153 lines
3.8 KiB
Go
153 lines
3.8 KiB
Go
package pixel
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import (
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"fmt"
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"math"
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"math/cmplx"
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)
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// Vec is a 2d vector type. It is unusually implemented as complex128 for convenience. Since Go does
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// not allow operator overloading, implementing vector as a struct leads to a bunch of methods for
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// addition, subtraction and multiplication of vectors. With complex128, much of this functionality
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// is given through operators.
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//
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// Create vectors with the V constructor:
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//
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// u := pixel.V(1, 2)
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// v := pixel.V(8, -3)
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//
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// Add and subtract them using the standard + and - operators:
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//
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// w := u + v
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// fmt.Println(w) // Vec(9, -1)
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// fmt.Println(u - v) // Vec(-7, 5)
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//
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// Additional standard vector operations can be obtained with methods:
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//
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// u := pixel.V(2, 3)
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// v := pixel.V(8, 1)
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// if u.X() < 0 {
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// fmt.Println("this won't happen")
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// }
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// x := u.Unit().Dot(v.Unit())
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type Vec complex128
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// V returns a new 2d vector with the given coordinates.
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func V(x, y float64) Vec {
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return Vec(complex(x, y))
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}
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// String returns the string representation of a vector u.
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//
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// u := pixel.V(4.5, -1.3)
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// u.String() // returns "Vec(4.5, -1.3)"
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// fmt.Println(u) // Vec(4.5, -1.3)
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func (u Vec) String() string {
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return fmt.Sprintf("Vec(%v, %v)", u.X(), u.Y())
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}
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// X returns the x coordinate of a vector u.
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func (u Vec) X() float64 {
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return real(u)
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}
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// Y returns the y coordinate of a vector u.
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func (u Vec) Y() float64 {
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return imag(u)
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}
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// XY returns the components of a vector in two return values.
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func (u Vec) XY() (x, y float64) {
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return real(u), imag(u)
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}
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// Len returns the length of a vector u.
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func (u Vec) Len() float64 {
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return cmplx.Abs(complex128(u))
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}
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// Angle returns the angle between a vector u and the x-axis. The result is in the range [-Pi, Pi].
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func (u Vec) Angle() float64 {
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return cmplx.Phase(complex128(u))
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}
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// Unit returns a vector of length 1 with the same angle as u.
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func (u Vec) Unit() Vec {
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return u / V(u.Len(), 0)
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}
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// Scaled returns a vector u multiplied by c.
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func (u Vec) Scaled(c float64) Vec {
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return u * V(c, 0)
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}
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// Rotated returns a vector u rotated by the given angle in radians.
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func (u Vec) Rotated(angle float64) Vec {
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sin, cos := math.Sincos(angle)
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return u * V(cos, sin)
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}
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// Dot returns the dot product of vectors u and v.
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func (u Vec) Dot(v Vec) float64 {
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return u.X()*v.X() + u.Y()*v.Y()
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}
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// Cross return the cross product of vectors u and v.
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func (u Vec) Cross(v Vec) float64 {
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return u.X()*v.Y() - v.X()*u.Y()
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}
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// Rect is a 2d rectangle aligned with the axis of the coordinate system. It has a position and a size.
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//
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// You can manipulate the position and the size using the usual vector operations.
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type Rect struct {
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Pos, Size Vec
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}
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// R returns a new 2d rectangle with the given position (x, y) and size (w, h).
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func R(x, y, w, h float64) Rect {
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return Rect{
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Pos: V(x, y),
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Size: V(w, h),
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}
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}
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// String returns the string representation of a rectangle.
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//
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// r := pixel.R(100, 50, 200, 300)
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// r.String() // returns "Rect(100, 50, 200, 300)"
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// fmt.Println(r) // Rect(100, 50, 200, 300)
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func (r Rect) String() string {
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return fmt.Sprintf("Rect(%v, %v, %v, %v)", r.X(), r.Y(), r.W(), r.H())
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}
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// X returns the x coordinate of the position of a rectangle.
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func (r Rect) X() float64 {
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return r.Pos.X()
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}
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// Y returns the y coordinate of the position of a rectangle
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func (r Rect) Y() float64 {
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return r.Pos.Y()
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}
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// W returns the width of a rectangle.
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func (r Rect) W() float64 {
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return r.Size.X()
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}
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// H returns the height of a rectangle.
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func (r Rect) H() float64 {
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return r.Size.Y()
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}
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// XYWH returns all of the four components of a rectangle in four return values.
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func (r Rect) XYWH() (x, y, w, h float64) {
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return r.X(), r.Y(), r.W(), r.H()
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}
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// Center returns the position of the center of a rectangle.
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func (r Rect) Center() Vec {
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return r.Pos + r.Size.Scaled(0.5)
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}
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