add 2d vector type

vec.go

@@ -0,0 +1,88 @@
+package pixel
+
+import (
+	"fmt"
+	"math"
+	"math/cmplx"
+)
+
+// Vec2 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)     // Vec2(9, -1)
+//   fmt.Println(u - v) // Vec2(-7, 5)
+//
+// Additional standard vector operations can be obtained with methods:
+//
+//   u := pixel.Vec(2, 3)
+//   v := pixel.Vec(8, 1)
+//   if u.X() < 0 {
+//       fmt.Println("this won't happend")
+//   }
+//   x := u.Unit().Dot(v.Unit())
+type Vec2 complex128
+
+// V returns a new 2d vector with the given coordinates.
+func V(x, y float64) Vec2 {
+	return Vec2(complex(x, y))
+}
+
+// String returns the string representation of a vector u as "Vec2(x, y)".
+func (u Vec2) String() string {
+	return fmt.Sprintf("Vec2(%v, %v)", u.X(), u.Y())
+}
+
+// X returns the x coordinate of a vector u.
+func (u Vec2) X() float64 {
+	return real(u)
+}
+
+// Y returns the y coordinate of a vector u.
+func (u Vec2) Y() float64 {
+	return imag(u)
+}
+
+// Len returns the length of a vector u.
+func (u Vec2) 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 Vec2) Angle() float64 {
+	return cmplx.Phase(complex128(u))
+}
+
+// Unit returns a vector of length 1 with the same angle as u.
+func (u Vec2) Unit() Vec2 {
+	return u / V(u.Len(), 0)
+}
+
+// Scaled returns a vector u multiplied by k.
+func (u Vec2) Scaled(k float64) Vec2 {
+	return u * V(k, 0)
+}
+
+// Rotated returns a vector u rotated by the given angle in radians.
+func (u Vec2) Rotated(angle float64) Vec2 {
+	return u * V(math.Cos(angle), math.Sin(angle))
+}
+
+// Dot returns the dot product of vectors u and v.
+func (u Vec2) Dot(v Vec2) float64 {
+	return u.X()*v.X() + u.Y()*v.Y()
+}
+
+// Cross return the cross product of vectors u and v.
+func (u Vec2) Cross(v Vec2) float64 {
+	return u.X()*v.Y() - v.X()*u.Y()
+}