From cc9247c627adbfd99a6b093e1552dff833a746af Mon Sep 17 00:00:00 2001
From: Thomas Friedel <tomee6@gmail.com>
Date: Sun, 22 Mar 2020 10:07:18 +0100
Subject: [PATCH] moved math code to backendbase package so that backends can
 also use it

---
 backend/backendbase/math.go | 140 +++++++++++++++++++++++++++
 canvas.go                   |  30 +++---
 gradients.go                |  12 +--
 images.go                   |  18 ++--
 math.go                     | 140 ---------------------------
 path2d.go                   | 132 +++++++++++++-------------
 paths.go                    | 184 ++++++++++++++++++------------------
 text.go                     |  25 ++---
 triangulation.go            |  40 ++++----
 9 files changed, 364 insertions(+), 357 deletions(-)
 create mode 100644 backend/backendbase/math.go
 delete mode 100644 math.go

diff --git a/backend/backendbase/math.go b/backend/backendbase/math.go
new file mode 100644
index 0000000..05717bf
--- /dev/null
+++ b/backend/backendbase/math.go
@@ -0,0 +1,140 @@
+package backendbase
+
+import (
+	"fmt"
+	"math"
+)
+
+type Vec [2]float64
+
+func (v Vec) String() string {
+	return fmt.Sprintf("[%f,%f]", v[0], v[1])
+}
+
+func (v Vec) Add(v2 Vec) Vec {
+	return Vec{v[0] + v2[0], v[1] + v2[1]}
+}
+
+func (v Vec) Sub(v2 Vec) Vec {
+	return Vec{v[0] - v2[0], v[1] - v2[1]}
+}
+
+func (v Vec) Mul(v2 Vec) Vec {
+	return Vec{v[0] * v2[0], v[1] * v2[1]}
+}
+
+func (v Vec) Mulf(f float64) Vec {
+	return Vec{v[0] * f, v[1] * f}
+}
+
+func (v Vec) MulMat(m Mat) Vec {
+	return Vec{
+		m[0]*v[0] + m[2]*v[1] + m[4],
+		m[1]*v[0] + m[3]*v[1] + m[5]}
+}
+
+func (v Vec) MulMat2(m Mat2) Vec {
+	return Vec{m[0]*v[0] + m[2]*v[1], m[1]*v[0] + m[3]*v[1]}
+}
+
+func (v Vec) Div(v2 Vec) Vec {
+	return Vec{v[0] / v2[0], v[1] / v2[1]}
+}
+
+func (v Vec) Divf(f float64) Vec {
+	return Vec{v[0] / f, v[1] / f}
+}
+
+func (v Vec) Dot(v2 Vec) float64 {
+	return v[0]*v2[0] + v[1]*v2[1]
+}
+
+func (v Vec) Len() float64 {
+	return math.Sqrt(v[0]*v[0] + v[1]*v[1])
+}
+
+func (v Vec) LenSqr() float64 {
+	return v[0]*v[0] + v[1]*v[1]
+}
+
+func (v Vec) Norm() Vec {
+	return v.Mulf(1.0 / v.Len())
+}
+
+func (v Vec) Atan2() float64 {
+	return math.Atan2(v[1], v[0])
+}
+
+func (v Vec) Angle() float64 {
+	return math.Pi*0.5 - math.Atan2(v[1], v[0])
+}
+
+func (v Vec) AngleTo(v2 Vec) float64 {
+	return math.Acos(v.Norm().Dot(v2.Norm()))
+}
+
+type Mat [6]float64
+
+func (m *Mat) String() string {
+	return fmt.Sprintf("[%f,%f,0,\n %f,%f,0,\n %f,%f,1,]", m[0], m[2], m[4], m[1], m[3], m[5])
+}
+
+var MatIdentity = Mat{
+	1, 0,
+	0, 1,
+	0, 0}
+
+func MatTranslate(v Vec) Mat {
+	return Mat{
+		1, 0,
+		0, 1,
+		v[0], v[1]}
+}
+
+func MatScale(v Vec) Mat {
+	return Mat{
+		v[0], 0,
+		0, v[1],
+		0, 0}
+}
+
+func MatRotate(radians float64) Mat {
+	s, c := math.Sincos(radians)
+	return Mat{
+		c, s,
+		-s, c,
+		0, 0}
+}
+
+func (m Mat) Mul(m2 Mat) Mat {
+	return Mat{
+		m[0]*m2[0] + m[1]*m2[2],
+		m[0]*m2[1] + m[1]*m2[3],
+		m[2]*m2[0] + m[3]*m2[2],
+		m[2]*m2[1] + m[3]*m2[3],
+		m[4]*m2[0] + m[5]*m2[2] + m2[4],
+		m[4]*m2[1] + m[5]*m2[3] + m2[5]}
+}
+
+func (m Mat) Invert() Mat {
+	identity := 1.0 / (m[0]*m[3] - m[2]*m[1])
+
+	return Mat{
+		m[3] * identity,
+		-m[1] * identity,
+		-m[2] * identity,
+		m[0] * identity,
+		(m[2]*m[5] - m[3]*m[4]) * identity,
+		(m[1]*m[4] - m[0]*m[5]) * identity,
+	}
+}
+
+type Mat2 [4]float64
+
+func (m Mat) Mat2() Mat2 {
+	return Mat2{m[0], m[1], m[2], m[3]}
+}
+
+func (m *Mat2) String() string {
+	return fmt.Sprintf("[%f,%f,\n %f,%f]", m[0], m[2], m[1], m[3])
+}
diff --git a/canvas.go b/canvas.go
index 8863b5e..3326bc7 100644
--- a/canvas.go
+++ b/canvas.go
@@ -35,7 +35,7 @@ type Canvas struct {
 }
 
 type drawState struct {
-	transform     mat
+	transform     backendbase.Mat
 	fill          drawStyle
 	stroke        drawStyle
 	font          *Font
@@ -150,7 +150,7 @@ func New(backend backendbase.Backend) *Canvas {
 	cv.state.globalAlpha = 1
 	cv.state.fill.color = color.RGBA{A: 255}
 	cv.state.stroke.color = color.RGBA{A: 255}
-	cv.state.transform = matIdentity
+	cv.state.transform = backendbase.MatIdentity
 	cv.path.cv = cv
 	return cv
 }
@@ -170,8 +170,8 @@ func (cv *Canvas) Height() int {
 // Size returns the internal width and height of the canvas
 func (cv *Canvas) Size() (int, int) { return cv.b.Size() }
 
-func (cv *Canvas) tf(v vec) vec {
-	return v.mulMat(cv.state.transform)
+func (cv *Canvas) tf(v backendbase.Vec) backendbase.Vec {
+	return v.MulMat(cv.state.transform)
 }
 
 const alphaTexSize = 2048
@@ -380,7 +380,7 @@ func (cv *Canvas) Restore() {
 	cv.b.ClearClip()
 	for _, st := range cv.stateStack {
 		if len(st.clip.p) > 0 {
-			cv.clip(&st.clip, matIdentity)
+			cv.clip(&st.clip, backendbase.MatIdentity)
 		}
 	}
 	cv.state = cv.stateStack[l-1]
@@ -389,27 +389,27 @@ func (cv *Canvas) Restore() {
 
 // Scale updates the current transformation with a scaling by the given values
 func (cv *Canvas) Scale(x, y float64) {
-	cv.state.transform = matScale(vec{x, y}).mul(cv.state.transform)
+	cv.state.transform = backendbase.MatScale(backendbase.Vec{x, y}).Mul(cv.state.transform)
 }
 
 // Translate updates the current transformation with a translation by the given values
 func (cv *Canvas) Translate(x, y float64) {
-	cv.state.transform = matTranslate(vec{x, y}).mul(cv.state.transform)
+	cv.state.transform = backendbase.MatTranslate(backendbase.Vec{x, y}).Mul(cv.state.transform)
 }
 
 // Rotate updates the current transformation with a rotation by the given angle
 func (cv *Canvas) Rotate(angle float64) {
-	cv.state.transform = matRotate(angle).mul(cv.state.transform)
+	cv.state.transform = backendbase.MatRotate(angle).Mul(cv.state.transform)
 }
 
 // Transform updates the current transformation with the given matrix
 func (cv *Canvas) Transform(a, b, c, d, e, f float64) {
-	cv.state.transform = mat{a, b, c, d, e, f}.mul(cv.state.transform)
+	cv.state.transform = backendbase.Mat{a, b, c, d, e, f}.Mul(cv.state.transform)
 }
 
 // SetTransform replaces the current transformation with the given matrix
 func (cv *Canvas) SetTransform(a, b, c, d, e, f float64) {
-	cv.state.transform = mat{a, b, c, d, e, f}
+	cv.state.transform = backendbase.Mat{a, b, c, d, e, f}
 }
 
 // SetShadowColor sets the color of the shadow. If it is fully transparent (default)
@@ -456,14 +456,14 @@ func (cv *Canvas) IsPointInStroke(x, y float64) bool {
 	}
 
 	var triBuf [500][2]float64
-	tris := cv.strokeTris(&cv.path, cv.state.transform.invert(), true, triBuf[:0])
+	tris := cv.strokeTris(&cv.path, cv.state.transform.Invert(), true, triBuf[:0])
 
-	pt := vec{x, y}
+	pt := backendbase.Vec{x, y}
 
 	for i := 0; i < len(tris); i += 3 {
-		a := vec{tris[i][0], tris[i][1]}
-		b := vec{tris[i+1][0], tris[i+1][1]}
-		c := vec{tris[i+2][0], tris[i+2][1]}
+		a := backendbase.Vec{tris[i][0], tris[i][1]}
+		b := backendbase.Vec{tris[i+1][0], tris[i+1][1]}
+		c := backendbase.Vec{tris[i+2][0], tris[i+2][1]}
 		if triangleContainsPoint(a, b, c, pt) {
 			return true
 		}
diff --git a/gradients.go b/gradients.go
index 50d2ebb..af815f7 100644
--- a/gradients.go
+++ b/gradients.go
@@ -13,7 +13,7 @@ import (
 // will correspond to a straight line
 type LinearGradient struct {
 	cv       *Canvas
-	from, to vec
+	from, to backendbase.Vec
 	created  bool
 	loaded   bool
 	opaque   bool
@@ -27,7 +27,7 @@ type LinearGradient struct {
 // will correspond to a circle
 type RadialGradient struct {
 	cv       *Canvas
-	from, to vec
+	from, to backendbase.Vec
 	radFrom  float64
 	radTo    float64
 	created  bool
@@ -44,8 +44,8 @@ func (cv *Canvas) CreateLinearGradient(x0, y0, x1, y1 float64) *LinearGradient {
 	lg := &LinearGradient{
 		cv:     cv,
 		opaque: true,
-		from:   vec{x0, y0},
-		to:     vec{x1, y1},
+		from:   backendbase.Vec{x0, y0},
+		to:     backendbase.Vec{x1, y1},
 		data:   make(backendbase.Gradient, 0, 20),
 	}
 	runtime.SetFinalizer(lg, func(*LinearGradient) {
@@ -62,8 +62,8 @@ func (cv *Canvas) CreateRadialGradient(x0, y0, r0, x1, y1, r1 float64) *RadialGr
 	rg := &RadialGradient{
 		cv:      cv,
 		opaque:  true,
-		from:    vec{x0, y0},
-		to:      vec{x1, y1},
+		from:    backendbase.Vec{x0, y0},
+		to:      backendbase.Vec{x1, y1},
 		radFrom: r0,
 		radTo:   r1,
 		data:    make(backendbase.Gradient, 0, 20),
diff --git a/images.go b/images.go
index ce09e52..aac45b5 100644
--- a/images.go
+++ b/images.go
@@ -182,10 +182,10 @@ func (cv *Canvas) DrawImage(image interface{}, coords ...float64) {
 	}
 
 	var data [4][2]float64
-	data[0] = cv.tf(vec{dx, dy})
-	data[1] = cv.tf(vec{dx, dy + dh})
-	data[2] = cv.tf(vec{dx + dw, dy + dh})
-	data[3] = cv.tf(vec{dx + dw, dy})
+	data[0] = cv.tf(backendbase.Vec{dx, dy})
+	data[1] = cv.tf(backendbase.Vec{dx, dy + dh})
+	data[2] = cv.tf(backendbase.Vec{dx + dw, dy + dh})
+	data[3] = cv.tf(backendbase.Vec{dx + dw, dy})
 
 	cv.drawShadow(data[:], nil, false)
 
@@ -207,7 +207,7 @@ func (cv *Canvas) PutImageData(img *image.RGBA, x, y int) {
 type ImagePattern struct {
 	cv  *Canvas
 	img *Image
-	tf  mat
+	tf  backendbase.Mat
 	rep imagePatternRepeat
 	ip  backendbase.ImagePattern
 }
@@ -222,8 +222,8 @@ const (
 	NoRepeat                    = imagePatternRepeat(backendbase.NoRepeat)
 )
 
-func (ip *ImagePattern) data(tf mat) backendbase.ImagePatternData {
-	m := tf.invert().mul(ip.tf.invert())
+func (ip *ImagePattern) data(tf backendbase.Mat) backendbase.ImagePatternData {
+	m := tf.Invert().Mul(ip.tf.Invert())
 	return backendbase.ImagePatternData{
 		Image: ip.img.img,
 		Transform: [9]float64{
@@ -239,7 +239,7 @@ func (ip *ImagePattern) data(tf mat) backendbase.ImagePatternData {
 // to the given matrix. The matrix is a 3x3 matrix, but three
 // of the values are always identity values
 func (ip *ImagePattern) SetTransform(tf [6]float64) {
-	ip.tf = mat(tf)
+	ip.tf = backendbase.Mat(tf)
 }
 
 // CreatePattern creates a new image pattern with the specified
@@ -249,7 +249,7 @@ func (cv *Canvas) CreatePattern(src interface{}, repeat imagePatternRepeat) *Ima
 		cv:  cv,
 		img: cv.getImage(src),
 		rep: repeat,
-		tf:  mat{1, 0, 0, 1, 0, 0},
+		tf:  backendbase.Mat{1, 0, 0, 1, 0, 0},
 	}
 	if ip.img != nil {
 		ip.ip = cv.b.LoadImagePattern(ip.data(cv.state.transform))
diff --git a/math.go b/math.go
deleted file mode 100644
index d4fc183..0000000
--- a/math.go
+++ /dev/null
@@ -1,140 +0,0 @@
-package canvas
-
-import (
-	"fmt"
-	"math"
-)
-
-type vec [2]float64
-
-func (v vec) String() string {
-	return fmt.Sprintf("[%f,%f]", v[0], v[1])
-}
-
-func (v vec) add(v2 vec) vec {
-	return vec{v[0] + v2[0], v[1] + v2[1]}
-}
-
-func (v vec) sub(v2 vec) vec {
-	return vec{v[0] - v2[0], v[1] - v2[1]}
-}
-
-func (v vec) mul(v2 vec) vec {
-	return vec{v[0] * v2[0], v[1] * v2[1]}
-}
-
-func (v vec) mulf(f float64) vec {
-	return vec{v[0] * f, v[1] * f}
-}
-
-func (v vec) mulMat(m mat) vec {
-	return vec{
-		m[0]*v[0] + m[2]*v[1] + m[4],
-		m[1]*v[0] + m[3]*v[1] + m[5]}
-}
-
-func (v vec) mulMat2(m mat2) vec {
-	return vec{m[0]*v[0] + m[2]*v[1], m[1]*v[0] + m[3]*v[1]}
-}
-
-func (v vec) div(v2 vec) vec {
-	return vec{v[0] / v2[0], v[1] / v2[1]}
-}
-
-func (v vec) divf(f float64) vec {
-	return vec{v[0] / f, v[1] / f}
-}
-
-func (v vec) dot(v2 vec) float64 {
-	return v[0]*v2[0] + v[1]*v2[1]
-}
-
-func (v vec) len() float64 {
-	return math.Sqrt(v[0]*v[0] + v[1]*v[1])
-}
-
-func (v vec) lenSqr() float64 {
-	return v[0]*v[0] + v[1]*v[1]
-}
-
-func (v vec) norm() vec {
-	return v.mulf(1.0 / v.len())
-}
-
-func (v vec) atan2() float64 {
-	return math.Atan2(v[1], v[0])
-}
-
-func (v vec) angle() float64 {
-	return math.Pi*0.5 - math.Atan2(v[1], v[0])
-}
-
-func (v vec) angleTo(v2 vec) float64 {
-	return math.Acos(v.norm().dot(v2.norm()))
-}
-
-type mat [6]float64
-
-func (m *mat) String() string {
-	return fmt.Sprintf("[%f,%f,0,\n %f,%f,0,\n %f,%f,1,]", m[0], m[2], m[4], m[1], m[3], m[5])
-}
-
-var matIdentity = mat{
-	1, 0,
-	0, 1,
-	0, 0}
-
-func matTranslate(v vec) mat {
-	return mat{
-		1, 0,
-		0, 1,
-		v[0], v[1]}
-}
-
-func matScale(v vec) mat {
-	return mat{
-		v[0], 0,
-		0, v[1],
-		0, 0}
-}
-
-func matRotate(radians float64) mat {
-	s, c := math.Sincos(radians)
-	return mat{
-		c, s,
-		-s, c,
-		0, 0}
-}
-
-func (m mat) mul(m2 mat) mat {
-	return mat{
-		m[0]*m2[0] + m[1]*m2[2],
-		m[0]*m2[1] + m[1]*m2[3],
-		m[2]*m2[0] + m[3]*m2[2],
-		m[2]*m2[1] + m[3]*m2[3],
-		m[4]*m2[0] + m[5]*m2[2] + m2[4],
-		m[4]*m2[1] + m[5]*m2[3] + m2[5]}
-}
-
-func (m mat) invert() mat {
-	identity := 1.0 / (m[0]*m[3] - m[2]*m[1])
-
-	return mat{
-		m[3] * identity,
-		-m[1] * identity,
-		-m[2] * identity,
-		m[0] * identity,
-		(m[2]*m[5] - m[3]*m[4]) * identity,
-		(m[1]*m[4] - m[0]*m[5]) * identity,
-	}
-}
-
-type mat2 [4]float64
-
-func (m mat) mat2() mat2 {
-	return mat2{m[0], m[1], m[2], m[3]}
-}
-
-func (m *mat2) String() string {
-	return fmt.Sprintf("[%f,%f,\n %f,%f]", m[0], m[2], m[1], m[3])
-}
diff --git a/path2d.go b/path2d.go
index 4ad1e4a..aa6293d 100644
--- a/path2d.go
+++ b/path2d.go
@@ -2,6 +2,8 @@ package canvas
 
 import (
 	"math"
+
+	"github.com/tfriedel6/canvas/backend/backendbase"
 )
 
 // Path2D is a type that holds a predefined path which can be drawn
@@ -9,13 +11,13 @@ import (
 type Path2D struct {
 	cv    *Canvas
 	p     []pathPoint
-	move  vec
+	move  backendbase.Vec
 	cwSum float64
 }
 
 type pathPoint struct {
-	pos   vec
-	next  vec
+	pos   backendbase.Vec
+	next  backendbase.Vec
 	flags pathPointFlag
 }
 
@@ -40,12 +42,12 @@ func (cv *Canvas) NewPath2D() *Path2D {
 
 // MoveTo (see equivalent function on canvas type)
 func (p *Path2D) MoveTo(x, y float64) {
-	if len(p.p) > 0 && isSamePoint(p.p[len(p.p)-1].pos, vec{x, y}, 0.1) {
+	if len(p.p) > 0 && isSamePoint(p.p[len(p.p)-1].pos, backendbase.Vec{x, y}, 0.1) {
 		return
 	}
-	p.p = append(p.p, pathPoint{pos: vec{x, y}, flags: pathMove | pathIsConvex})
+	p.p = append(p.p, pathPoint{pos: backendbase.Vec{x, y}, flags: pathMove | pathIsConvex})
 	p.cwSum = 0
-	p.move = vec{x, y}
+	p.move = backendbase.Vec{x, y}
 }
 
 // LineTo (see equivalent function on canvas type)
@@ -55,7 +57,7 @@ func (p *Path2D) LineTo(x, y float64) {
 
 func (p *Path2D) lineTo(x, y float64, checkSelfIntersection bool) {
 	count := len(p.p)
-	if count > 0 && isSamePoint(p.p[len(p.p)-1].pos, vec{x, y}, 0.1) {
+	if count > 0 && isSamePoint(p.p[len(p.p)-1].pos, backendbase.Vec{x, y}, 0.1) {
 		return
 	}
 	if count == 0 {
@@ -63,9 +65,9 @@ func (p *Path2D) lineTo(x, y float64, checkSelfIntersection bool) {
 		return
 	}
 	prev := &p.p[count-1]
-	prev.next = vec{x, y}
+	prev.next = backendbase.Vec{x, y}
 	prev.flags |= pathAttach
-	p.p = append(p.p, pathPoint{pos: vec{x, y}})
+	p.p = append(p.p, pathPoint{pos: backendbase.Vec{x, y}})
 	newp := &p.p[count]
 
 	if prev.flags&pathIsConvex > 0 {
@@ -84,9 +86,9 @@ func (p *Path2D) lineTo(x, y float64, checkSelfIntersection bool) {
 		prev2 := &p.p[count-2]
 		cw := (prev.flags & pathIsClockwise) > 0
 
-		ln := prev.pos.sub(prev2.pos)
-		lo := vec{ln[1], -ln[0]}
-		dot := newp.pos.sub(prev2.pos).dot(lo)
+		ln := prev.pos.Sub(prev2.pos)
+		lo := backendbase.Vec{ln[1], -ln[0]}
+		dot := newp.pos.Sub(prev2.pos).Dot(lo)
 
 		if (cw && dot <= 0) || (!cw && dot >= 0) {
 			newp.flags |= pathIsConvex
@@ -97,8 +99,8 @@ func (p *Path2D) lineTo(x, y float64, checkSelfIntersection bool) {
 		newp.flags |= pathSelfIntersects
 	} else if newp.flags&pathIsConvex == 0 && newp.flags&pathSelfIntersects == 0 && checkSelfIntersection && !Performance.IgnoreSelfIntersections {
 		cuts := false
-		var cutPoint vec
-		b0, b1 := prev.pos, vec{x, y}
+		var cutPoint backendbase.Vec
+		b0, b1 := prev.pos, backendbase.Vec{x, y}
 		for i := 1; i < count; i++ {
 			a0, a1 := p.p[i-1].pos, p.p[i].pos
 			var r1, r2 float64
@@ -108,7 +110,7 @@ func (p *Path2D) lineTo(x, y float64, checkSelfIntersection bool) {
 				break
 			}
 		}
-		if cuts && !isSamePoint(cutPoint, vec{x, y}, samePointTolerance) {
+		if cuts && !isSamePoint(cutPoint, backendbase.Vec{x, y}, samePointTolerance) {
 			newp.flags |= pathSelfIntersects
 		}
 	}
@@ -116,19 +118,19 @@ func (p *Path2D) lineTo(x, y float64, checkSelfIntersection bool) {
 
 // Arc (see equivalent function on canvas type)
 func (p *Path2D) Arc(x, y, radius, startAngle, endAngle float64, anticlockwise bool) {
-	p.arc(x, y, radius, startAngle, endAngle, anticlockwise, matIdentity, true)
+	p.arc(x, y, radius, startAngle, endAngle, anticlockwise, backendbase.MatIdentity, true)
 }
 
-func (p *Path2D) arc(x, y, radius, startAngle, endAngle float64, anticlockwise bool, m mat, ident bool) {
+func (p *Path2D) arc(x, y, radius, startAngle, endAngle float64, anticlockwise bool, m backendbase.Mat, ident bool) {
 	checkSelfIntersection := len(p.p) > 0
 
 	lastWasMove := len(p.p) == 0 || p.p[len(p.p)-1].flags&pathMove != 0
 
 	if endAngle == startAngle {
 		s, c := math.Sincos(endAngle)
-		pt := vec{x + radius*c, y + radius*s}
+		pt := backendbase.Vec{x + radius*c, y + radius*s}
 		if !ident {
-			pt = pt.mulMat(m)
+			pt = pt.MulMat(m)
 		}
 		p.lineTo(pt[0], pt[1], checkSelfIntersection)
 
@@ -163,26 +165,26 @@ func (p *Path2D) arc(x, y, radius, startAngle, endAngle float64, anticlockwise b
 	if !anticlockwise {
 		for a := startAngle; a < endAngle; a += step {
 			s, c := math.Sincos(a)
-			pt := vec{x + radius*c, y + radius*s}
+			pt := backendbase.Vec{x + radius*c, y + radius*s}
 			if !ident {
-				pt = pt.mulMat(m)
+				pt = pt.MulMat(m)
 			}
 			p.lineTo(pt[0], pt[1], checkSelfIntersection)
 		}
 	} else {
 		for a := startAngle; a > endAngle; a -= step {
 			s, c := math.Sincos(a)
-			pt := vec{x + radius*c, y + radius*s}
+			pt := backendbase.Vec{x + radius*c, y + radius*s}
 			if !ident {
-				pt = pt.mulMat(m)
+				pt = pt.MulMat(m)
 			}
 			p.lineTo(pt[0], pt[1], checkSelfIntersection)
 		}
 	}
 	s, c := math.Sincos(endAngle)
-	pt := vec{x + radius*c, y + radius*s}
+	pt := backendbase.Vec{x + radius*c, y + radius*s}
 	if !ident {
-		pt = pt.mulMat(m)
+		pt = pt.MulMat(m)
 	}
 	p.lineTo(pt[0], pt[1], checkSelfIntersection)
 
@@ -193,34 +195,34 @@ func (p *Path2D) arc(x, y, radius, startAngle, endAngle float64, anticlockwise b
 
 // ArcTo (see equivalent function on canvas type)
 func (p *Path2D) ArcTo(x1, y1, x2, y2, radius float64) {
-	p.arcTo(x1, y1, x2, y2, radius, matIdentity, true)
+	p.arcTo(x1, y1, x2, y2, radius, backendbase.MatIdentity, true)
 }
 
-func (p *Path2D) arcTo(x1, y1, x2, y2, radius float64, m mat, ident bool) {
+func (p *Path2D) arcTo(x1, y1, x2, y2, radius float64, m backendbase.Mat, ident bool) {
 	if len(p.p) == 0 {
 		return
 	}
-	p0, p1, p2 := p.p[len(p.p)-1].pos, vec{x1, y1}, vec{x2, y2}
+	p0, p1, p2 := p.p[len(p.p)-1].pos, backendbase.Vec{x1, y1}, backendbase.Vec{x2, y2}
 	if !ident {
-		p0 = p0.mulMat(m.invert())
+		p0 = p0.MulMat(m.Invert())
 	}
-	v0, v1 := p0.sub(p1).norm(), p2.sub(p1).norm()
-	angle := math.Acos(v0.dot(v1))
+	v0, v1 := p0.Sub(p1).Norm(), p2.Sub(p1).Norm()
+	angle := math.Acos(v0.Dot(v1))
 	// should be in the range [0-pi]. if parallel, use a straight line
 	if angle <= 0 || angle >= math.Pi {
 		p.LineTo(x2, y2)
 		return
 	}
 	// cv0 and cv1 are vectors that point to the center of the circle
-	cv0 := vec{-v0[1], v0[0]}
-	cv1 := vec{v1[1], -v1[0]}
-	x := cv1.sub(cv0).div(v0.sub(v1))[0] * radius
+	cv0 := backendbase.Vec{-v0[1], v0[0]}
+	cv1 := backendbase.Vec{v1[1], -v1[0]}
+	x := cv1.Sub(cv0).Div(v0.Sub(v1))[0] * radius
 	if x < 0 {
-		cv0 = cv0.mulf(-1)
-		cv1 = cv1.mulf(-1)
+		cv0 = cv0.Mulf(-1)
+		cv1 = cv1.Mulf(-1)
 	}
-	center := p1.add(v0.mulf(math.Abs(x))).add(cv0.mulf(radius))
-	a0, a1 := cv0.mulf(-1).atan2(), cv1.mulf(-1).atan2()
+	center := p1.Add(v0.Mulf(math.Abs(x))).Add(cv0.Mulf(radius))
+	a0, a1 := cv0.Mulf(-1).Atan2(), cv1.Mulf(-1).Atan2()
 	if x > 0 {
 		if a1-a0 > 0 {
 			a0 += math.Pi * 2
@@ -239,17 +241,17 @@ func (p *Path2D) QuadraticCurveTo(x1, y1, x2, y2 float64) {
 		return
 	}
 	p0 := p.p[len(p.p)-1].pos
-	p1 := vec{x1, y1}
-	p2 := vec{x2, y2}
-	v0 := p1.sub(p0)
-	v1 := p2.sub(p1)
+	p1 := backendbase.Vec{x1, y1}
+	p2 := backendbase.Vec{x2, y2}
+	v0 := p1.Sub(p0)
+	v1 := p2.Sub(p1)
 
 	const step = 0.01
 
 	for r := 0.0; r < 1; r += step {
-		i0 := v0.mulf(r).add(p0)
-		i1 := v1.mulf(r).add(p1)
-		pt := i1.sub(i0).mulf(r).add(i0)
+		i0 := v0.Mulf(r).Add(p0)
+		i1 := v1.Mulf(r).Add(p1)
+		pt := i1.Sub(i0).Mulf(r).Add(i0)
 		p.LineTo(pt[0], pt[1])
 	}
 	p.LineTo(x2, y2)
@@ -261,24 +263,24 @@ func (p *Path2D) BezierCurveTo(x1, y1, x2, y2, x3, y3 float64) {
 		return
 	}
 	p0 := p.p[len(p.p)-1].pos
-	p1 := vec{x1, y1}
-	p2 := vec{x2, y2}
-	p3 := vec{x3, y3}
-	v0 := p1.sub(p0)
-	v1 := p2.sub(p1)
-	v2 := p3.sub(p2)
+	p1 := backendbase.Vec{x1, y1}
+	p2 := backendbase.Vec{x2, y2}
+	p3 := backendbase.Vec{x3, y3}
+	v0 := p1.Sub(p0)
+	v1 := p2.Sub(p1)
+	v2 := p3.Sub(p2)
 
 	const step = 0.01
 
 	for r := 0.0; r < 1; r += step {
-		i0 := v0.mulf(r).add(p0)
-		i1 := v1.mulf(r).add(p1)
-		i2 := v2.mulf(r).add(p2)
-		iv0 := i1.sub(i0)
-		iv1 := i2.sub(i1)
-		j0 := iv0.mulf(r).add(i0)
-		j1 := iv1.mulf(r).add(i1)
-		pt := j1.sub(j0).mulf(r).add(j0)
+		i0 := v0.Mulf(r).Add(p0)
+		i1 := v1.Mulf(r).Add(p1)
+		i2 := v2.Mulf(r).Add(p2)
+		iv0 := i1.Sub(i0)
+		iv1 := i2.Sub(i1)
+		j0 := iv0.Mulf(r).Add(i0)
+		j1 := iv1.Mulf(r).Add(i1)
+		pt := j1.Sub(j0).Mulf(r).Add(j0)
 		p.LineTo(pt[0], pt[1])
 	}
 	p.LineTo(x3, y3)
@@ -434,7 +436,7 @@ func (p *Path2D) IsPointInPath(x, y float64, rule pathRule) bool {
 		num := 0
 		prev := sp[len(sp)-1].pos
 		for _, pt := range sp {
-			r, dir := pointIsRightOfLine(prev, pt.pos, vec{x, y})
+			r, dir := pointIsRightOfLine(prev, pt.pos, backendbase.Vec{x, y})
 			prev = pt.pos
 			if !r {
 				continue
@@ -464,14 +466,14 @@ func (p *Path2D) IsPointInStroke(x, y float64) bool {
 	}
 
 	var triBuf [500][2]float64
-	tris := p.cv.strokeTris(p, mat{}, false, triBuf[:0])
+	tris := p.cv.strokeTris(p, backendbase.Mat{}, false, triBuf[:0])
 
-	pt := vec{x, y}
+	pt := backendbase.Vec{x, y}
 
 	for i := 0; i < len(tris); i += 3 {
-		a := vec{tris[i][0], tris[i][1]}
-		b := vec{tris[i+1][0], tris[i+1][1]}
-		c := vec{tris[i+2][0], tris[i+2][1]}
+		a := backendbase.Vec{tris[i][0], tris[i][1]}
+		b := backendbase.Vec{tris[i+1][0], tris[i+1][1]}
+		c := backendbase.Vec{tris[i+2][0], tris[i+2][1]}
 		if triangleContainsPoint(a, b, c, pt) {
 			return true
 		}
diff --git a/paths.go b/paths.go
index d9b0fb2..6a2b2a3 100644
--- a/paths.go
+++ b/paths.go
@@ -2,6 +2,8 @@ package canvas
 
 import (
 	"math"
+
+	"github.com/tfriedel6/canvas/backend/backendbase"
 )
 
 // BeginPath clears the current path and starts a new one
@@ -12,19 +14,19 @@ func (cv *Canvas) BeginPath() {
 	cv.path.p = cv.path.p[:0]
 }
 
-func isSamePoint(a, b vec, maxDist float64) bool {
+func isSamePoint(a, b backendbase.Vec, maxDist float64) bool {
 	return math.Abs(b[0]-a[0]) <= maxDist && math.Abs(b[1]-a[1]) <= maxDist
 }
 
 // MoveTo adds a gap and moves the end of the path to x/y
 func (cv *Canvas) MoveTo(x, y float64) {
-	tf := cv.tf(vec{x, y})
+	tf := cv.tf(backendbase.Vec{x, y})
 	cv.path.MoveTo(tf[0], tf[1])
 }
 
 // LineTo adds a line to the end of the path
 func (cv *Canvas) LineTo(x, y float64) {
-	tf := cv.tf(vec{x, y})
+	tf := cv.tf(backendbase.Vec{x, y})
 	cv.path.LineTo(tf[0], tf[1])
 }
 
@@ -33,7 +35,7 @@ func (cv *Canvas) LineTo(x, y float64) {
 // means that the line is added anticlockwise
 func (cv *Canvas) Arc(x, y, radius, startAngle, endAngle float64, anticlockwise bool) {
 	ax, ay := math.Sincos(startAngle)
-	startAngle2 := vec{ay, ax}.mulMat2(cv.state.transform.mat2()).atan2()
+	startAngle2 := backendbase.Vec{ay, ax}.MulMat2(cv.state.transform.Mat2()).Atan2()
 	endAngle2 := startAngle2 + (endAngle - startAngle)
 	cv.path.arc(x, y, radius, startAngle2, endAngle2, anticlockwise, cv.state.transform, false)
 }
@@ -49,17 +51,17 @@ func (cv *Canvas) ArcTo(x1, y1, x2, y2, radius float64) {
 // QuadraticCurveTo adds a quadratic curve to the path. It uses the current end
 // point of the path, x1/y1 defines the curve, and x2/y2 is the end point
 func (cv *Canvas) QuadraticCurveTo(x1, y1, x2, y2 float64) {
-	tf1 := cv.tf(vec{x1, y1})
-	tf2 := cv.tf(vec{x2, y2})
+	tf1 := cv.tf(backendbase.Vec{x1, y1})
+	tf2 := cv.tf(backendbase.Vec{x2, y2})
 	cv.path.QuadraticCurveTo(tf1[0], tf1[1], tf2[0], tf2[1])
 }
 
 // BezierCurveTo adds a bezier curve to the path. It uses the current end point
 // of the path, x1/y1 and x2/y2 define the curve, and x3/y3 is the end point
 func (cv *Canvas) BezierCurveTo(x1, y1, x2, y2, x3, y3 float64) {
-	tf1 := cv.tf(vec{x1, y1})
-	tf2 := cv.tf(vec{x2, y2})
-	tf3 := cv.tf(vec{x3, y3})
+	tf1 := cv.tf(backendbase.Vec{x1, y1})
+	tf2 := cv.tf(backendbase.Vec{x2, y2})
+	tf3 := cv.tf(backendbase.Vec{x3, y3})
 	cv.path.BezierCurveTo(tf1[0], tf1[1], tf2[0], tf2[1], tf3[0], tf3[1])
 }
 
@@ -69,9 +71,9 @@ func (cv *Canvas) BezierCurveTo(x1, y1, x2, y2, x3, y3 float64) {
 // are angles in radians, and anticlockwise means that the line is added
 // anticlockwise
 func (cv *Canvas) Ellipse(x, y, radiusX, radiusY, rotation, startAngle, endAngle float64, anticlockwise bool) {
-	tf := cv.tf(vec{x, y})
+	tf := cv.tf(backendbase.Vec{x, y})
 	ax, ay := math.Sincos(startAngle)
-	startAngle2 := vec{ay, ax}.mulMat2(cv.state.transform.mat2()).atan2()
+	startAngle2 := backendbase.Vec{ay, ax}.MulMat2(cv.state.transform.Mat2()).Atan2()
 	endAngle2 := startAngle2 + (endAngle - startAngle)
 	cv.path.Ellipse(tf[0], tf[1], radiusX, radiusY, rotation, startAngle2, endAngle2, anticlockwise)
 }
@@ -84,7 +86,7 @@ func (cv *Canvas) ClosePath() {
 
 // Stroke uses the current StrokeStyle to draw the current path
 func (cv *Canvas) Stroke() {
-	cv.strokePath(&cv.path, cv.state.transform.invert(), true)
+	cv.strokePath(&cv.path, cv.state.transform.Invert(), true)
 }
 
 // StrokePath uses the current StrokeStyle to draw the given path
@@ -94,10 +96,10 @@ func (cv *Canvas) StrokePath(path *Path2D) {
 		p: make([]pathPoint, len(path.p)),
 	}
 	copy(path2.p, path.p)
-	cv.strokePath(&path2, mat{}, false)
+	cv.strokePath(&path2, backendbase.Mat{}, false)
 }
 
-func (cv *Canvas) strokePath(path *Path2D, inv mat, doInv bool) {
+func (cv *Canvas) strokePath(path *Path2D, inv backendbase.Mat, doInv bool) {
 	if len(path.p) == 0 {
 		return
 	}
@@ -111,7 +113,7 @@ func (cv *Canvas) strokePath(path *Path2D, inv mat, doInv bool) {
 	cv.b.Fill(&stl, tris, true)
 }
 
-func (cv *Canvas) strokeTris(path *Path2D, inv mat, doInv bool, target [][2]float64) [][2]float64 {
+func (cv *Canvas) strokeTris(path *Path2D, inv backendbase.Mat, doInv bool, target [][2]float64) [][2]float64 {
 	if len(path.p) == 0 {
 		return target
 	}
@@ -126,8 +128,8 @@ func (cv *Canvas) strokeTris(path *Path2D, inv mat, doInv bool, target [][2]floa
 		}
 
 		for i, pt := range path.p {
-			pt.pos = pt.pos.mulMat(inv)
-			pt.next = pt.next.mulMat(inv)
+			pt.pos = pt.pos.MulMat(inv)
+			pt.next = pt.next.MulMat(inv)
 			pcopy.p[i] = pt
 		}
 		path = &pcopy
@@ -136,7 +138,7 @@ func (cv *Canvas) strokeTris(path *Path2D, inv mat, doInv bool, target [][2]floa
 	dashedPath := cv.applyLineDash(path.p)
 
 	start := true
-	var p0 vec
+	var p0 backendbase.Vec
 	for _, p := range dashedPath {
 		if p.flags&pathMove != 0 {
 			p0 = p.pos
@@ -145,22 +147,22 @@ func (cv *Canvas) strokeTris(path *Path2D, inv mat, doInv bool, target [][2]floa
 		}
 		p1 := p.pos
 
-		v0 := p1.sub(p0).norm()
-		v1 := vec{v0[1], -v0[0]}.mulf(cv.state.lineWidth * 0.5)
-		v0 = v0.mulf(cv.state.lineWidth * 0.5)
+		v0 := p1.Sub(p0).Norm()
+		v1 := backendbase.Vec{v0[1], -v0[0]}.Mulf(cv.state.lineWidth * 0.5)
+		v0 = v0.Mulf(cv.state.lineWidth * 0.5)
 
-		lp0 := p0.add(v1)
-		lp1 := p1.add(v1)
-		lp2 := p0.sub(v1)
-		lp3 := p1.sub(v1)
+		lp0 := p0.Add(v1)
+		lp1 := p1.Add(v1)
+		lp2 := p0.Sub(v1)
+		lp3 := p1.Sub(v1)
 
 		if start {
 			switch cv.state.lineCap {
 			case Butt:
 				// no need to do anything
 			case Square:
-				lp0 = lp0.sub(v0)
-				lp2 = lp2.sub(v0)
+				lp0 = lp0.Sub(v0)
+				lp2 = lp2.Sub(v0)
 			case Round:
 				target = cv.addCircleTris(p0, cv.state.lineWidth*0.5, target)
 			}
@@ -171,8 +173,8 @@ func (cv *Canvas) strokeTris(path *Path2D, inv mat, doInv bool, target [][2]floa
 			case Butt:
 				// no need to do anything
 			case Square:
-				lp1 = lp1.add(v0)
-				lp3 = lp3.add(v0)
+				lp1 = lp1.Add(v0)
+				lp3 = lp3.Add(v0)
 			case Round:
 				target = cv.addCircleTris(p1, cv.state.lineWidth*0.5, target)
 			}
@@ -209,8 +211,8 @@ func (cv *Canvas) applyLineDash(path []pathPoint) []pathPoint {
 			continue
 		}
 
-		v := pp.pos.sub(lp.pos)
-		vl := v.len()
+		v := pp.pos.Sub(lp.pos)
+		vl := v.Len()
 		prev := ldo
 		for vl > 0 {
 			draw := ldp%2 == 0
@@ -220,7 +222,7 @@ func (cv *Canvas) applyLineDash(path []pathPoint) []pathPoint {
 				ldo = 0
 				dl := cv.state.lineDash[ldp] - prev
 				dist := dl / vl
-				newp.pos = lp.pos.add(v.mulf(dist))
+				newp.pos = lp.pos.Add(v.Mulf(dist))
 				vl -= dl
 				ldp++
 				ldp %= len(cv.state.lineDash)
@@ -239,7 +241,7 @@ func (cv *Canvas) applyLineDash(path []pathPoint) []pathPoint {
 			}
 
 			lp = newp
-			v = pp.pos.sub(lp.pos)
+			v = pp.pos.Sub(lp.pos)
 		}
 		lp = pp
 	}
@@ -247,50 +249,50 @@ func (cv *Canvas) applyLineDash(path []pathPoint) []pathPoint {
 	return path2
 }
 
-func (cv *Canvas) lineJoint(p0, p1, p2, l0p0, l0p1, l0p2, l0p3 vec, tris [][2]float64) [][2]float64 {
-	v2 := p1.sub(p2).norm()
-	v3 := vec{v2[1], -v2[0]}.mulf(cv.state.lineWidth * 0.5)
+func (cv *Canvas) lineJoint(p0, p1, p2, l0p0, l0p1, l0p2, l0p3 backendbase.Vec, tris [][2]float64) [][2]float64 {
+	v2 := p1.Sub(p2).Norm()
+	v3 := backendbase.Vec{v2[1], -v2[0]}.Mulf(cv.state.lineWidth * 0.5)
 
 	switch cv.state.lineJoin {
 	case Miter:
-		l1p0 := p2.sub(v3)
-		l1p1 := p1.sub(v3)
-		l1p2 := p2.add(v3)
-		l1p3 := p1.add(v3)
+		l1p0 := p2.Sub(v3)
+		l1p1 := p1.Sub(v3)
+		l1p2 := p2.Add(v3)
+		l1p3 := p1.Add(v3)
 
-		var ip0, ip1 vec
-		if l0p1.sub(l1p1).lenSqr() < 0.000000001 {
-			ip0 = l0p1.sub(l1p1).mulf(0.5).add(l1p1)
+		var ip0, ip1 backendbase.Vec
+		if l0p1.Sub(l1p1).LenSqr() < 0.000000001 {
+			ip0 = l0p1.Sub(l1p1).Mulf(0.5).Add(l1p1)
 		} else {
 			var q float64
 			ip0, _, q = lineIntersection(l0p0, l0p1, l1p1, l1p0)
 			if q >= 1 {
-				ip0 = l0p1.add(l1p1).mulf(0.5)
+				ip0 = l0p1.Add(l1p1).Mulf(0.5)
 			}
 		}
 
-		if dist := ip0.sub(l0p1).lenSqr(); dist > cv.state.miterLimitSqr {
-			l1p1 := p1.sub(v3)
-			l1p3 := p1.add(v3)
+		if dist := ip0.Sub(l0p1).LenSqr(); dist > cv.state.miterLimitSqr {
+			l1p1 := p1.Sub(v3)
+			l1p3 := p1.Add(v3)
 
 			tris = append(tris, cv.tf(p1), cv.tf(l0p1), cv.tf(l1p1),
 				cv.tf(p1), cv.tf(l1p3), cv.tf(l0p3))
 			return tris
 		}
 
-		if l0p3.sub(l1p3).lenSqr() < 0.000000001 {
-			ip1 = l0p3.sub(l1p3).mulf(0.5).add(l1p3)
+		if l0p3.Sub(l1p3).LenSqr() < 0.000000001 {
+			ip1 = l0p3.Sub(l1p3).Mulf(0.5).Add(l1p3)
 		} else {
 			var q float64
 			ip1, _, q = lineIntersection(l0p2, l0p3, l1p3, l1p2)
 			if q >= 1 {
-				ip1 = l0p3.add(l1p3).mulf(0.5)
+				ip1 = l0p3.Add(l1p3).Mulf(0.5)
 			}
 		}
 
-		if dist := ip1.sub(l1p1).lenSqr(); dist > cv.state.miterLimitSqr {
-			l1p1 := p1.sub(v3)
-			l1p3 := p1.add(v3)
+		if dist := ip1.Sub(l1p1).LenSqr(); dist > cv.state.miterLimitSqr {
+			l1p1 := p1.Sub(v3)
+			l1p3 := p1.Add(v3)
 
 			tris = append(tris, cv.tf(p1), cv.tf(l0p1), cv.tf(l1p1),
 				cv.tf(p1), cv.tf(l1p3), cv.tf(l0p3))
@@ -302,8 +304,8 @@ func (cv *Canvas) lineJoint(p0, p1, p2, l0p0, l0p1, l0p2, l0p3 vec, tris [][2]fl
 			cv.tf(p1), cv.tf(l1p3), cv.tf(ip1),
 			cv.tf(p1), cv.tf(ip1), cv.tf(l0p3))
 	case Bevel:
-		l1p1 := p1.sub(v3)
-		l1p3 := p1.add(v3)
+		l1p1 := p1.Sub(v3)
+		l1p3 := p1.Add(v3)
 
 		tris = append(tris, cv.tf(p1), cv.tf(l0p1), cv.tf(l1p1),
 			cv.tf(p1), cv.tf(l1p3), cv.tf(l0p3))
@@ -314,7 +316,7 @@ func (cv *Canvas) lineJoint(p0, p1, p2, l0p0, l0p1, l0p2, l0p3 vec, tris [][2]fl
 	return tris
 }
 
-func (cv *Canvas) addCircleTris(center vec, radius float64, tris [][2]float64) [][2]float64 {
+func (cv *Canvas) addCircleTris(center backendbase.Vec, radius float64, tris [][2]float64) [][2]float64 {
 	step := 6 / radius
 	if step > 0.8 {
 		step = 0.8
@@ -322,26 +324,26 @@ func (cv *Canvas) addCircleTris(center vec, radius float64, tris [][2]float64) [
 		step = 0.05
 	}
 	centertf := cv.tf(center)
-	p0 := cv.tf(vec{center[0], center[1] + radius})
+	p0 := cv.tf(backendbase.Vec{center[0], center[1] + radius})
 	for angle := step; angle <= math.Pi*2+step; angle += step {
 		s, c := math.Sincos(angle)
-		p1 := cv.tf(vec{center[0] + s*radius, center[1] + c*radius})
+		p1 := cv.tf(backendbase.Vec{center[0] + s*radius, center[1] + c*radius})
 		tris = append(tris, centertf, p0, p1)
 		p0 = p1
 	}
 	return tris
 }
 
-func lineIntersection(a0, a1, b0, b1 vec) (vec, float64, float64) {
-	va := a1.sub(a0)
-	vb := b1.sub(b0)
+func lineIntersection(a0, a1, b0, b1 backendbase.Vec) (backendbase.Vec, float64, float64) {
+	va := a1.Sub(a0)
+	vb := b1.Sub(b0)
 
 	if (va[0] == 0 && vb[0] == 0) || (va[1] == 0 && vb[1] == 0) || (va[0] == 0 && va[1] == 0) || (vb[0] == 0 && vb[1] == 0) {
-		return vec{}, float64(math.Inf(1)), float64(math.Inf(1))
+		return backendbase.Vec{}, float64(math.Inf(1)), float64(math.Inf(1))
 	}
 	d := va[1]*vb[0] - va[0]*vb[1]
 	if d == 0 {
-		return vec{}, float64(math.Inf(1)), float64(math.Inf(1))
+		return backendbase.Vec{}, float64(math.Inf(1)), float64(math.Inf(1))
 	}
 	p := (vb[1]*(a0[0]-b0[0]) - a0[1]*vb[0] + b0[1]*vb[0]) / d
 	var q float64
@@ -351,21 +353,21 @@ func lineIntersection(a0, a1, b0, b1 vec) (vec, float64, float64) {
 		q = (a0[0] + p*va[0] - b0[0]) / vb[0]
 	}
 
-	return a0.add(va.mulf(p)), p, q
+	return a0.Add(va.Mulf(p)), p, q
 }
 
-func linePointDistSqr(a, b, p vec) float64 {
-	v := b.sub(a)
-	vl := v.len()
-	vn := v.divf(vl)
-	d := p.sub(a).dot(vn)
-	c := a.add(vn.mulf(d))
-	return p.sub(c).lenSqr()
+func linePointDistSqr(a, b, p backendbase.Vec) float64 {
+	v := b.Sub(a)
+	vl := v.Len()
+	vn := v.Divf(vl)
+	d := p.Sub(a).Dot(vn)
+	c := a.Add(vn.Mulf(d))
+	return p.Sub(c).LenSqr()
 }
 
 // Fill fills the current path with the current FillStyle
 func (cv *Canvas) Fill() {
-	cv.fillPath(&cv.path, matIdentity)
+	cv.fillPath(&cv.path, backendbase.MatIdentity)
 }
 
 // FillPath fills the given path with the current FillStyle
@@ -374,7 +376,7 @@ func (cv *Canvas) FillPath(path *Path2D) {
 }
 
 // FillPath fills the given path with the current FillStyle
-func (cv *Canvas) fillPath(path *Path2D, tf mat) {
+func (cv *Canvas) fillPath(path *Path2D, tf backendbase.Mat) {
 	if len(path.p) < 3 {
 		return
 	}
@@ -396,16 +398,16 @@ func (cv *Canvas) fillPath(path *Path2D, tf mat) {
 	cv.b.Fill(&stl, tris, false)
 }
 
-func appendSubPathTriangles(tris [][2]float64, mat mat, path []pathPoint) [][2]float64 {
+func appendSubPathTriangles(tris [][2]float64, mat backendbase.Mat, path []pathPoint) [][2]float64 {
 	last := path[len(path)-1]
 	if last.flags&pathIsConvex != 0 {
-		p0, p1 := path[0].pos.mulMat(mat), path[1].pos.mulMat(mat)
+		p0, p1 := path[0].pos.MulMat(mat), path[1].pos.MulMat(mat)
 		lastIdx := len(path)
 		if path[0].pos == path[lastIdx-1].pos {
 			lastIdx--
 		}
 		for i := 2; i < lastIdx; i++ {
-			p2 := path[i].pos.mulMat(mat)
+			p2 := path[i].pos.MulMat(mat)
 			tris = append(tris, p0, p1, p2)
 			p1 = p2
 		}
@@ -423,10 +425,10 @@ func appendSubPathTriangles(tris [][2]float64, mat mat, path []pathPoint) [][2]f
 // Clip uses the current path to clip any further drawing. Use Save/Restore to
 // remove the clipping again
 func (cv *Canvas) Clip() {
-	cv.clip(&cv.path, matIdentity)
+	cv.clip(&cv.path, backendbase.MatIdentity)
 }
 
-func (cv *Canvas) clip(path *Path2D, tf mat) {
+func (cv *Canvas) clip(path *Path2D, tf backendbase.Mat) {
 	if len(path.p) < 3 {
 		return
 	}
@@ -476,10 +478,10 @@ func (cv *Canvas) Rect(x, y, w, h float64) {
 
 // StrokeRect draws a rectangle using the current stroke style
 func (cv *Canvas) StrokeRect(x, y, w, h float64) {
-	v0 := vec{x, y}
-	v1 := vec{x + w, y}
-	v2 := vec{x + w, y + h}
-	v3 := vec{x, y + h}
+	v0 := backendbase.Vec{x, y}
+	v1 := backendbase.Vec{x + w, y}
+	v2 := backendbase.Vec{x + w, y + h}
+	v3 := backendbase.Vec{x, y + h}
 	var p [5]pathPoint
 	p[0] = pathPoint{pos: v0, flags: pathMove | pathAttach, next: v1}
 	p[1] = pathPoint{pos: v1, next: v2, flags: pathAttach}
@@ -487,15 +489,15 @@ func (cv *Canvas) StrokeRect(x, y, w, h float64) {
 	p[3] = pathPoint{pos: v3, next: v0, flags: pathAttach}
 	p[4] = pathPoint{pos: v0, next: v1, flags: pathAttach}
 	path := Path2D{p: p[:]}
-	cv.strokePath(&path, mat{}, false)
+	cv.strokePath(&path, backendbase.Mat{}, false)
 }
 
 // FillRect fills a rectangle with the active fill style
 func (cv *Canvas) FillRect(x, y, w, h float64) {
-	p0 := cv.tf(vec{x, y})
-	p1 := cv.tf(vec{x, y + h})
-	p2 := cv.tf(vec{x + w, y + h})
-	p3 := cv.tf(vec{x + w, y})
+	p0 := cv.tf(backendbase.Vec{x, y})
+	p1 := cv.tf(backendbase.Vec{x, y + h})
+	p2 := cv.tf(backendbase.Vec{x + w, y + h})
+	p3 := cv.tf(backendbase.Vec{x + w, y})
 
 	data := [4][2]float64{{p0[0], p0[1]}, {p1[0], p1[1]}, {p2[0], p2[1]}, {p3[0], p3[1]}}
 
@@ -507,10 +509,10 @@ func (cv *Canvas) FillRect(x, y, w, h float64) {
 
 // ClearRect sets the color of the rectangle to transparent black
 func (cv *Canvas) ClearRect(x, y, w, h float64) {
-	p0 := cv.tf(vec{x, y})
-	p1 := cv.tf(vec{x, y + h})
-	p2 := cv.tf(vec{x + w, y + h})
-	p3 := cv.tf(vec{x + w, y})
+	p0 := cv.tf(backendbase.Vec{x, y})
+	p1 := cv.tf(backendbase.Vec{x, y + h})
+	p2 := cv.tf(backendbase.Vec{x + w, y + h})
+	p3 := cv.tf(backendbase.Vec{x + w, y})
 	data := [4][2]float64{{p0[0], p0[1]}, {p1[0], p1[1]}, {p2[0], p2[1]}, {p3[0], p3[1]}}
 
 	cv.b.Clear(data)
diff --git a/text.go b/text.go
index fb92102..0e8649e 100644
--- a/text.go
+++ b/text.go
@@ -12,6 +12,7 @@ import (
 
 	"github.com/golang/freetype"
 	"github.com/golang/freetype/truetype"
+	"github.com/tfriedel6/canvas/backend/backendbase"
 	"golang.org/x/image/font"
 	"golang.org/x/image/math/fixed"
 )
@@ -117,8 +118,8 @@ func (cv *Canvas) FillText(str string, x, y float64) {
 		return
 	}
 
-	scaleX := vec{cv.state.transform[0], cv.state.transform[1]}.len()
-	scaleY := vec{cv.state.transform[2], cv.state.transform[3]}.len()
+	scaleX := backendbase.Vec{cv.state.transform[0], cv.state.transform[1]}.Len()
+	scaleY := backendbase.Vec{cv.state.transform[2], cv.state.transform[3]}.Len()
 	scale := (scaleX + scaleY) * 0.5
 	fontSize := fixed.Int26_6(math.Round(float64(cv.state.fontSize) * scale))
 
@@ -213,10 +214,10 @@ func (cv *Canvas) FillText(str string, x, y float64) {
 		w, h := cv.b.Size()
 		fw, fh := float64(w), float64(h)
 
-		p0 := cv.tf(vec{float64(bounds.Min.X)/scale + curX, float64(bounds.Min.Y)/scale + y})
-		p1 := cv.tf(vec{float64(bounds.Min.X)/scale + curX, float64(bounds.Max.Y)/scale + y})
-		p2 := cv.tf(vec{float64(bounds.Max.X)/scale + curX, float64(bounds.Max.Y)/scale + y})
-		p3 := cv.tf(vec{float64(bounds.Max.X)/scale + curX, float64(bounds.Min.Y)/scale + y})
+		p0 := cv.tf(backendbase.Vec{float64(bounds.Min.X)/scale + curX, float64(bounds.Min.Y)/scale + y})
+		p1 := cv.tf(backendbase.Vec{float64(bounds.Min.X)/scale + curX, float64(bounds.Max.Y)/scale + y})
+		p2 := cv.tf(backendbase.Vec{float64(bounds.Max.X)/scale + curX, float64(bounds.Max.Y)/scale + y})
+		p3 := cv.tf(backendbase.Vec{float64(bounds.Max.X)/scale + curX, float64(bounds.Min.Y)/scale + y})
 		inside := (p0[0] >= 0 || p1[0] >= 0 || p2[0] >= 0 || p3[0] >= 0) &&
 			(p0[1] >= 0 || p1[1] >= 0 || p2[1] >= 0 || p3[1] >= 0) &&
 			(p0[0] < fw || p1[0] < fw || p2[0] < fw || p3[0] < fw) &&
@@ -299,10 +300,10 @@ func (cv *Canvas) FillText(str string, x, y float64) {
 
 	// render textImage to the screen
 	var pts [4][2]float64
-	pts[0] = cv.tf(vec{float64(textOffset.X)/scale + x, float64(textOffset.Y)/scale + y})
-	pts[1] = cv.tf(vec{float64(textOffset.X)/scale + x, float64(textOffset.Y)/scale + fstrHeight + y})
-	pts[2] = cv.tf(vec{float64(textOffset.X)/scale + fstrWidth + x, float64(textOffset.Y)/scale + fstrHeight + y})
-	pts[3] = cv.tf(vec{float64(textOffset.X)/scale + fstrWidth + x, float64(textOffset.Y)/scale + y})
+	pts[0] = cv.tf(backendbase.Vec{float64(textOffset.X)/scale + x, float64(textOffset.Y)/scale + y})
+	pts[1] = cv.tf(backendbase.Vec{float64(textOffset.X)/scale + x, float64(textOffset.Y)/scale + fstrHeight + y})
+	pts[2] = cv.tf(backendbase.Vec{float64(textOffset.X)/scale + fstrWidth + x, float64(textOffset.Y)/scale + fstrHeight + y})
+	pts[3] = cv.tf(backendbase.Vec{float64(textOffset.X)/scale + fstrWidth + x, float64(textOffset.Y)/scale + y})
 
 	mask := textImage.SubImage(image.Rect(0, 0, strWidth, strHeight)).(*image.Alpha)
 
@@ -345,7 +346,7 @@ func (cv *Canvas) StrokeText(str string, x, y float64) {
 			continue
 		}
 
-		cv.runePath(rn, vec{x, y})
+		cv.runePath(rn, backendbase.Vec{x, y})
 
 		x += float64(advance) / 64
 	}
@@ -354,7 +355,7 @@ func (cv *Canvas) StrokeText(str string, x, y float64) {
 	cv.path = prevPath
 }
 
-func (cv *Canvas) runePath(rn rune, pos vec) {
+func (cv *Canvas) runePath(rn rune, pos backendbase.Vec) {
 	gb := &truetype.GlyphBuf{}
 	gb.Load(cv.state.font.font, cv.state.fontSize, cv.state.font.font.Index(rn), font.HintingNone)
 
diff --git a/triangulation.go b/triangulation.go
index 40e8ae3..23ee512 100644
--- a/triangulation.go
+++ b/triangulation.go
@@ -3,11 +3,13 @@ package canvas
 import (
 	"math"
 	"sort"
+
+	"github.com/tfriedel6/canvas/backend/backendbase"
 )
 
 const samePointTolerance = 1e-20
 
-func pointIsRightOfLine(a, b, p vec) (bool, bool) {
+func pointIsRightOfLine(a, b, p backendbase.Vec) (bool, bool) {
 	if a[1] == b[1] {
 		return false, false
 	}
@@ -19,13 +21,13 @@ func pointIsRightOfLine(a, b, p vec) (bool, bool) {
 	if p[1] < a[1] || p[1] >= b[1] {
 		return false, false
 	}
-	v := b.sub(a)
+	v := b.Sub(a)
 	r := (p[1] - a[1]) / v[1]
 	x := a[0] + r*v[0]
 	return p[0] > x, dir
 }
 
-func triangleContainsPoint(a, b, c, p vec) bool {
+func triangleContainsPoint(a, b, c, p backendbase.Vec) bool {
 	// if point is outside triangle bounds, return false
 	if p[0] < a[0] && p[0] < b[0] && p[0] < c[0] {
 		return false
@@ -56,12 +58,12 @@ func triangleContainsPoint(a, b, c, p vec) bool {
 
 const parallelTolerance = 1e-10
 
-func parallel(a1, b1, a2, b2 vec) bool {
-	ang := b1.sub(a1).angleTo(b2.sub(a2))
+func parallel(a1, b1, a2, b2 backendbase.Vec) bool {
+	ang := b1.Sub(a1).AngleTo(b2.Sub(a2))
 	return math.Abs(ang) < parallelTolerance || math.Abs(ang-math.Pi) < parallelTolerance
 }
 
-func polygonContainsLine(polygon []vec, ia, ib int, a, b vec) bool {
+func polygonContainsLine(polygon []backendbase.Vec, ia, ib int, a, b backendbase.Vec) bool {
 	for i := range polygon {
 		if i == ia || i == ib {
 			continue
@@ -80,7 +82,7 @@ func polygonContainsLine(polygon []vec, ia, ib int, a, b vec) bool {
 
 const onLineToleranceSqr = 1e-20
 
-func polygonContainsPoint(polygon []vec, p vec) bool {
+func polygonContainsPoint(polygon []backendbase.Vec, p backendbase.Vec) bool {
 	a := polygon[len(polygon)-1]
 	count := 0
 	for _, b := range polygon {
@@ -95,15 +97,15 @@ func polygonContainsPoint(polygon []vec, p vec) bool {
 	return count%2 == 1
 }
 
-func triangulatePath(path []pathPoint, mat mat, target [][2]float64) [][2]float64 {
+func triangulatePath(path []pathPoint, mat backendbase.Mat, target [][2]float64) [][2]float64 {
 	if path[0].pos == path[len(path)-1].pos {
 		path = path[:len(path)-1]
 	}
 
-	var buf [500]vec
+	var buf [500]backendbase.Vec
 	polygon := buf[:0]
 	for _, p := range path {
-		polygon = append(polygon, p.pos.mulMat(mat))
+		polygon = append(polygon, p.pos.MulMat(mat))
 	}
 
 	for len(polygon) > 3 {
@@ -117,7 +119,7 @@ func triangulatePath(path []pathPoint, mat mat, target [][2]float64) [][2]float6
 			if isSamePoint(a, c, math.SmallestNonzeroFloat64) {
 				break
 			}
-			if len(polygon) > 3 && !polygonContainsPoint(polygon, a.add(c).divf(2)) {
+			if len(polygon) > 3 && !polygonContainsPoint(polygon, a.Add(c).Divf(2)) {
 				continue
 			}
 			if !polygonContainsLine(polygon, i, ic, a, c) {
@@ -156,7 +158,7 @@ type tessNet struct {
 }
 
 type tessVert struct {
-	pos      vec
+	pos      backendbase.Vec
 	attached []int
 	count    int
 }
@@ -183,7 +185,7 @@ func cutIntersections(path []pathPoint) tessNet {
 	type cut struct {
 		from, to int
 		ratio    float64
-		point    vec
+		point    backendbase.Vec
 	}
 
 	var cutBuf [50]cut
@@ -296,8 +298,8 @@ func cutIntersections(path []pathPoint) tessNet {
 func setPathLeftRightInside(net *tessNet) {
 	for i, e1 := range net.edges {
 		a1, b1 := net.verts[e1.a], net.verts[e1.b]
-		diff := b1.pos.sub(a1.pos)
-		mid := a1.pos.add(diff.mulf(0.5))
+		diff := b1.pos.Sub(a1.pos)
+		mid := a1.pos.Add(diff.Mulf(0.5))
 
 		left, right := 0, 0
 		if math.Abs(diff[1]) > math.Abs(diff[0]) {
@@ -315,7 +317,7 @@ func setPathLeftRightInside(net *tessNet) {
 				if mid[1] < a2[1] || mid[1] > b2[1] {
 					continue
 				}
-				v := b2.sub(a2)
+				v := b2.Sub(a2)
 				r := (mid[1] - a2[1]) / v[1]
 				x := a2[0] + r*v[0]
 				if mid[0] > x {
@@ -342,7 +344,7 @@ func setPathLeftRightInside(net *tessNet) {
 				if mid[0] < a2[0] || mid[0] > b2[0] {
 					continue
 				}
-				v := b2.sub(a2)
+				v := b2.Sub(a2)
 				r := (mid[0] - a2[0]) / v[0]
 				y := a2[1] + r*v[1]
 				if mid[1] > y {
@@ -404,7 +406,7 @@ func selfIntersectingPathParts(p []pathPoint, partFn func(sp []pathPoint) bool)
 			for limit := 0; limit < len(net.edges); limit++ {
 				ecur := net.edges[from]
 				acur, bcur := net.verts[ecur.a], net.verts[ecur.b]
-				dir := bcur.pos.sub(acur.pos)
+				dir := bcur.pos.Sub(acur.pos)
 				dirAngle := math.Atan2(dir[1], dir[0])
 				minAngleDiff := math.Pi * 2
 				var next, nextEdge int
@@ -421,7 +423,7 @@ func selfIntersectingPathParts(p []pathPoint, partFn func(sp []pathPoint) bool)
 					if e.b == cur {
 						na, nb = nb, na
 					}
-					ndir := nb.pos.sub(na.pos)
+					ndir := nb.pos.Sub(na.pos)
 					nextAngle := math.Atan2(ndir[1], ndir[0]) + math.Pi
 					if nextAngle < dirAngle {
 						nextAngle += math.Pi * 2