matrix2.go

// Copyright (c) 2020, The GoKi Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

package mat32

import (
	"fmt"
	"log"
	"strconv"
	"strings"
	"unicode"
)

/*
This is heavily modified from: https://github.com/fogleman/gg

Copyright (C) 2016 Michael Fogleman

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/

// note: golang.org/x/image/math/f64 defines Vec2 as [2]float64
// elabored then by https://godoc.org/github.com/go-gl/mathgl/mgl64
// it is instead very convenient and clear to use .X .Y fields for 2D math
// original gg package used Point2D but Vec2 is more general, e.g., for sizes etc
// in go much better to use fewer types so only using Vec2

type Mat2 struct {
	XX, YX, XY, YY, X0, Y0 float32
}

func Identity2D() Mat2 {
	return Mat2{
		1, 0,
		0, 1,
		0, 0,
	}
}

func Translate2D(x, y float32) Mat2 {
	return Mat2{
		1, 0,
		0, 1,
		x, y,
	}
}

func Scale2D(x, y float32) Mat2 {
	return Mat2{
		x, 0,
		0, y,
		0, 0,
	}
}

func Rotate2D(angle float32) Mat2 {
	c := float32(Cos(angle))
	s := float32(Sin(angle))
	return Mat2{
		c, s,
		-s, c,
		0, 0,
	}
}

func Shear2D(x, y float32) Mat2 {
	return Mat2{
		1, y,
		x, 1,
		0, 0,
	}
}

func Skew2D(x, y float32) Mat2 {
	return Mat2{
		1, Tan(y),
		Tan(x), 1,
		0, 0,
	}
}

func (a Mat2) Mul(b Mat2) Mat2 {
	return Mat2{
		a.XX*b.XX + a.YX*b.XY,
		a.XX*b.YX + a.YX*b.YY,
		a.XY*b.XX + a.YY*b.XY,
		a.XY*b.YX + a.YY*b.YY,
		a.X0*b.XX + a.Y0*b.XY + b.X0,
		a.X0*b.YX + a.Y0*b.YY + b.Y0,
	}
}

// MulVec2AsVec multiplies the Vec2 as a vector -- does not add translations.
// This is for directional vectors and not points.
func (a Mat2) MulVec2AsVec(v Vec2) Vec2 {
	tx := a.XX*v.X + a.XY*v.Y
	ty := a.YX*v.X + a.YY*v.Y
	return Vec2{tx, ty}
}

// MulVec2AsPt multiplies the Vec2 as a point, including adding translations.
func (a Mat2) MulVec2AsPt(v Vec2) Vec2 {
	tx := a.XX*v.X + a.XY*v.Y + a.X0
	ty := a.YX*v.X + a.YY*v.Y + a.Y0
	return Vec2{tx, ty}
}

func (a Mat2) Translate(x, y float32) Mat2 {
	return Translate2D(x, y).Mul(a)
}

func (a Mat2) Scale(x, y float32) Mat2 {
	return Scale2D(x, y).Mul(a)
}

func (a Mat2) Rotate(angle float32) Mat2 {
	return Rotate2D(angle).Mul(a)
}

func (a Mat2) Shear(x, y float32) Mat2 {
	return Shear2D(x, y).Mul(a)
}

func (a Mat2) Skew(x, y float32) Mat2 {
	return Skew2D(x, y).Mul(a)
}

// ExtractRot extracts the rotation component from a given matrix
func (a Mat2) ExtractRot() float32 {
	return Atan2(-a.XY, a.XX)
}

// ExtractXYScale extracts the X and Y scale factors after undoing any
// rotation present -- i.e., in the original X, Y coordinates
func (a Mat2) ExtractScale() (scx, scy float32) {
	rot := a.ExtractRot()
	tx := a.Rotate(-rot)
	scxv := tx.MulVec2AsVec(Vec2{1, 0})
	scyv := tx.MulVec2AsVec(Vec2{0, 1})
	return scxv.X, scyv.Y
}

// ParseFloat32 logs any strconv.ParseFloat errors
func ParseFloat32(pstr string) (float32, error) {
	r, err := strconv.ParseFloat(pstr, 32)
	if err != nil {
		log.Printf("gi.ParseFloat32: error parsing float32 number from: %v, %v\n", pstr, err)
		return float32(0.0), err
	}
	return float32(r), nil
}

// ParseAngle32 returns radians angle from string that can specify units (deg,
// grad, rad) -- deg is assumed if not specified
func ParseAngle32(pstr string) (float32, error) {
	units := "deg"
	lstr := strings.ToLower(pstr)
	if strings.Contains(lstr, "deg") {
		units = "deg"
		lstr = strings.TrimSuffix(lstr, "deg")
	} else if strings.Contains(lstr, "grad") {
		units = "grad"
		lstr = strings.TrimSuffix(lstr, "grad")
	} else if strings.Contains(lstr, "rad") {
		units = "rad"
		lstr = strings.TrimSuffix(lstr, "rad")
	}
	r, err := strconv.ParseFloat(lstr, 32)
	if err != nil {
		log.Printf("gi.ParseAngle32: error parsing float32 number from: %v, %v\n", lstr, err)
		return float32(0.0), err
	}
	switch units {
	case "deg":
		return float32(r) * Pi / 180, nil
	case "grad":
		return float32(r) * Pi / 200, nil
	case "rad":
		return float32(r), nil
	}
	return float32(r), nil
}

// ReadPoints reads a set of floating point values from a SVG format number
// string -- returns a slice or nil if there was an error
func ReadPoints(pstr string) []float32 {
	lastIdx := -1
	var pts []float32
	lr := ' '
	for i, r := range pstr {
		if unicode.IsNumber(r) == false && r != '.' && !(r == '-' && lr == 'e') && r != 'e' {
			if lastIdx != -1 {
				s := pstr[lastIdx:i]
				p, err := ParseFloat32(s)
				if err != nil {
					return nil
				}
				pts = append(pts, p)
			}
			if r == '-' {
				lastIdx = i
			} else {
				lastIdx = -1
			}
		} else if lastIdx == -1 {
			lastIdx = i
		}
		lr = r
	}
	if lastIdx != -1 && lastIdx != len(pstr) {
		s := pstr[lastIdx:len(pstr)]
		p, err := ParseFloat32(s)
		if err != nil {
			return nil
		}
		pts = append(pts, p)
	}
	return pts
}

// PointsCheckN checks the number of points read and emits an error if not equal to n
func PointsCheckN(pts []float32, n int, errmsg string) error {
	if len(pts) != n {
		return fmt.Errorf("%v incorrect number of points: %v != %v\n", errmsg, len(pts), n)
	}
	return nil
}

// SetString processes the standard SVG-style transform strings
func (a *Mat2) SetString(str string) error {
	errmsg := "gi.Mat2 SetString"
	str = strings.ToLower(strings.TrimSpace(str))
	*a = Identity2D()
	if str == "none" {
		return nil
	}
	// could have multiple transforms
	for {
		pidx := strings.IndexByte(str, '(')
		if pidx < 0 {
			err := fmt.Errorf("gi.Mat2 SetString: no params for xform: %v\n", str)
			log.Println(err)
			return err
		}
		cmd := str[:pidx]
		vals := str[pidx+1:]
		nxt := ""
		eidx := strings.IndexByte(vals, ')')
		if eidx > 0 {
			nxt = strings.TrimSpace(vals[eidx+1:])
			if strings.HasPrefix(nxt, ";") {
				nxt = strings.TrimSpace(strings.TrimPrefix(nxt, ";"))
			}
			vals = vals[:eidx]
		}
		pts := ReadPoints(vals)
		switch cmd {
		case "matrix":
			if err := PointsCheckN(pts, 6, errmsg); err != nil {
				log.Println(err)
				return err
			}
			*a = Mat2{pts[0], pts[1], pts[2], pts[3], pts[4], pts[5]}
		case "translate":
			if err := PointsCheckN(pts, 2, errmsg); err != nil {
				log.Println(err)
				return err
			}
			*a = a.Translate(pts[0], pts[1])
		case "translatex":
			if err := PointsCheckN(pts, 1, errmsg); err != nil {
				log.Println(err)
				return err
			}
			*a = a.Translate(pts[0], 0)
		case "translatey":
			if err := PointsCheckN(pts, 1, errmsg); err != nil {
				log.Println(err)
				return err
			}
			*a = a.Translate(0, pts[0])
		case "scale":
			if len(pts) == 1 {
				*a = a.Scale(pts[0], pts[0])
			} else if len(pts) == 2 {
				*a = a.Scale(pts[0], pts[1])
			} else {
				err := fmt.Errorf("%v incorrect number of points: 2 != %v\n", errmsg, len(pts))
				log.Println(err)
			}
		case "scalex":
			if err := PointsCheckN(pts, 1, errmsg); err != nil {
				log.Println(err)
				return err
			}
			*a = a.Scale(pts[0], 1)
		case "scaley":
			if err := PointsCheckN(pts, 1, errmsg); err != nil {
				log.Println(err)
				return err
			}
			*a = a.Scale(1, pts[0])
		case "rotate":
			ang := pts[0] * Pi / 180 // always in degrees in this form
			if len(pts) == 3 {
				*a = a.Translate(pts[1], pts[2]).Rotate(ang).Translate(-pts[1], -pts[2])
			} else if len(pts) == 1 {
				*a = a.Rotate(ang)
			} else {
				return PointsCheckN(pts, 1, errmsg)
			}
		case "skew":
			if err := PointsCheckN(pts, 2, errmsg); err != nil {
				log.Println(err)
				return err
			}
			*a = a.Skew(pts[0], pts[1])
		case "skewx":
			if err := PointsCheckN(pts, 1, errmsg); err != nil {
				log.Println(err)
				return err
			}
			*a = a.Skew(pts[0], 0)
		case "skewy":
			if err := PointsCheckN(pts, 1, errmsg); err != nil {
				log.Println(err)
				return err
			}
			*a = a.Skew(0, pts[0])
		}
		if nxt == "" {
			break
		}
		if !strings.Contains(nxt, "(") {
			break
		}
		str = nxt
	}
	return nil
}