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, | ||
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE | ||
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER | ||
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, | ||
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN | ||
THE SOFTWARE. |
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@@ -0,0 +1,18 @@ | ||
# dubins demo | ||
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> dubins Length, Interpolate demo, based on python [pydubins](https://github.com/AndrewWalker/pydubins) demo | ||
## Results | ||
| | | | | ||
|:-------------------:|:-------------------:|:-------------------:| | ||
| ![](demo_path0.png) | ![](demo_path1.png) | ![](demo_path2.png) | | ||
| ![](demo_path3.png) | ![](demo_path4.png) | ![](demo_path5.png) | | ||
| ![](demo_path6.png) | ![](demo_path7.png) | ![](demo_path8.png) | | ||
| ![](demo_path9.png) | | | | ||
|
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## Run | ||
```bash | ||
go mod tidy | ||
go run main.go | ||
``` | ||
|
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module github.com/dohyeunglee/dubins/demo | ||
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go 1.22.3 | ||
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replace github.com/dohyeunglee/dubins v0.0.1 => ../ | ||
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require ( | ||
github.com/dohyeunglee/dubins v0.0.1 | ||
gonum.org/v1/plot v0.14.0 | ||
) | ||
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require ( | ||
git.sr.ht/~sbinet/gg v0.5.0 // indirect | ||
github.com/ajstarks/svgo v0.0.0-20211024235047-1546f124cd8b // indirect | ||
github.com/campoy/embedmd v1.0.0 // indirect | ||
github.com/go-fonts/liberation v0.3.1 // indirect | ||
github.com/go-latex/latex v0.0.0-20230307184459-12ec69307ad9 // indirect | ||
github.com/go-pdf/fpdf v0.8.0 // indirect | ||
github.com/golang/freetype v0.0.0-20170609003504-e2365dfdc4a0 // indirect | ||
github.com/pmezard/go-difflib v1.0.0 // indirect | ||
golang.org/x/image v0.11.0 // indirect | ||
golang.org/x/text v0.12.0 // indirect | ||
) |
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---|---|---|
@@ -0,0 +1,88 @@ | ||
git.sr.ht/~sbinet/cmpimg v0.1.0 h1:E0zPRk2muWuCqSKSVZIWsgtU9pjsw3eKHi8VmQeScxo= | ||
git.sr.ht/~sbinet/cmpimg v0.1.0/go.mod h1:FU12psLbF4TfNXkKH2ZZQ29crIqoiqTZmeQ7dkp/pxE= | ||
git.sr.ht/~sbinet/gg v0.5.0 h1:6V43j30HM623V329xA9Ntq+WJrMjDxRjuAB1LFWF5m8= | ||
git.sr.ht/~sbinet/gg v0.5.0/go.mod h1:G2C0eRESqlKhS7ErsNey6HHrqU1PwsnCQlekFi9Q2Oo= | ||
github.com/BurntSushi/toml v0.3.1/go.mod h1:xHWCNGjB5oqiDr8zfno3MHue2Ht5sIBksp03qcyfWMU= | ||
github.com/ajstarks/deck v0.0.0-20200831202436-30c9fc6549a9/go.mod h1:JynElWSGnm/4RlzPXRlREEwqTHAN3T56Bv2ITsFT3gY= | ||
github.com/ajstarks/deck/generate v0.0.0-20210309230005-c3f852c02e19/go.mod h1:T13YZdzov6OU0A1+RfKZiZN9ca6VeKdBdyDV+BY97Tk= | ||
github.com/ajstarks/svgo v0.0.0-20211024235047-1546f124cd8b h1:slYM766cy2nI3BwyRiyQj/Ud48djTMtMebDqepE95rw= | ||
github.com/ajstarks/svgo v0.0.0-20211024235047-1546f124cd8b/go.mod h1:1KcenG0jGWcpt8ov532z81sp/kMMUG485J2InIOyADM= | ||
github.com/campoy/embedmd v1.0.0 h1:V4kI2qTJJLf4J29RzI/MAt2c3Bl4dQSYPuflzwFH2hY= | ||
github.com/campoy/embedmd v1.0.0/go.mod h1:oxyr9RCiSXg0M3VJ3ks0UGfp98BpSSGr0kpiX3MzVl8= | ||
github.com/davecgh/go-spew v1.1.1 h1:vj9j/u1bqnvCEfJOwUhtlOARqs3+rkHYY13jYWTU97c= | ||
github.com/davecgh/go-spew v1.1.1/go.mod h1:J7Y8YcW2NihsgmVo/mv3lAwl/skON4iLHjSsI+c5H38= | ||
github.com/go-fonts/dejavu v0.1.0 h1:JSajPXURYqpr+Cu8U9bt8K+XcACIHWqWrvWCKyeFmVQ= | ||
github.com/go-fonts/dejavu v0.1.0/go.mod h1:4Wt4I4OU2Nq9asgDCteaAaWZOV24E+0/Pwo0gppep4g= | ||
github.com/go-fonts/latin-modern v0.3.1 h1:/cT8A7uavYKvglYXvrdDw4oS5ZLkcOU22fa2HJ1/JVM= | ||
github.com/go-fonts/latin-modern v0.3.1/go.mod h1:ysEQXnuT/sCDOAONxC7ImeEDVINbltClhasMAqEtRK0= | ||
github.com/go-fonts/liberation v0.3.1 h1:9RPT2NhUpxQ7ukUvz3jeUckmN42T9D9TpjtQcqK/ceM= | ||
github.com/go-fonts/liberation v0.3.1/go.mod h1:jdJ+cqF+F4SUL2V+qxBth8fvBpBDS7yloUL5Fi8GTGY= | ||
github.com/go-latex/latex v0.0.0-20230307184459-12ec69307ad9 h1:NxXI5pTAtpEaU49bpLpQoDsu1zrteW/vxzTz8Cd2UAs= | ||
github.com/go-latex/latex v0.0.0-20230307184459-12ec69307ad9/go.mod h1:gWuR/CrFDDeVRFQwHPvsv9soJVB/iqymhuZQuJ3a9OM= | ||
github.com/go-pdf/fpdf v0.8.0 h1:IJKpdaagnWUeSkUFUjTcSzTppFxmv8ucGQyNPQWxYOQ= | ||
github.com/go-pdf/fpdf v0.8.0/go.mod h1:gfqhcNwXrsd3XYKte9a7vM3smvU/jB4ZRDrmWSxpfdc= | ||
github.com/golang/freetype v0.0.0-20170609003504-e2365dfdc4a0 h1:DACJavvAHhabrF08vX0COfcOBJRhZ8lUbR+ZWIs0Y5g= | ||
github.com/golang/freetype v0.0.0-20170609003504-e2365dfdc4a0/go.mod h1:E/TSTwGwJL78qG/PmXZO1EjYhfJinVAhrmmHX6Z8B9k= | ||
github.com/kisielk/gotool v1.0.0/go.mod h1:XhKaO+MFFWcvkIS/tQcRk01m1F5IRFswLeQ+oQHNcck= | ||
github.com/pmezard/go-difflib v1.0.0 h1:4DBwDE0NGyQoBHbLQYPwSUPoCMWR5BEzIk/f1lZbAQM= | ||
github.com/pmezard/go-difflib v1.0.0/go.mod h1:iKH77koFhYxTK1pcRnkKkqfTogsbg7gZNVY4sRDYZ/4= | ||
github.com/stretchr/testify v1.9.0 h1:HtqpIVDClZ4nwg75+f6Lvsy/wHu+3BoSGCbBAcpTsTg= | ||
github.com/stretchr/testify v1.9.0/go.mod h1:r2ic/lqez/lEtzL7wO/rwa5dbSLXVDPFyf8C91i36aY= | ||
github.com/yuin/goldmark v1.2.1/go.mod h1:3hX8gzYuyVAZsxl0MRgGTJEmQBFcNTphYh9decYSb74= | ||
github.com/yuin/goldmark v1.4.13/go.mod h1:6yULJ656Px+3vBD8DxQVa3kxgyrAnzto9xy5taEt/CY= | ||
golang.org/x/crypto v0.0.0-20190308221718-c2843e01d9a2/go.mod h1:djNgcEr1/C05ACkg1iLfiJU5Ep61QUkGW8qpdssI0+w= | ||
golang.org/x/crypto v0.0.0-20191011191535-87dc89f01550/go.mod h1:yigFU9vqHzYiE8UmvKecakEJjdnWj3jj499lnFckfCI= | ||
golang.org/x/crypto v0.0.0-20200622213623-75b288015ac9/go.mod h1:LzIPMQfyMNhhGPhUkYOs5KpL4U8rLKemX1yGLhDgUto= | ||
golang.org/x/crypto v0.0.0-20210921155107-089bfa567519/go.mod h1:GvvjBRRGRdwPK5ydBHafDWAxML/pGHZbMvKqRZ5+Abc= | ||
golang.org/x/exp v0.0.0-20230801115018-d63ba01acd4b h1:r+vk0EmXNmekl0S0BascoeeoHk/L7wmaW2QF90K+kYI= | ||
golang.org/x/exp v0.0.0-20230801115018-d63ba01acd4b/go.mod h1:FXUEEKJgO7OQYeo8N01OfiKP8RXMtf6e8aTskBGqWdc= | ||
golang.org/x/image v0.11.0 h1:ds2RoQvBvYTiJkwpSFDwCcDFNX7DqjL2WsUgTNk0Ooo= | ||
golang.org/x/image v0.11.0/go.mod h1:bglhjqbqVuEb9e9+eNR45Jfu7D+T4Qan+NhQk8Ck2P8= | ||
golang.org/x/mod v0.3.0/go.mod h1:s0Qsj1ACt9ePp/hMypM3fl4fZqREWJwdYDEqhRiZZUA= | ||
golang.org/x/mod v0.6.0-dev.0.20220419223038-86c51ed26bb4/go.mod h1:jJ57K6gSWd91VN4djpZkiMVwK6gcyfeH4XE8wZrZaV4= | ||
golang.org/x/mod v0.8.0/go.mod h1:iBbtSCu2XBx23ZKBPSOrRkjjQPZFPuis4dIYUhu/chs= | ||
golang.org/x/net v0.0.0-20190404232315-eb5bcb51f2a3/go.mod h1:t9HGtf8HONx5eT2rtn7q6eTqICYqUVnKs3thJo3Qplg= | ||
golang.org/x/net v0.0.0-20190620200207-3b0461eec859/go.mod h1:z5CRVTTTmAJ677TzLLGU+0bjPO0LkuOLi4/5GtJWs/s= | ||
golang.org/x/net v0.0.0-20201021035429-f5854403a974/go.mod h1:sp8m0HH+o8qH0wwXwYZr8TS3Oi6o0r6Gce1SSxlDquU= | ||
golang.org/x/net v0.0.0-20210226172049-e18ecbb05110/go.mod h1:m0MpNAwzfU5UDzcl9v0D8zg8gWTRqZa9RBIspLL5mdg= | ||
golang.org/x/net v0.0.0-20220722155237-a158d28d115b/go.mod h1:XRhObCWvk6IyKnWLug+ECip1KBveYUHfp+8e9klMJ9c= | ||
golang.org/x/net v0.6.0/go.mod h1:2Tu9+aMcznHK/AK1HMvgo6xiTLG5rD5rZLDS+rp2Bjs= | ||
golang.org/x/sync v0.0.0-20190423024810-112230192c58/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM= | ||
golang.org/x/sync v0.0.0-20201020160332-67f06af15bc9/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM= | ||
golang.org/x/sync v0.0.0-20220722155255-886fb9371eb4/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM= | ||
golang.org/x/sync v0.1.0/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM= | ||
golang.org/x/sys v0.0.0-20190215142949-d0b11bdaac8a/go.mod h1:STP8DvDyc/dI5b8T5hshtkjS+E42TnysNCUPdjciGhY= | ||
golang.org/x/sys v0.0.0-20190412213103-97732733099d/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs= | ||
golang.org/x/sys v0.0.0-20200930185726-fdedc70b468f/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs= | ||
golang.org/x/sys v0.0.0-20201119102817-f84b799fce68/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs= | ||
golang.org/x/sys v0.0.0-20210119212857-b64e53b001e4/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs= | ||
golang.org/x/sys v0.0.0-20210615035016-665e8c7367d1/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg= | ||
golang.org/x/sys v0.0.0-20220520151302-bc2c85ada10a/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg= | ||
golang.org/x/sys v0.0.0-20220722155257-8c9f86f7a55f/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg= | ||
golang.org/x/sys v0.5.0/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg= | ||
golang.org/x/term v0.0.0-20201126162022-7de9c90e9dd1/go.mod h1:bj7SfCRtBDWHUb9snDiAeCFNEtKQo2Wmx5Cou7ajbmo= | ||
golang.org/x/term v0.0.0-20210927222741-03fcf44c2211/go.mod h1:jbD1KX2456YbFQfuXm/mYQcufACuNUgVhRMnK/tPxf8= | ||
golang.org/x/term v0.5.0/go.mod h1:jMB1sMXY+tzblOD4FWmEbocvup2/aLOaQEp7JmGp78k= | ||
golang.org/x/text v0.3.0/go.mod h1:NqM8EUOU14njkJ3fqMW+pc6Ldnwhi/IjpwHt7yyuwOQ= | ||
golang.org/x/text v0.3.3/go.mod h1:5Zoc/QRtKVWzQhOtBMvqHzDpF6irO9z98xDceosuGiQ= | ||
golang.org/x/text v0.3.7/go.mod h1:u+2+/6zg+i71rQMx5EYifcz6MCKuco9NR6JIITiCfzQ= | ||
golang.org/x/text v0.7.0/go.mod h1:mrYo+phRRbMaCq/xk9113O4dZlRixOauAjOtrjsXDZ8= | ||
golang.org/x/text v0.12.0 h1:k+n5B8goJNdU7hSvEtMUz3d1Q6D/XW4COJSJR6fN0mc= | ||
golang.org/x/text v0.12.0/go.mod h1:TvPlkZtksWOMsz7fbANvkp4WM8x/WCo/om8BMLbz+aE= | ||
golang.org/x/tools v0.0.0-20180917221912-90fa682c2a6e/go.mod h1:n7NCudcB/nEzxVGmLbDWY5pfWTLqBcC2KZ6jyYvM4mQ= | ||
golang.org/x/tools v0.0.0-20191119224855-298f0cb1881e/go.mod h1:b+2E5dAYhXwXZwtnZ6UAqBI28+e2cm9otk0dWdXHAEo= | ||
golang.org/x/tools v0.1.0/go.mod h1:xkSsbof2nBLbhDlRMhhhyNLN/zl3eTqcnHD5viDpcZ0= | ||
golang.org/x/tools v0.1.12/go.mod h1:hNGJHUnrk76NpqgfD5Aqm5Crs+Hm0VOH/i9J2+nxYbc= | ||
golang.org/x/tools v0.6.0/go.mod h1:Xwgl3UAJ/d3gWutnCtw505GrjyAbvKui8lOU390QaIU= | ||
golang.org/x/xerrors v0.0.0-20190717185122-a985d3407aa7/go.mod h1:I/5z698sn9Ka8TeJc9MKroUUfqBBauWjQqLJ2OPfmY0= | ||
golang.org/x/xerrors v0.0.0-20191011141410-1b5146add898/go.mod h1:I/5z698sn9Ka8TeJc9MKroUUfqBBauWjQqLJ2OPfmY0= | ||
golang.org/x/xerrors v0.0.0-20200804184101-5ec99f83aff1/go.mod h1:I/5z698sn9Ka8TeJc9MKroUUfqBBauWjQqLJ2OPfmY0= | ||
gonum.org/v1/gonum v0.14.0 h1:2NiG67LD1tEH0D7kM+ps2V+fXmsAnpUeec7n8tcr4S0= | ||
gonum.org/v1/gonum v0.14.0/go.mod h1:AoWeoz0becf9QMWtE8iWXNXc27fK4fNeHNf/oMejGfU= | ||
gonum.org/v1/plot v0.14.0 h1:+LBDVFYwFe4LHhdP8coW6296MBEY4nQ+Y4vuUpJopcE= | ||
gonum.org/v1/plot v0.14.0/go.mod h1:MLdR9424SJed+5VqC6MsouEpig9pZX2VZ57H9ko2bXU= | ||
gopkg.in/yaml.v3 v3.0.1 h1:fxVm/GzAzEWqLHuvctI91KS9hhNmmWOoWu0XTYJS7CA= | ||
gopkg.in/yaml.v3 v3.0.1/go.mod h1:K4uyk7z7BCEPqu6E+C64Yfv1cQ7kz7rIZviUmN+EgEM= | ||
honnef.co/go/tools v0.1.3/go.mod h1:NgwopIslSNH47DimFoV78dnkksY2EFtX0ajyb3K/las= | ||
rsc.io/pdf v0.1.1 h1:k1MczvYDUvJBe93bYd7wrZLLUEcLZAuF824/I4e5Xr4= | ||
rsc.io/pdf v0.1.1/go.mod h1:n8OzWcQ6Sp37PL01nO98y4iUCRdTGarVfzxY20ICaU4= |
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