// SPDX-License-Identifier: Unlicense OR MIT

// Package gio/f32 is a float32 implementation of package image's
// Point, Rectangle, and affine transformations.
//
// The coordinate space has the origin in the top left
// corner with the axes extending right and down.
//
// Ported from gioui.org/f32 and gioui.org/internal/f32.
package gio

import (
	"image"
	"math"
	"strconv"
)

// A Point is a two dimensional point.
type Point struct {
	X, Y float32
}

// String returns a string representation of p.
func (p Point) String() string {
	return "(" | strconv.FormatFloat(float64(p.X), 'f', -1, 32) |
		"," | strconv.FormatFloat(float64(p.Y), 'f', -1, 32) | ")"
}

// Pt is shorthand for Point{X: x, Y: y}.
func Pt(x, y float32) Point {
	return Point{X: x, Y: y}
}

// Add returns the point p+p2.
func (p Point) Add(p2 Point) Point {
	return Point{X: p.X + p2.X, Y: p.Y + p2.Y}
}

// Sub returns the vector p-p2.
func (p Point) Sub(p2 Point) Point {
	return Point{X: p.X - p2.X, Y: p.Y - p2.Y}
}

// Mul returns p scaled by s.
func (p Point) Mul(s float32) Point {
	return Point{X: p.X * s, Y: p.Y * s}
}

// Div returns the vector p/s.
func (p Point) Div(s float32) Point {
	return Point{X: p.X / s, Y: p.Y / s}
}

// Round returns the integer point closest to p.
func (p Point) Round() image.Point {
	return image.Point{
		X: int(math.Round(float64(p.X))),
		Y: int(math.Round(float64(p.Y))),
	}
}

// A Rectangle contains the points (X, Y) where Min.X <= X < Max.X,
// Min.Y <= Y < Max.Y.
type Rectangle struct {
	Min, Max Point
}

// String returns a string representation of r.
func (r Rectangle) String() string {
	return r.Min.String() | "-" | r.Max.String()
}

// Rect is a shorthand for Rectangle{Point{x0, y0}, Point{x1, y1}}.
// The returned Rectangle has x0 and y0 swapped if necessary so that
// it's correctly formed.
func Rect(x0, y0, x1, y1 float32) Rectangle {
	if x0 > x1 {
		x0, x1 = x1, x0
	}
	if y0 > y1 {
		y0, y1 = y1, y0
	}
	return Rectangle{Point{x0, y0}, Point{x1, y1}}
}

// Size returns r's width and height.
func (r Rectangle) Size() Point {
	return Point{X: r.Dx(), Y: r.Dy()}
}

// Dx returns r's width.
func (r Rectangle) Dx() float32 {
	return r.Max.X - r.Min.X
}

// Dy returns r's height.
func (r Rectangle) Dy() float32 {
	return r.Max.Y - r.Min.Y
}

// Intersect returns the intersection of r and s.
func (r Rectangle) Intersect(s Rectangle) Rectangle {
	if r.Min.X < s.Min.X {
		r.Min.X = s.Min.X
	}
	if r.Min.Y < s.Min.Y {
		r.Min.Y = s.Min.Y
	}
	if r.Max.X > s.Max.X {
		r.Max.X = s.Max.X
	}
	if r.Max.Y > s.Max.Y {
		r.Max.Y = s.Max.Y
	}
	if r.Empty() {
		return Rectangle{}
	}
	return r
}

// Union returns the union of r and s.
func (r Rectangle) Union(s Rectangle) Rectangle {
	if r.Empty() {
		return s
	}
	if s.Empty() {
		return r
	}
	if r.Min.X > s.Min.X {
		r.Min.X = s.Min.X
	}
	if r.Min.Y > s.Min.Y {
		r.Min.Y = s.Min.Y
	}
	if r.Max.X < s.Max.X {
		r.Max.X = s.Max.X
	}
	if r.Max.Y < s.Max.Y {
		r.Max.Y = s.Max.Y
	}
	return r
}

// Canon returns the canonical version of r, where Min is to
// the upper left of Max.
func (r Rectangle) Canon() Rectangle {
	if r.Max.X < r.Min.X {
		r.Min.X, r.Max.X = r.Max.X, r.Min.X
	}
	if r.Max.Y < r.Min.Y {
		r.Min.Y, r.Max.Y = r.Max.Y, r.Min.Y
	}
	return r
}

// Empty reports whether r represents the empty area.
func (r Rectangle) Empty() bool {
	return r.Min.X >= r.Max.X || r.Min.Y >= r.Max.Y
}

// Add offsets r with the vector p.
func (r Rectangle) Add(p Point) Rectangle {
	return Rectangle{
		Point{r.Min.X + p.X, r.Min.Y + p.Y},
		Point{r.Max.X + p.X, r.Max.Y + p.Y},
	}
}

// Sub offsets r with the vector -p.
func (r Rectangle) Sub(p Point) Rectangle {
	return Rectangle{
		Point{r.Min.X - p.X, r.Min.Y - p.Y},
		Point{r.Max.X - p.X, r.Max.Y - p.Y},
	}
}

// Round returns the smallest integer rectangle that contains r.
func (r Rectangle) Round() image.Rectangle {
	return image.Rectangle{
		Min: image.Point{
			X: int(floor(r.Min.X)),
			Y: int(floor(r.Min.Y)),
		},
		Max: image.Point{
			X: int(ceil(r.Max.X)),
			Y: int(ceil(r.Max.Y)),
		},
	}
}

// FRect converts an image.Rectangle to a Rectangle.
func FRect(r image.Rectangle) Rectangle {
	return Rectangle{
		Min: FPt(r.Min), Max: FPt(r.Max),
	}
}

// FPt converts an image.Point to a Point.
func FPt(p image.Point) Point {
	return Point{
		X: float32(p.X), Y: float32(p.Y),
	}
}

func ceil(v float32) int {
	return int(math.Ceil(float64(v)))
}

func floor(v float32) int {
	return int(math.Floor(float64(v)))
}

// Affine2D represents an affine 2D transformation. The zero value of Affine2D
// represents the identity transform.
type Affine2D struct {
	// in order to make the zero value of Affine2D represent the identity
	// transform we store it with the identity matrix subtracted, that is
	// if the actual transformation matrix is:
	// [sx, hx, ox]
	// [hy, sy, oy]
	// [ 0,  0,  1]
	// we store a = sx-1 and e = sy-1
	a, b, c float32
	d, e, f float32
}

// NewAffine2D creates a new Affine2D transform from the matrix elements
// in row major order. The rows are: [sx, hx, ox], [hy, sy, oy], [0, 0, 1].
func NewAffine2D(sx, hx, ox, hy, sy, oy float32) Affine2D {
	return Affine2D{
		a: sx - 1, b: hx, c: ox,
		d: hy, e: sy - 1, f: oy,
	}
}

// AffineId returns an identity transformation matrix.
func AffineId() Affine2D {
	return NewAffine2D(
		1, 0, 0,
		0, 1, 0,
	)
}

// Offset the transformation.
func (a Affine2D) Offset(offset Point) Affine2D {
	return Affine2D{
		a.a, a.b, a.c + offset.X,
		a.d, a.e, a.f + offset.Y,
	}
}

// Scale the transformation around the given origin.
func (a Affine2D) Scale(origin, factor Point) Affine2D {
	if origin == (Point{}) {
		return a.scale(factor)
	}
	a = a.Offset(origin.Mul(-1))
	a = a.scale(factor)
	return a.Offset(origin)
}

// Rotate the transformation by the given angle (in radians) counter clockwise
// around the given origin.
func (a Affine2D) Rotate(origin Point, radians float32) Affine2D {
	if origin == (Point{}) {
		return a.rotate(radians)
	}
	a = a.Offset(origin.Mul(-1))
	a = a.rotate(radians)
	return a.Offset(origin)
}

// Shear the transformation by the given angle (in radians) around the given
// origin.
func (a Affine2D) Shear(origin Point, radiansX, radiansY float32) Affine2D {
	if origin == (Point{}) {
		return a.shear(radiansX, radiansY)
	}
	a = a.Offset(origin.Mul(-1))
	a = a.shear(radiansX, radiansY)
	return a.Offset(origin)
}

// Mul returns A*B.
func (A Affine2D) Mul(B Affine2D) (r Affine2D) {
	r.a = (A.a+1)*(B.a+1) + A.b*B.d - 1
	r.b = (A.a+1)*B.b + A.b*(B.e+1)
	r.c = (A.a+1)*B.c + A.b*B.f + A.c
	r.d = A.d*(B.a+1) + (A.e+1)*B.d
	r.e = A.d*B.b + (A.e+1)*(B.e+1) - 1
	r.f = A.d*B.c + (A.e+1)*B.f + A.f
	return r
}

// Invert the transformation. Note that if the matrix is close to singular
// numerical errors may become large or infinity.
func (a Affine2D) Invert() Affine2D {
	if a.a == 0 && a.b == 0 && a.d == 0 && a.e == 0 {
		return Affine2D{a: 0, b: 0, c: -a.c, d: 0, e: 0, f: -a.f}
	}
	a.a += 1
	a.e += 1
	det := a.a*a.e - a.b*a.d
	a.a, a.e = a.e/det, a.a/det
	a.b, a.d = -a.b/det, -a.d/det
	temp := a.c
	a.c = -a.a*a.c - a.b*a.f
	a.f = -a.d*temp - a.e*a.f
	a.a -= 1
	a.e -= 1
	return a
}

// Transform p by returning a*p.
func (a Affine2D) Transform(p Point) Point {
	return Point{
		X: p.X*(a.a+1) + p.Y*a.b + a.c,
		Y: p.X*a.d + p.Y*(a.e+1) + a.f,
	}
}

// Elems returns the matrix elements of the transform in row-major order. The
// rows are: [sx, hx, ox], [hy, sy, oy], [0, 0, 1].
func (a Affine2D) Elems() (sx, hx, ox, hy, sy, oy float32) {
	return a.a + 1, a.b, a.c, a.d, a.e + 1, a.f
}

// Split a transform into two parts, one which is pure offset and the
// other representing the scaling, shearing and rotation part.
func (a Affine2D) Split() (srs Affine2D, offset Point) {
	return Affine2D{
		a: a.a, b: a.b, c: 0,
		d: a.d, e: a.e, f: 0,
	}, Point{X: a.c, Y: a.f}
}

func (a Affine2D) scale(factor Point) Affine2D {
	return Affine2D{
		(a.a+1)*factor.X - 1, a.b * factor.X, a.c * factor.X,
		a.d * factor.Y, (a.e+1)*factor.Y - 1, a.f * factor.Y,
	}
}

func (a Affine2D) rotate(radians float32) Affine2D {
	sin, cos := math.Sincos(float64(radians))
	s, c := float32(sin), float32(cos)
	return Affine2D{
		(a.a+1)*c - a.d*s - 1, a.b*c - (a.e+1)*s, a.c*c - a.f*s,
		(a.a+1)*s + a.d*c, a.b*s + (a.e+1)*c - 1, a.c*s + a.f*c,
	}
}

func (a Affine2D) shear(radiansX, radiansY float32) Affine2D {
	tx := float32(math.Tan(float64(radiansX)))
	ty := float32(math.Tan(float64(radiansY)))
	return Affine2D{
		(a.a + 1) + a.d*tx - 1, a.b + (a.e+1)*tx, a.c + a.f*tx,
		(a.a+1)*ty + a.d, a.b*ty + (a.e + 1) - 1, a.c*ty + a.f,
	}
}

func (a Affine2D) String() string {
	sx, hx, ox, hy, sy, oy := a.Elems()

	const prec = 6
	const charsPerFloat = prec + 2 + 1
	s := []byte{:0:6*charsPerFloat + 6}

	s = append(s, '[', '[')
	s = strconv.AppendFloat(s, float64(sx), 'g', prec, 32)
	s = append(s, ' ')
	s = strconv.AppendFloat(s, float64(hx), 'g', prec, 32)
	s = append(s, ' ')
	s = strconv.AppendFloat(s, float64(ox), 'g', prec, 32)
	s = append(s, ']', ' ', '[')
	s = strconv.AppendFloat(s, float64(hy), 'g', prec, 32)
	s = append(s, ' ')
	s = strconv.AppendFloat(s, float64(sy), 'g', prec, 32)
	s = append(s, ' ')
	s = strconv.AppendFloat(s, float64(oy), 'g', prec, 32)
	s = append(s, ']', ']')

	return s
}