staticmap/vendor/github.com/golang/geo/r3/precisevector.go

/*
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 divison 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}
}

// Equals reports whether v and ov are equal.
func (v PreciseVector) Equals(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("(%v, %v, %v)", 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
}