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vector implementation with big.Float (#527)
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43
d2common/d2interface/vector.go
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43
d2common/d2interface/vector.go
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package d2interface
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import "math/big"
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// Vector is a 2-dimensional vector implementation using big.Float
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type Vector interface {
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X() *big.Float
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Y() *big.Float
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Marshal() ([]byte, error)
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Unmarshal(buf []byte) error
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Clone() Vector
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Copy(src Vector) Vector
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// SetFromEntity(entity WorldEntity) Vector
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Set(x, y *big.Float) Vector
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SetToPolar(azimuth, radius *big.Float) Vector
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Equals(src Vector) bool
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FuzzyEquals(src Vector) bool
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Abs() Vector
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Angle() *big.Float
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SetAngle(angle *big.Float) Vector
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Add(src Vector) Vector
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Subtract(src Vector) Vector
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Multiply(src Vector) Vector
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Scale(value *big.Float) Vector
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Divide(src Vector) Vector
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Negate() Vector
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Distance(src Vector) *big.Float
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DistanceSq(src Vector) *big.Float
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Length() *big.Float
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SetLength(length *big.Float) Vector
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LengthSq() (*big.Float, *big.Float)
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Normalize() Vector
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NormalizeRightHand() Vector
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NormalizeLeftHand() Vector
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Dot(src Vector) *big.Float
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Cross(src Vector) *big.Float
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Lerp(src Vector, t *big.Float) Vector
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Reset() Vector
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Limit(max *big.Float) Vector
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Reflect(normal Vector) Vector
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Mirror(axis Vector) Vector
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Rotate(delta *big.Float) Vector
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}
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367
d2common/d2math/vector.go
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367
d2common/d2math/vector.go
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package d2math
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import (
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"math"
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"math/big"
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"github.com/OpenDiablo2/OpenDiablo2/d2common/d2interface"
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)
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// I want to put these somewhere convenient...
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// ZERO *Vector = &Vector{}
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// ONE *Vector = &Vector{1, 1}
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// RIGHT *Vector = &Vector{1, 0}
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// LEFT *Vector = &Vector{-1, 0}
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// UP *Vector = &Vector{0, -1}
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// DOWN *Vector = &Vector{0, 1}
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const (
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// Epsilon is the threshold for what is `smol enough`
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epsilon float64 = 0.0001
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// d2precision is how much precision we want from big.Float
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d2precision uint = 64 // was chosen arbitrarily
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// for convenience in negating sign
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negative1 float64 = -1.0
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// for convenience
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zero float64 = 0.0
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)
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// NewVector2 creates a new Vector
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func NewVector2(x, y float64) *Vector2 {
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xbf, ybf := big.NewFloat(x), big.NewFloat(y)
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xbf.SetPrec(d2precision)
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ybf.SetPrec(d2precision)
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result := &Vector2{xbf, ybf}
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return result
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}
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// Vector is an Implementation of 2-dimensional vectors with
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// big.Float components
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type Vector2 struct {
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x *big.Float
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y *big.Float
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}
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// X returns the x member of the Vector
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func (v *Vector2) X() *big.Float {
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return v.x
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}
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// Y returns the y member of the Vector
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func (v *Vector2) Y() *big.Float {
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return v.y
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}
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// Marshal converts the Vector into a slice of bytes
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func (v *Vector2) Marshal() ([]byte, error) {
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// TODO not sure how to do this properly
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return nil, nil
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}
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// Unmarshal converts a slice of bytes to x/y *big.Float
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// and assigns them to itself
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func (v *Vector2) Unmarshal(buf []byte) error {
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// TODO not sure how to do this properly
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return nil
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}
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// Clone creates a copy of this Vector
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func (v *Vector2) Clone() d2interface.Vector {
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result := &Vector2{}
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result.Copy(v)
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return result
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}
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// Copy copies the src x/y members to this Vector x/y members
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func (v *Vector2) Copy(src d2interface.Vector) d2interface.Vector {
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v.x.Copy(src.X())
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v.y.Copy(src.Y())
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return v
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}
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// SetFromEntity copies the vector of a world entity
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// func (v *Vector2) SetFromEntity(entity d2interface.WorldEntity) d2interface.Vector {
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// return v.Copy(entity.Position())
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// }
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// Set the x,y members of the Vector
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func (v *Vector2) Set(x, y *big.Float) d2interface.Vector {
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v.x = x
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v.y = y
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return v
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}
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// SetToPolar sets the `x` and `y` values of this object
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// from a given polar coordinate.
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func (v *Vector2) SetToPolar(azimuth, radius *big.Float) d2interface.Vector {
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// HACK we should do this better, with the big.Float
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a, _ := azimuth.Float64()
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r, _ := radius.Float64()
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v.x.SetFloat64(math.Cos(a) * r)
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v.y.SetFloat64(math.Sin(a) * r)
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return v
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}
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// Equals check whether this Vector is equal to a given Vector.
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func (v *Vector2) Equals(src d2interface.Vector) bool {
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return v.x.Cmp(src.X()) == 0 && v.y.Cmp(src.Y()) == 0
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}
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// FuzzyEquals checks if the Vector is approximately equal
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// to the given Vector. epsilon is what we consider `smol enough`
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func (v *Vector2) FuzzyEquals(src d2interface.Vector) bool {
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smol := big.NewFloat(epsilon)
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d := v.Distance(src)
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d.Abs(d)
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return d.Cmp(smol) < 1 || d.Cmp(smol) < 1
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}
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// Abs returns a clone that is positive
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func (v *Vector2) Abs() d2interface.Vector {
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clone := v.Clone()
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neg1 := big.NewFloat(-1.0)
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if clone.X().Sign() == -1 { // is negative1
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clone.X().Mul(clone.X(), neg1)
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}
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if v.Y().Sign() == -1 { // is negative1
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clone.Y().Mul(clone.Y(), neg1)
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}
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return clone
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}
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// Angle computes the angle in radians with respect
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// to the positive x-axis
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func (v *Vector2) Angle() *big.Float {
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// HACK we should find a way to do this purely
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// with big.Float
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floatX, _ := v.X().Float64()
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floatY, _ := v.Y().Float64()
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floatAngle := math.Atan2(floatY, floatX)
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if floatAngle < 0 {
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floatAngle += 2.0 * math.Pi
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}
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return big.NewFloat(floatAngle)
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}
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// SetAngle sets the angle of this Vector
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func (v *Vector2) SetAngle(angle *big.Float) d2interface.Vector {
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return v.SetToPolar(angle, v.Length())
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}
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// Add to this Vector the components of the given Vector
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func (v *Vector2) Add(src d2interface.Vector) d2interface.Vector {
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v.x.Add(v.x, src.X())
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v.y.Add(v.y, src.Y())
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return v
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}
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// Subtract from this Vector the components of the given Vector
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func (v *Vector2) Subtract(src d2interface.Vector) d2interface.Vector {
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v.x.Sub(v.x, src.X())
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v.y.Sub(v.y, src.Y())
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return v
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}
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// Multiply this Vector with the components of the given Vector
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func (v *Vector2) Multiply(src d2interface.Vector) d2interface.Vector {
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v.x.Mul(v.x, src.X())
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v.y.Mul(v.y, src.Y())
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return v
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}
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// Scale this Vector by the given value
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func (v *Vector2) Scale(s *big.Float) d2interface.Vector {
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v.x.Sub(v.x, s)
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v.y.Sub(v.y, s)
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return v
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}
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// Divide this Vector by the given Vector
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func (v *Vector2) Divide(src d2interface.Vector) d2interface.Vector {
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v.x.Quo(v.x, src.X())
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v.y.Quo(v.y, src.Y())
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return v
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}
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// Negate thex and y components of this Vector
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func (v *Vector2) Negate() d2interface.Vector {
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return v.Scale(big.NewFloat(negative1))
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}
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// Distance calculate the distance between this Vector and the given Vector
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func (v *Vector2) Distance(src d2interface.Vector) *big.Float {
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dist := v.DistanceSq(src)
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return dist.Sqrt(dist)
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}
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// DistanceSq calculate the distance suared between this Vector and the given
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// Vector
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func (v *Vector2) DistanceSq(src d2interface.Vector) *big.Float {
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delta := src.Clone().Subtract(v)
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deltaSq := delta.Multiply(delta)
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return big.NewFloat(zero).Add(deltaSq.X(), deltaSq.Y())
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}
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// Length returns the length of this Vector
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func (v *Vector2) Length() *big.Float {
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xsq, ysq := v.LengthSq()
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return xsq.Add(xsq, ysq)
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}
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func (v *Vector2) LengthSq() (*big.Float, *big.Float) {
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clone := v.Clone()
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x, y := clone.X(), clone.Y()
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return x.Mul(x, x), y.Mul(y, y)
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}
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// SetLength sets the length of this Vector
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func (v *Vector2) SetLength(length *big.Float) d2interface.Vector {
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return v.Normalize().Scale(length)
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}
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// Normalize Makes the vector a unit length vector (magnitude of 1) in the same
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// direction.
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func (v *Vector2) Normalize() d2interface.Vector {
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xsq, ysq := v.LengthSq()
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length := big.NewFloat(zero).Add(xsq, ysq)
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one := big.NewFloat(1.0)
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if length.Cmp(one) > 0 {
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length.Quo(one, length.Sqrt(length))
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v.x.Mul(v.x, length)
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v.y.Mul(v.y, length)
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}
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return v
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}
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// NormalizeRightHand rotate this Vector to its perpendicular,
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//in the positive direction.
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func (v *Vector2) NormalizeRightHand() d2interface.Vector {
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x := v.x
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v.x = v.y.Mul(v.y, big.NewFloat(negative1))
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v.y = x
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return v
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}
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// NormalizeLeftHand rotate this Vector to its perpendicular,
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//in the negative1 direction.
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func (v *Vector2) NormalizeLeftHand() d2interface.Vector {
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x := v.x
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v.x = v.y
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v.y = x.Mul(x, big.NewFloat(negative1))
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return v
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}
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// Calculate the dot product of this Vector and the given Vector
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func (v *Vector2) Dot(src d2interface.Vector) *big.Float {
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c := v.Clone()
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c.X().Mul(c.X(), src.X())
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c.Y().Mul(c.Y(), src.Y())
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return c.X().Add(c.X(), c.Y())
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}
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// Cross Calculate the cross product of this Vector and the given Vector.
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func (v *Vector2) Cross(src d2interface.Vector) *big.Float {
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c := v.Clone()
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c.X().Mul(c.X(), src.X())
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c.Y().Mul(c.Y(), src.Y())
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return c.X().Sub(c.X(), c.Y())
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}
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// Lerp Linearly interpolate between this Vector and the given Vector.
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func (v *Vector2) Lerp(
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src d2interface.Vector,
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t *big.Float,
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) d2interface.Vector {
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vc, sc := v.Clone(), src.Clone()
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x, y := vc.X(), vc.Y()
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v.x.Set(x.Add(x, t.Mul(t, sc.X().Sub(sc.X(), x))))
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v.y.Set(y.Add(y, t.Mul(t, sc.Y().Sub(sc.Y(), y))))
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return v
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}
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// Reset this Vector the zero vector (0, 0).
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func (v *Vector2) Reset() d2interface.Vector {
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v.x.SetFloat64(zero)
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v.y.SetFloat64(zero)
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return v
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}
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// Limit the length (or magnitude) of this Vector
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func (v *Vector2) Limit(max *big.Float) d2interface.Vector {
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length := v.Length()
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if max.Cmp(length) < 0 {
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v.Scale(length.Quo(max, length))
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}
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return v
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}
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// Reflect this Vector off a line defined by a normal.
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func (v *Vector2) Reflect(normal d2interface.Vector) d2interface.Vector {
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clone := v.Clone()
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clone.Normalize()
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two := big.NewFloat(2.0) // there's some matrix algebra magic here
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dot := v.Clone().Dot(normal)
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normal.Scale(two.Mul(two, dot))
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return v.Subtract(normal)
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}
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// Mirror reflect this Vector across another.
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func (v *Vector2) Mirror(axis d2interface.Vector) d2interface.Vector {
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return v.Reflect(axis).Negate()
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}
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// Rotate this Vector by an angle amount.
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func (v *Vector2) Rotate(angle *big.Float) d2interface.Vector {
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// HACK we should do this only with big.Float, not float64
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// we are throwing away the precision here
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floatAngle, _ := angle.Float64()
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cos := math.Cos(floatAngle)
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sin := math.Sin(floatAngle)
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oldX, _ := v.x.Float64()
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oldY, _ := v.y.Float64()
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newX := big.NewFloat(cos*oldX - sin*oldY)
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newY := big.NewFloat(sin*oldX + cos*oldY)
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v.Set(newX, newY)
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return v
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}
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