diff --git a/geometry.go b/geometry.go
index f9348398a5e580db38b180683cea2fb708829623..928c9c5f089573b17da46d2757704845654f0496 100644
--- a/geometry.go
+++ b/geometry.go
@@ -3,8 +3,6 @@ package pixel
import (
"fmt"
"math"
-
- "github.com/go-gl/mathgl/mgl64"
)
// Vec is a 2D vector type with X and Y coordinates.
@@ -251,7 +249,7 @@ func (r Rect) Union(s Rect) Rect {
)
}
-// Matrix is a 3x3 transformation matrix that can be used for all kinds of spacial transforms, such
+// Matrix is a 3x2 affine matrix that can be used for all kinds of spatial transforms, such
// as movement, scaling and rotations.
//
// Matrix has a handful of useful methods, each of which adds a transformation to the matrix. For
@@ -261,38 +259,41 @@ func (r Rect) Union(s Rect) Rect {
//
// This code creates a Matrix that first moves everything by 100 units horizontally and 200 units
// vertically and then rotates everything by 90 degrees around the origin.
-type Matrix [9]float64
+//
+// Layout is:
+// [0] [2] [4]
+// [1] [3] [5]
+// 0 0 1 [implicit row]
+type Matrix [6]float64
// IM stands for identity matrix. Does nothing, no transformation.
-var IM = Matrix(mgl64.Ident3())
+var IM = Matrix{1, 0, 0, 1, 0, 0}
// String returns a string representation of the Matrix.
//
// m := pixel.IM
-// fmt.Println(m) // Matrix(1 0 0 | 0 1 0 | 0 0 1)
+// fmt.Println(m) // Matrix(1 0 0 | 0 1 0)
func (m Matrix) String() string {
return fmt.Sprintf(
- "Matrix(%v %v %v | %v %v %v | %v %v %v)",
- m[0], m[3], m[6],
- m[1], m[4], m[7],
- m[2], m[5], m[8],
+ "Matrix(%v %v %v | %v %v %v)",
+ m[0], m[2], m[4],
+ m[1], m[3], m[5],
)
}
// Moved moves everything by the delta vector.
func (m Matrix) Moved(delta Vec) Matrix {
- m3 := mgl64.Mat3(m)
- m3 = mgl64.Translate2D(delta.XY()).Mul3(m3)
- return Matrix(m3)
+ m[4], m[5] = m[4]+delta.X, m[5]+delta.Y
+ return m
}
// ScaledXY scales everything around a given point by the scale factor in each axis respectively.
func (m Matrix) ScaledXY(around Vec, scale Vec) Matrix {
- m3 := mgl64.Mat3(m)
- m3 = mgl64.Translate2D(around.Scaled(-1).XY()).Mul3(m3)
- m3 = mgl64.Scale2D(scale.XY()).Mul3(m3)
- m3 = mgl64.Translate2D(around.XY()).Mul3(m3)
- return Matrix(m3)
+ m[4], m[5] = m[4]-around.X, m[5]-around.Y
+ m[0], m[2], m[4] = m[0]*scale.X, m[2]*scale.X, m[4]*scale.X
+ m[1], m[3], m[5] = m[1]*scale.Y, m[3]*scale.Y, m[5]*scale.Y
+ m[4], m[5] = m[4]+around.X, m[5]+around.Y
+ return m
}
// Scaled scales everything around a given point by the scale factor.
@@ -302,36 +303,44 @@ func (m Matrix) Scaled(around Vec, scale float64) Matrix {
// Rotated rotates everything around a given point by the given angle in radians.
func (m Matrix) Rotated(around Vec, angle float64) Matrix {
- m3 := mgl64.Mat3(m)
- m3 = mgl64.Translate2D(around.Scaled(-1).XY()).Mul3(m3)
- m3 = mgl64.Rotate3DZ(angle).Mul3(m3)
- m3 = mgl64.Translate2D(around.XY()).Mul3(m3)
- return Matrix(m3)
+ sint, cost := math.Sincos(angle)
+ m[4], m[5] = m[4]-around.X, m[5]-around.Y
+ m = m.Chained(Matrix{cost, sint, -sint, cost, 0, 0})
+ m[4], m[5] = m[4]+around.X, m[5]+around.Y
+ return m
}
// Chained adds another Matrix to this one. All tranformations by the next Matrix will be applied
// after the transformations of this Matrix.
func (m Matrix) Chained(next Matrix) Matrix {
- m3 := mgl64.Mat3(m)
- m3 = mgl64.Mat3(next).Mul3(m3)
- return Matrix(m3)
+ return Matrix{
+ m[0]*next[0] + m[2]*next[1],
+ m[1]*next[0] + m[3]*next[1],
+ m[0]*next[2] + m[2]*next[3],
+ m[1]*next[2] + m[3]*next[3],
+ m[0]*next[4] + m[2]*next[5] + m[4],
+ m[1]*next[4] + m[3]*next[5] + m[5],
+ }
}
// Project applies all transformations added to the Matrix to a vector u and returns the result.
//
// Time complexity is O(1).
func (m Matrix) Project(u Vec) Vec {
- m3 := mgl64.Mat3(m)
- proj := m3.Mul3x1(mgl64.Vec3{u.X, u.Y, 1})
- return V(proj.X(), proj.Y())
+ return Vec{X: m[0]*u.X + m[2]*u.Y + m[4], Y: m[1]*u.X + m[3]*u.Y + m[5]}
}
// Unproject does the inverse operation to Project.
//
+// It turns out that multiplying a vector by the inverse matrix of m
+// can be nearly-accomplished by subtracting the translate part of the
+// matrix and multplying by the inverse of the top-left 2x2 matrix,
+// and the inverse of a 2x2 matrix is simple enough to just be
+// inlined in the computation.
+//
// Time complexity is O(1).
func (m Matrix) Unproject(u Vec) Vec {
- m3 := mgl64.Mat3(m)
- inv := m3.Inv()
- unproj := inv.Mul3x1(mgl64.Vec3{u.X, u.Y, 1})
- return V(unproj.X(), unproj.Y())
+ d := (m[0] * m[3]) - (m[1] * m[2])
+ u.X, u.Y = (u.X-m[4])/d, (u.Y-m[5])/d
+ return Vec{u.X*m[3] - u.Y*m[1], u.Y*m[0] - u.X*m[2]}
}
diff --git a/pixelgl/canvas.go b/pixelgl/canvas.go
index a08835033d97d51f941cc2480b3c5727ed52bf02..b7b5cfc09e14c44b49ffab454a82b243b92452fc 100644
--- a/pixelgl/canvas.go
+++ b/pixelgl/canvas.go
@@ -90,9 +90,16 @@ func (c *Canvas) MakePicture(p pixel.Picture) pixel.TargetPicture {
}
// SetMatrix sets a Matrix that every point will be projected by.
+// pixel.Matrix is 3x2 with an implicit 0, 0, 1 row after it. So
+// [0] [2] [4] [0] [3] [6]
+// [1] [3] [5] => [1] [4] [7]
+// 0 0 1 0 0 1
+// since all matrix ops are affine, the last row never changes,
+// and we don't need to copy it
+//
func (c *Canvas) SetMatrix(m pixel.Matrix) {
- for i := range m {
- c.mat[i] = float32(m[i])
+ for i, j := range [6]int{ 0, 1, 3, 4, 6, 7} {
+ c.mat[j] = float32(m[i])
}
}