diff --git a/geom.go b/geom.go
index f199c59ce..9a5fd3ec5 100644
--- a/geom.go
+++ b/geom.go
@@ -61,6 +61,10 @@ func (g *GeoM) apply32(x, y float32) (x2, y2 float32) {
 	return (g.a_1+1)*x + g.b*y + g.tx, g.c*x + (g.d_1+1)*y + g.ty
 }
 
+func (g *GeoM) elements() (a, b, c, d, tx, ty float32) {
+	return g.a_1 + 1, g.b, g.c, g.d_1 + 1, g.tx, g.ty
+}
+
 // Element returns a value of a matrix at (i, j).
 func (g *GeoM) Element(i, j int) float64 {
 	switch {
@@ -136,6 +140,10 @@ func (g *GeoM) Translate(tx, ty float64) {
 // Rotate rotates the matrix by theta.
 // The unit is radian.
 func (g *GeoM) Rotate(theta float64) {
+	if theta == 0 {
+		return
+	}
+
 	sin64, cos64 := math.Sincos(theta)
 	sin, cos := float32(sin64), float32(cos64)
 
diff --git a/image.go b/image.go
index 5b3df3e2d..8da0e5245 100644
--- a/image.go
+++ b/image.go
@@ -130,8 +130,8 @@ type geoM32 struct {
 	inner *GeoM
 }
 
-func (g geoM32) Apply(x, y float32) (x2, y2 float32) {
-	return g.inner.apply32(x, y)
+func (g geoM32) Elements() (a, b, c, d, tx, ty float32) {
+	return g.inner.elements()
 }
 
 // DrawImage draws the given image on the image i.
diff --git a/internal/graphicsutil/vertices.go b/internal/graphicsutil/vertices.go
index ac14ee157..1505905ce 100644
--- a/internal/graphicsutil/vertices.go
+++ b/internal/graphicsutil/vertices.go
@@ -44,7 +44,7 @@ func (v *verticesBackend) sliceForOneQuad() []float32 {
 }
 
 type GeoM interface {
-	Apply(x, y float32) (x2, y2 float32)
+	Elements() (a, b, c, d, tx, ty float32)
 }
 
 func QuadVertices(width, height int, sx0, sy0, sx1, sy1 int, geom GeoM) []float32 {
@@ -55,9 +55,6 @@ func QuadVertices(width, height int, sx0, sy0, sx1, sy1 int, geom GeoM) []float3
 		return nil
 	}
 
-	x0, y0 := float32(0.0), float32(0.0)
-	x1, y1 := float32(sx1-sx0), float32(sy1-sy0)
-
 	// it really feels like we should be able to cache this computation
 	// but it may not matter.
 	w := 1
@@ -71,16 +68,16 @@ func QuadVertices(width, height int, sx0, sy0, sx1, sy1 int, geom GeoM) []float3
 	wf := float32(w)
 	hf := float32(h)
 	u0, v0, u1, v1 := float32(sx0)/wf, float32(sy0)/hf, float32(sx1)/wf, float32(sy1)/hf
-	return quadVerticesImpl(u0, v0, u1, v1, x0, y0, x1, y1, geom)
+	return quadVerticesImpl(float32(sx1-sx0), float32(sy1-sy0), u0, v0, u1, v1, geom)
 }
 
-func quadVerticesImpl(u0, v0, u1, v1, x0, y0, x1, y1 float32, geom GeoM) []float32 {
+func quadVerticesImpl(x, y, u0, v0, u1, v1 float32, geom GeoM) []float32 {
 	vs := theVerticesBackend.sliceForOneQuad()
 
-	x, y := geom.Apply(x0, y0)
+	a, b, c, d, tx, ty := geom.Elements()
 	// Vertex coordinates
-	vs[0] = x
-	vs[1] = y
+	vs[0] = tx
+	vs[1] = ty
 
 	// Texture coordinates: first 2 values indicates the actual coodinate, and
 	// the second indicates diagonally opposite coodinates.
@@ -91,25 +88,22 @@ func quadVerticesImpl(u0, v0, u1, v1, x0, y0, x1, y1 float32, geom GeoM) []float
 	vs[5] = v1
 
 	// and the same for the other three coordinates
-	x, y = geom.Apply(x1, y0)
-	vs[6] = x
-	vs[7] = y
+	vs[6] = a*x + tx
+	vs[7] = c*x + ty
 	vs[8] = u1
 	vs[9] = v0
 	vs[10] = u0
 	vs[11] = v1
 
-	x, y = geom.Apply(x0, y1)
-	vs[12] = x
-	vs[13] = y
+	vs[12] = b*y + tx
+	vs[13] = d*y + ty
 	vs[14] = u0
 	vs[15] = v1
 	vs[16] = u1
 	vs[17] = v0
 
-	x, y = geom.Apply(x1, y1)
-	vs[18] = x
-	vs[19] = y
+	vs[18] = a*x + b*y + tx
+	vs[19] = c*x + d*y + ty
 	vs[20] = u1
 	vs[21] = v1
 	vs[22] = u0
diff --git a/internal/restorable/image.go b/internal/restorable/image.go
index 762b40cdc..7f045e7bb 100644
--- a/internal/restorable/image.go
+++ b/internal/restorable/image.go
@@ -129,8 +129,8 @@ type geoM struct {
 	ty     float32
 }
 
-func (g *geoM) Apply(x, y float32) (float32, float32) {
-	return x*g.scaleX + g.tx, y*g.scaleY + g.ty
+func (g *geoM) Elements() (a, b, c, d, tx, ty float32) {
+	return g.scaleX, 0, 0, g.scaleY, g.tx, g.ty
 }
 
 // ReplacePixels replaces the image pixels with the given pixels slice.
diff --git a/internal/restorable/images_test.go b/internal/restorable/images_test.go
index cdd037a32..da0a774c7 100644
--- a/internal/restorable/images_test.go
+++ b/internal/restorable/images_test.go
@@ -107,8 +107,8 @@ var (
 
 type idGeoM struct{}
 
-func (idGeoM) Apply(x, y float32) (x2, y2 float32) {
-	return x, y
+func (idGeoM) Elements() (a, b, c, d, tx, ty float32) {
+	return 1, 0, 0, 1, 0, 0
 }
 
 func TestRestoreChain(t *testing.T) {
@@ -267,8 +267,8 @@ type geoM struct {
 	ty float32
 }
 
-func (g *geoM) Apply(x, y float32) (x2, y2 float32) {
-	return x + g.tx, y + g.ty
+func (g *geoM) Elements() (a, b, c, d, tx, ty float32) {
+	return 1, 0, 0, 1, g.tx, g.ty
 }
 
 func TestRestoreComplexGraph(t *testing.T) {
diff --git a/internal/shareable/shareable.go b/internal/shareable/shareable.go
index fd83b1947..dd7200c73 100644
--- a/internal/shareable/shareable.go
+++ b/internal/shareable/shareable.go
@@ -100,8 +100,8 @@ type Image struct {
 
 type idGeoM struct{}
 
-func (idGeoM) Apply(x, y float32) (x2, y2 float32) {
-	return x, y
+func (idGeoM) Elements() (a, b, c, d, tx, ty float32) {
+	return 1, 0, 0, 1, 0, 0
 }
 
 func (i *Image) ensureNotShared() {
diff --git a/internal/shareable/shareable_test.go b/internal/shareable/shareable_test.go
index b2a929959..fff536142 100644
--- a/internal/shareable/shareable_test.go
+++ b/internal/shareable/shareable_test.go
@@ -50,8 +50,8 @@ type geoM struct {
 	ty float32
 }
 
-func (g *geoM) Apply(x, y float32) (x2, y2 float32) {
-	return x + g.tx, y + g.ty
+func (g *geoM) Elements() (a, b, c, d, tx, ty float32) {
+	return 1, 0, 0, 1, g.tx, g.ty
 }
 
 func TestEnsureNotShared(t *testing.T) {