diff options
Diffstat (limited to 'vendor/github.com/golang/geo/r3')
| -rw-r--r-- | vendor/github.com/golang/geo/r3/doc.go | 20 | ||||
| -rw-r--r-- | vendor/github.com/golang/geo/r3/precisevector.go | 198 | ||||
| -rw-r--r-- | vendor/github.com/golang/geo/r3/vector.go | 183 |
3 files changed, 0 insertions, 401 deletions
diff --git a/vendor/github.com/golang/geo/r3/doc.go b/vendor/github.com/golang/geo/r3/doc.go deleted file mode 100644 index 1eb4710c8..000000000 --- a/vendor/github.com/golang/geo/r3/doc.go +++ /dev/null @@ -1,20 +0,0 @@ -// Copyright 2014 Google Inc. All rights reserved. -// -// Licensed under the Apache License, Version 2.0 (the "License"); -// you may not use this file except in compliance with the License. -// You may obtain a copy of the License at -// -// http://www.apache.org/licenses/LICENSE-2.0 -// -// Unless required by applicable law or agreed to in writing, software -// distributed under the License is distributed on an "AS IS" BASIS, -// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. -// See the License for the specific language governing permissions and -// limitations under the License. - -/* -Package r3 implements types and functions for working with geometry in ℝ³. - -See ../s2 for a more detailed overview. -*/ -package r3 diff --git a/vendor/github.com/golang/geo/r3/precisevector.go b/vendor/github.com/golang/geo/r3/precisevector.go deleted file mode 100644 index b13393dbc..000000000 --- a/vendor/github.com/golang/geo/r3/precisevector.go +++ /dev/null @@ -1,198 +0,0 @@ -// Copyright 2016 Google Inc. All rights reserved. -// -// Licensed under the Apache License, Version 2.0 (the "License"); -// you may not use this file except in compliance with the License. -// You may obtain a copy of the License at -// -// http://www.apache.org/licenses/LICENSE-2.0 -// -// Unless required by applicable law or agreed to in writing, software -// distributed under the License is distributed on an "AS IS" BASIS, -// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. -// See the License for the specific language governing permissions and -// limitations under the License. - -package r3 - -import ( - "fmt" - "math/big" -) - -const ( - // prec is the number of bits of precision to use for the Float values. - // To keep things simple, we use the maximum allowable precision on big - // values. This allows us to handle all values we expect in the s2 library. - prec = big.MaxPrec -) - -// define some commonly referenced values. -var ( - precise0 = precInt(0) - precise1 = precInt(1) -) - -// precStr wraps the conversion from a string into a big.Float. For results that -// actually can be represented exactly, this should only be used on values that -// are integer multiples of integer powers of 2. -func precStr(s string) *big.Float { - // Explicitly ignoring the bool return for this usage. - f, _ := new(big.Float).SetPrec(prec).SetString(s) - return f -} - -func precInt(i int64) *big.Float { - return new(big.Float).SetPrec(prec).SetInt64(i) -} - -func precFloat(f float64) *big.Float { - return new(big.Float).SetPrec(prec).SetFloat64(f) -} - -func precAdd(a, b *big.Float) *big.Float { - return new(big.Float).SetPrec(prec).Add(a, b) -} - -func precSub(a, b *big.Float) *big.Float { - return new(big.Float).SetPrec(prec).Sub(a, b) -} - -func precMul(a, b *big.Float) *big.Float { - return new(big.Float).SetPrec(prec).Mul(a, b) -} - -// PreciseVector represents a point in ℝ³ using high-precision values. -// Note that this is NOT a complete implementation because there are some -// operations that Vector supports that are not feasible with arbitrary precision -// math. (e.g., methods that need division like Normalize, or methods needing a -// square root operation such as Norm) -type PreciseVector struct { - X, Y, Z *big.Float -} - -// PreciseVectorFromVector creates a high precision vector from the given Vector. -func PreciseVectorFromVector(v Vector) PreciseVector { - return NewPreciseVector(v.X, v.Y, v.Z) -} - -// NewPreciseVector creates a high precision vector from the given floating point values. -func NewPreciseVector(x, y, z float64) PreciseVector { - return PreciseVector{ - X: precFloat(x), - Y: precFloat(y), - Z: precFloat(z), - } -} - -// Vector returns this precise vector converted to a Vector. -func (v PreciseVector) Vector() Vector { - // The accuracy flag is ignored on these conversions back to float64. - x, _ := v.X.Float64() - y, _ := v.Y.Float64() - z, _ := v.Z.Float64() - return Vector{x, y, z}.Normalize() -} - -// Equal reports whether v and ov are equal. -func (v PreciseVector) Equal(ov PreciseVector) bool { - return v.X.Cmp(ov.X) == 0 && v.Y.Cmp(ov.Y) == 0 && v.Z.Cmp(ov.Z) == 0 -} - -func (v PreciseVector) String() string { - return fmt.Sprintf("(%10g, %10g, %10g)", v.X, v.Y, v.Z) -} - -// Norm2 returns the square of the norm. -func (v PreciseVector) Norm2() *big.Float { return v.Dot(v) } - -// IsUnit reports whether this vector is of unit length. -func (v PreciseVector) IsUnit() bool { - return v.Norm2().Cmp(precise1) == 0 -} - -// Abs returns the vector with nonnegative components. -func (v PreciseVector) Abs() PreciseVector { - return PreciseVector{ - X: new(big.Float).Abs(v.X), - Y: new(big.Float).Abs(v.Y), - Z: new(big.Float).Abs(v.Z), - } -} - -// Add returns the standard vector sum of v and ov. -func (v PreciseVector) Add(ov PreciseVector) PreciseVector { - return PreciseVector{ - X: precAdd(v.X, ov.X), - Y: precAdd(v.Y, ov.Y), - Z: precAdd(v.Z, ov.Z), - } -} - -// Sub returns the standard vector difference of v and ov. -func (v PreciseVector) Sub(ov PreciseVector) PreciseVector { - return PreciseVector{ - X: precSub(v.X, ov.X), - Y: precSub(v.Y, ov.Y), - Z: precSub(v.Z, ov.Z), - } -} - -// Mul returns the standard scalar product of v and f. -func (v PreciseVector) Mul(f *big.Float) PreciseVector { - return PreciseVector{ - X: precMul(v.X, f), - Y: precMul(v.Y, f), - Z: precMul(v.Z, f), - } -} - -// MulByFloat64 returns the standard scalar product of v and f. -func (v PreciseVector) MulByFloat64(f float64) PreciseVector { - return v.Mul(precFloat(f)) -} - -// Dot returns the standard dot product of v and ov. -func (v PreciseVector) Dot(ov PreciseVector) *big.Float { - return precAdd(precMul(v.X, ov.X), precAdd(precMul(v.Y, ov.Y), precMul(v.Z, ov.Z))) -} - -// Cross returns the standard cross product of v and ov. -func (v PreciseVector) Cross(ov PreciseVector) PreciseVector { - return PreciseVector{ - X: precSub(precMul(v.Y, ov.Z), precMul(v.Z, ov.Y)), - Y: precSub(precMul(v.Z, ov.X), precMul(v.X, ov.Z)), - Z: precSub(precMul(v.X, ov.Y), precMul(v.Y, ov.X)), - } -} - -// LargestComponent returns the axis that represents the largest component in this vector. -func (v PreciseVector) LargestComponent() Axis { - t := v.Abs() - - if t.X.Cmp(t.Y) > 0 { - if t.X.Cmp(t.Z) > 0 { - return XAxis - } - return ZAxis - } - if t.Y.Cmp(t.Z) > 0 { - return YAxis - } - return ZAxis -} - -// SmallestComponent returns the axis that represents the smallest component in this vector. -func (v PreciseVector) SmallestComponent() Axis { - t := v.Abs() - - if t.X.Cmp(t.Y) < 0 { - if t.X.Cmp(t.Z) < 0 { - return XAxis - } - return ZAxis - } - if t.Y.Cmp(t.Z) < 0 { - return YAxis - } - return ZAxis -} diff --git a/vendor/github.com/golang/geo/r3/vector.go b/vendor/github.com/golang/geo/r3/vector.go deleted file mode 100644 index ccda622f4..000000000 --- a/vendor/github.com/golang/geo/r3/vector.go +++ /dev/null @@ -1,183 +0,0 @@ -// Copyright 2014 Google Inc. All rights reserved. -// -// Licensed under the Apache License, Version 2.0 (the "License"); -// you may not use this file except in compliance with the License. -// You may obtain a copy of the License at -// -// http://www.apache.org/licenses/LICENSE-2.0 -// -// Unless required by applicable law or agreed to in writing, software -// distributed under the License is distributed on an "AS IS" BASIS, -// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. -// See the License for the specific language governing permissions and -// limitations under the License. - -package r3 - -import ( - "fmt" - "math" - - "github.com/golang/geo/s1" -) - -// Vector represents a point in ℝ³. -type Vector struct { - X, Y, Z float64 -} - -// ApproxEqual reports whether v and ov are equal within a small epsilon. -func (v Vector) ApproxEqual(ov Vector) bool { - const epsilon = 1e-16 - return math.Abs(v.X-ov.X) < epsilon && math.Abs(v.Y-ov.Y) < epsilon && math.Abs(v.Z-ov.Z) < epsilon -} - -func (v Vector) String() string { return fmt.Sprintf("(%0.24f, %0.24f, %0.24f)", v.X, v.Y, v.Z) } - -// Norm returns the vector's norm. -func (v Vector) Norm() float64 { return math.Sqrt(v.Dot(v)) } - -// Norm2 returns the square of the norm. -func (v Vector) Norm2() float64 { return v.Dot(v) } - -// Normalize returns a unit vector in the same direction as v. -func (v Vector) Normalize() Vector { - n2 := v.Norm2() - if n2 == 0 { - return Vector{0, 0, 0} - } - return v.Mul(1 / math.Sqrt(n2)) -} - -// IsUnit returns whether this vector is of approximately unit length. -func (v Vector) IsUnit() bool { - const epsilon = 5e-14 - return math.Abs(v.Norm2()-1) <= epsilon -} - -// Abs returns the vector with nonnegative components. -func (v Vector) Abs() Vector { return Vector{math.Abs(v.X), math.Abs(v.Y), math.Abs(v.Z)} } - -// Add returns the standard vector sum of v and ov. -func (v Vector) Add(ov Vector) Vector { return Vector{v.X + ov.X, v.Y + ov.Y, v.Z + ov.Z} } - -// Sub returns the standard vector difference of v and ov. -func (v Vector) Sub(ov Vector) Vector { return Vector{v.X - ov.X, v.Y - ov.Y, v.Z - ov.Z} } - -// Mul returns the standard scalar product of v and m. -func (v Vector) Mul(m float64) Vector { return Vector{m * v.X, m * v.Y, m * v.Z} } - -// Dot returns the standard dot product of v and ov. -func (v Vector) Dot(ov Vector) float64 { return v.X*ov.X + v.Y*ov.Y + v.Z*ov.Z } - -// Cross returns the standard cross product of v and ov. -func (v Vector) Cross(ov Vector) Vector { - return Vector{ - v.Y*ov.Z - v.Z*ov.Y, - v.Z*ov.X - v.X*ov.Z, - v.X*ov.Y - v.Y*ov.X, - } -} - -// Distance returns the Euclidean distance between v and ov. -func (v Vector) Distance(ov Vector) float64 { return v.Sub(ov).Norm() } - -// Angle returns the angle between v and ov. -func (v Vector) Angle(ov Vector) s1.Angle { - return s1.Angle(math.Atan2(v.Cross(ov).Norm(), v.Dot(ov))) * s1.Radian -} - -// Axis enumerates the 3 axes of ℝ³. -type Axis int - -// The three axes of ℝ³. -const ( - XAxis Axis = iota - YAxis - ZAxis -) - -// Ortho returns a unit vector that is orthogonal to v. -// Ortho(-v) = -Ortho(v) for all v. -func (v Vector) Ortho() Vector { - ov := Vector{0.012, 0.0053, 0.00457} - switch v.LargestComponent() { - case XAxis: - ov.Z = 1 - case YAxis: - ov.X = 1 - default: - ov.Y = 1 - } - return v.Cross(ov).Normalize() -} - -// LargestComponent returns the axis that represents the largest component in this vector. -func (v Vector) LargestComponent() Axis { - t := v.Abs() - - if t.X > t.Y { - if t.X > t.Z { - return XAxis - } - return ZAxis - } - if t.Y > t.Z { - return YAxis - } - return ZAxis -} - -// SmallestComponent returns the axis that represents the smallest component in this vector. -func (v Vector) SmallestComponent() Axis { - t := v.Abs() - - if t.X < t.Y { - if t.X < t.Z { - return XAxis - } - return ZAxis - } - if t.Y < t.Z { - return YAxis - } - return ZAxis -} - -// Cmp compares v and ov lexicographically and returns: -// -// -1 if v < ov -// 0 if v == ov -// +1 if v > ov -// -// This method is based on C++'s std::lexicographical_compare. Two entities -// are compared element by element with the given operator. The first mismatch -// defines which is less (or greater) than the other. If both have equivalent -// values they are lexicographically equal. -func (v Vector) Cmp(ov Vector) int { - if v.X < ov.X { - return -1 - } - if v.X > ov.X { - return 1 - } - - // First elements were the same, try the next. - if v.Y < ov.Y { - return -1 - } - if v.Y > ov.Y { - return 1 - } - - // Second elements were the same return the final compare. - if v.Z < ov.Z { - return -1 - } - if v.Z > ov.Z { - return 1 - } - - // Both are equal - return 0 -} |