338 lines
9.0 KiB
Go
338 lines
9.0 KiB
Go
package pixel
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import (
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"fmt"
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"math"
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"github.com/go-gl/mathgl/mgl64"
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)
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// Vec is a 2D vector type with X and Y coordinates.
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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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// Use various methods to manipulate them:
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//
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// w := u.Add(v)
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// fmt.Println(w) // Vec(9, -1)
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// fmt.Println(u.Sub(v)) // Vec(-7, 5)
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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 struct {
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X, Y float64
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}
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// ZV is a zero vector.
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var ZV = Vec{0, 0}
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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{x, y}
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}
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// String returns the string representation of the 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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// XY returns the components of the vector in two return values.
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func (u Vec) XY() (x, y float64) {
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return u.X, u.Y
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}
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// Add returns the sum of vectors u and v.
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func (u Vec) Add(v Vec) Vec {
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return Vec{
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u.X + v.X,
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u.Y + v.Y,
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}
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}
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// Sub returns the difference betweeen vectors u and v.
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func (u Vec) Sub(v Vec) Vec {
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return Vec{
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u.X - v.X,
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u.Y - v.Y,
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}
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}
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// Scaled returns the vector u multiplied by c.
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func (u Vec) Scaled(c float64) Vec {
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return Vec{u.X * c, u.Y * c}
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}
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// ScaledXY returns the vector u multiplied by the vector v component-wise.
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func (u Vec) ScaledXY(v Vec) Vec {
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return Vec{u.X * v.X, u.Y * v.Y}
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}
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// Len returns the length of the vector u.
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func (u Vec) Len() float64 {
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return math.Hypot(u.X, u.Y)
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}
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// Angle returns the angle between the vector u and the x-axis. The result is in range [-Pi, Pi].
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func (u Vec) Angle() float64 {
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return math.Atan2(u.Y, u.X)
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}
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// Unit returns a vector of length 1 facing the direction of u (has the same angle).
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func (u Vec) Unit() Vec {
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if u.X == 0 && u.Y == 0 {
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return Vec{1, 0}
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}
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return u.Scaled(1 / u.Len())
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}
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// Rotated returns the 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 Vec{
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u.X*cos - u.Y*sin,
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u.X*sin + u.Y*cos,
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}
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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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// Map applies the function f to both x and y components of the vector u and returns the modified
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// vector.
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//
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// u := pixel.V(10.5, -1.5)
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// v := u.Map(math.Floor) // v is Vec(10, -2), both components of u floored
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func (u Vec) Map(f func(float64) float64) Vec {
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return Vec{
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f(u.X),
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f(u.Y),
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}
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}
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// Lerp returns a linear interpolation between vectors a and b.
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//
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// This function basically returns a point along the line between a and b and t chooses which one.
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// If t is 0, then a will be returned, if t is 1, b will be returned. Anything between 0 and 1 will
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// return the appropriate point between a and b and so on.
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func Lerp(a, b Vec, t float64) Vec {
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return a.Scaled(1 - t).Add(b.Scaled(t))
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}
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// Rect is a 2D rectangle aligned with the axes of the coordinate system. It is defined by two
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// points, Min and Max.
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//
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// The invariant should hold, that Max's components are greater or equal than Min's components
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// respectively.
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type Rect struct {
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Min, Max Vec
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}
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// R returns a new Rect with given the Min and Max coordinates.
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//
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// Note that the returned rectangle is not automatically normalized.
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func R(minX, minY, maxX, maxY float64) Rect {
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return Rect{
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Min: V(minX, minY),
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Max: V(maxX, maxY),
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}
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}
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// String returns the string representation of the Rect.
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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.Min.X, r.Min.Y, r.Max.X, r.Max.Y)
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}
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// Norm returns the Rect in normal form, such that Max is component-wise greater or equal than Min.
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func (r Rect) Norm() Rect {
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return Rect{
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Min: Vec{
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math.Min(r.Min.X, r.Max.X),
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math.Min(r.Min.Y, r.Max.Y),
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},
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Max: Vec{
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math.Max(r.Min.X, r.Max.X),
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math.Max(r.Min.Y, r.Max.Y),
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},
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}
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}
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// W returns the width of the Rect.
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func (r Rect) W() float64 {
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return r.Max.X - r.Min.X
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}
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// H returns the height of the Rect.
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func (r Rect) H() float64 {
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return r.Max.Y - r.Min.Y
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}
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// Size returns the vector of width and height of the Rect.
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func (r Rect) Size() Vec {
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return V(r.W(), r.H())
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}
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// Center returns the position of the center of the Rect.
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func (r Rect) Center() Vec {
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return Lerp(r.Min, r.Max, 0.5)
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}
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// Moved returns the Rect moved (both Min and Max) by the given vector delta.
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func (r Rect) Moved(delta Vec) Rect {
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return Rect{
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Min: r.Min.Add(delta),
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Max: r.Max.Add(delta),
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}
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}
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// Resized returns the Rect resized to the given size while keeping the position of the given
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// anchor.
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//
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// r.Resized(r.Min, size) // resizes while keeping the position of the lower-left corner
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// r.Resized(r.Max, size) // same with the top-right corner
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// r.Resized(r.Center(), size) // resizes around the center
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//
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// This function does not make sense for resizing a rectangle of zero area and will panic. Use
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// ResizedMin in the case of zero area.
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func (r Rect) Resized(anchor, size Vec) Rect {
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if r.W()*r.H() == 0 {
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panic(fmt.Errorf("(%T).Resize: zero area", r))
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}
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fraction := Vec{size.X / r.W(), size.Y / r.H()}
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return Rect{
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Min: anchor.Add(r.Min.Sub(anchor)).ScaledXY(fraction),
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Max: anchor.Add(r.Max.Sub(anchor)).ScaledXY(fraction),
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}
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}
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// ResizedMin returns the Rect resized to the given size while keeping the position of the Rect's
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// Min.
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//
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// Sizes of zero area are safe here.
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func (r Rect) ResizedMin(size Vec) Rect {
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return Rect{
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Min: r.Min,
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Max: r.Min.Add(size),
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}
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}
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// Contains checks whether a vector u is contained within this Rect (including it's borders).
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func (r Rect) Contains(u Vec) bool {
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return r.Min.X <= u.X && u.X <= r.Max.X && r.Min.Y <= u.Y && u.Y <= r.Max.Y
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}
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// Union returns a minimal Rect which covers both r and s. Rects r and s should be normalized.
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func (r Rect) Union(s Rect) Rect {
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return R(
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math.Min(r.Min.X, s.Min.X),
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math.Min(r.Min.Y, s.Min.Y),
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math.Max(r.Max.X, s.Max.X),
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math.Max(r.Max.Y, s.Max.Y),
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)
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}
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// Matrix is a 3x3 transformation matrix that can be used for all kinds of spacial transforms, such
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// as movement, scaling and rotations.
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//
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// Matrix has a handful of useful methods, each of which adds a transformation to the matrix. For
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// example:
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//
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// pixel.IM.Moved(pixel.V(100, 200)).Rotated(pixel.ZV, math.Pi/2)
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//
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// This code creates a Matrix that first moves everything by 100 units horizontally and 200 units
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// vertically and then rotates everything by 90 degrees around the origin.
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type Matrix [9]float64
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// IM stands for identity matrix. Does nothing, no transformation.
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var IM = Matrix(mgl64.Ident3())
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// String returns a string representation of the Matrix.
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//
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// m := pixel.IM
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// fmt.Println(m) // Matrix(1 0 0 | 0 1 0 | 0 0 1)
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func (m Matrix) String() string {
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return fmt.Sprintf(
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"Matrix(%v %v %v | %v %v %v | %v %v %v)",
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m[0], m[3], m[6],
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m[1], m[4], m[7],
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m[2], m[5], m[8],
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)
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}
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// Moved moves everything by the delta vector.
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func (m Matrix) Moved(delta Vec) Matrix {
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m3 := mgl64.Mat3(m)
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m3 = mgl64.Translate2D(delta.XY()).Mul3(m3)
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return Matrix(m3)
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}
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// ScaledXY scales everything around a given point by the scale factor in each axis respectively.
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func (m Matrix) ScaledXY(around Vec, scale Vec) Matrix {
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m3 := mgl64.Mat3(m)
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m3 = mgl64.Translate2D(around.Scaled(-1).XY()).Mul3(m3)
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m3 = mgl64.Scale2D(scale.XY()).Mul3(m3)
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m3 = mgl64.Translate2D(around.XY()).Mul3(m3)
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return Matrix(m3)
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}
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// Scaled scales everything around a given point by the scale factor.
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func (m Matrix) Scaled(around Vec, scale float64) Matrix {
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return m.ScaledXY(around, V(scale, scale))
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}
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// Rotated rotates everything around a given point by the given angle in radians.
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func (m Matrix) Rotated(around Vec, angle float64) Matrix {
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m3 := mgl64.Mat3(m)
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m3 = mgl64.Translate2D(around.Scaled(-1).XY()).Mul3(m3)
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m3 = mgl64.Rotate3DZ(angle).Mul3(m3)
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m3 = mgl64.Translate2D(around.XY()).Mul3(m3)
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return Matrix(m3)
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}
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// Chained adds another Matrix to this one. All tranformations by the next Matrix will be applied
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// after the transformations of this Matrix.
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func (m Matrix) Chained(next Matrix) Matrix {
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m3 := mgl64.Mat3(m)
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m3 = mgl64.Mat3(next).Mul3(m3)
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return Matrix(m3)
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}
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// Project applies all transformations added to the Matrix to a vector u and returns the result.
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//
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// Time complexity is O(1).
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func (m Matrix) Project(u Vec) Vec {
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m3 := mgl64.Mat3(m)
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proj := m3.Mul3x1(mgl64.Vec3{u.X, u.Y, 1})
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return V(proj.X(), proj.Y())
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}
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// Unproject does the inverse operation to Project.
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//
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// Time complexity is O(1).
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func (m Matrix) Unproject(u Vec) Vec {
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m3 := mgl64.Mat3(m)
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inv := m3.Inv()
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unproj := inv.Mul3x1(mgl64.Vec3{u.X, u.Y, 1})
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return V(unproj.X(), unproj.Y())
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}
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