geometry.go

package pixel

import (
	"fmt"
	"math"
	"math/cmplx"
)

// Vec is a 2d vector type. It is unusually implemented as complex128 for convenience. Since Go does
// not allow operator overloading, implementing vector as a struct leads to a bunch of methods for
// addition, subtraction and multiplication of vectors. With complex128, much of this functionality
// is given through operators.
//
// Create vectors with the V constructor:
//
//   u := pixel.V(1, 2)
//   v := pixel.V(8, -3)
//
// Add and subtract them using the standard + and - operators:
//
//   w := u + v
//   fmt.Println(w)     // Vec(9, -1)
//   fmt.Println(u - v) // Vec(-7, 5)
//
// Additional standard vector operations can be obtained with methods:
//
//   u := pixel.V(2, 3)
//   v := pixel.V(8, 1)
//   if u.X() < 0 {
//       fmt.Println("this won't happen")
//   }
//   x := u.Unit().Dot(v.Unit())
type Vec complex128

// V returns a new 2d vector with the given coordinates.
func V(x, y float64) Vec {
	return Vec(complex(x, y))
}

// String returns the string representation of a vector u.
//
//   u := pixel.V(4.5, -1.3)
//   u.String()     // returns "Vec(4.5, -1.3)"
//   fmt.Println(u) // Vec(4.5, -1.3)
func (u Vec) String() string {
	return fmt.Sprintf("Vec(%v, %v)", u.X(), u.Y())
}

// X returns the x coordinate of a vector u.
func (u Vec) X() float64 {
	return real(u)
}

// Y returns the y coordinate of a vector u.
func (u Vec) Y() float64 {
	return imag(u)
}

// XY returns the components of a vector in two return values.
func (u Vec) XY() (x, y float64) {
	return real(u), imag(u)
}

// Len returns the length of a vector u.
func (u Vec) Len() float64 {
	return cmplx.Abs(complex128(u))
}

// Angle returns the angle between a vector u and the x-axis. The result is in the range [-Pi, Pi].
func (u Vec) Angle() float64 {
	return cmplx.Phase(complex128(u))
}

// Unit returns a vector of length 1 with the same angle as u.
func (u Vec) Unit() Vec {
	return u / V(u.Len(), 0)
}

// Scaled returns a vector u multiplied by c.
func (u Vec) Scaled(c float64) Vec {
	return u * V(c, 0)
}

// Rotated returns a vector u rotated by the given angle in radians.
func (u Vec) Rotated(angle float64) Vec {
	sin, cos := math.Sincos(angle)
	return u * V(cos, sin)
}

// Dot returns the dot product of vectors u and v.
func (u Vec) Dot(v Vec) float64 {
	return u.X()*v.X() + u.Y()*v.Y()
}

// Cross return the cross product of vectors u and v.
func (u Vec) Cross(v Vec) float64 {
	return u.X()*v.Y() - v.X()*u.Y()
}