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// Copyright 2014 Hajime Hoshi
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
package ebiten
import (
"fmt"
"math"
)
// GeoMDim is a dimension of a GeoM.
const GeoMDim = 3
// A GeoM represents a matrix to transform geometry when rendering an image.
//
// The initial value is identity.
type GeoM struct {
a_1 float32 // The actual 'a' value minus 1
b float32
c float32
d_1 float32 // The actual 'd' value minus 1
tx float32
ty float32
}
// String returns a string representation of GeoM.
func (g *GeoM) String() string {
return fmt.Sprintf("[[%f, %f, %f], [%f, %f, %f]]", g.a_1+1, g.b, g.tx, g.c, g.d_1+1, g.ty)
}
// Reset resets the GeoM as identity.
func (g *GeoM) Reset() {
g.a_1 = 0
g.b = 0
g.c = 0
g.d_1 = 0
g.tx = 0
g.ty = 0
}
// Apply pre-multiplies a vector (x, y, 1) by the matrix.
// In other words, Apply calculates GeoM * (x, y, 1)^T.
// The return value is x and y values of the result vector.
func (g *GeoM) Apply(x, y float64) (float64, float64) {
x2, y2 := g.apply32(float32(x), float32(y))
return float64(x2), float64(y2)
}
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 {
case i == 0 && j == 0:
return float64(g.a_1) + 1
case i == 0 && j == 1:
return float64(g.b)
case i == 0 && j == 2:
return float64(g.tx)
case i == 1 && j == 0:
return float64(g.c)
case i == 1 && j == 1:
return float64(g.d_1) + 1
case i == 1 && j == 2:
return float64(g.ty)
default:
panic("ebiten: i or j is out of index")
}
}
// Concat multiplies a geometry matrix with the other geometry matrix.
// This is same as muptiplying the matrix other and the matrix g in this order.
func (g *GeoM) Concat(other GeoM) {
a := (other.a_1+1)*(g.a_1+1) + other.b*g.c
b := (other.a_1+1)*g.b + other.b*(g.d_1+1)
tx := (other.a_1+1)*g.tx + other.b*g.ty + other.tx
c := other.c*(g.a_1+1) + (other.d_1+1)*g.c
d := other.c*g.b + (other.d_1+1)*(g.d_1+1)
ty := other.c*g.tx + (other.d_1+1)*g.ty + other.ty
g.a_1 = a - 1
g.b = b
g.c = c
g.d_1 = d - 1
g.tx = tx
g.ty = ty
}
// Add is deprecated as of 1.5.0-alpha.
// Note that this doesn't make sense as an operation for affine matrices.
func (g *GeoM) Add(other GeoM) {
g.a_1 += other.a_1
g.b += other.b
g.c += other.c
g.d_1 += other.d_1
g.tx += other.tx
g.ty += other.ty
}
// Scale scales the matrix by (x, y).
func (g *GeoM) Scale(x, y float64) {
a := (float64(g.a_1) + 1) * x
b := float64(g.b) * x
tx := float64(g.tx) * x
c := float64(g.c) * y
d := (float64(g.d_1) + 1) * y
ty := float64(g.ty) * y
g.a_1 = float32(a) - 1
g.b = float32(b)
g.c = float32(c)
g.d_1 = float32(d) - 1
g.tx = float32(tx)
g.ty = float32(ty)
}
// Translate translates the matrix by (tx, ty).
func (g *GeoM) Translate(tx, ty float64) {
g.tx += float32(tx)
g.ty += float32(ty)
}
// 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)
a := cos*(g.a_1+1) - sin*g.c
b := cos*g.b - sin*(g.d_1+1)
tx := cos*g.tx - sin*g.ty
c := sin*(g.a_1+1) + cos*g.c
d := sin*g.b + cos*(g.d_1+1)
ty := sin*g.tx + cos*g.ty
g.a_1 = a - 1
g.b = b
g.c = c
g.d_1 = d - 1
g.tx = tx
g.ty = ty
}
// Skew skews the matrix by (skewX, skewY). The unit is radian.
func (g *GeoM) Skew(skewX, skewY float64) {
sx64 := math.Tan(skewX)
sy64 := math.Tan(skewY)
sx, sy := float32(sx64), float32(sy64)
a := (g.a_1 + 1) + g.c*sx
b := g.b + (g.d_1+1)*sx
c := (g.a_1+1)*sy + g.c
d := g.b*sy + (g.d_1 + 1)
tx := g.tx + g.ty*sx
ty := g.ty + g.tx*sy
g.a_1 = a - 1
g.b = b
g.c = c
g.d_1 = d - 1
g.tx = tx
g.ty = ty
}
func (g *GeoM) det() float32 {
return (g.a_1+1)*(g.d_1+1) - g.b*g.c
}
// IsInvertible returns a boolean value indicating
// whether the matrix g is invertible or not.
func (g *GeoM) IsInvertible() bool {
return g.det() != 0
}
// Invert inverts the matrix.
// If g is not invertible, Invert panics.
func (g *GeoM) Invert() {
det := g.det()
if det == 0 {
panic("ebiten: g is not invertible")
}
a := (g.d_1 + 1) / det
b := -g.b / det
c := -g.c / det
d := (g.a_1 + 1) / det
tx := (-(g.d_1+1)*g.tx + g.b*g.ty) / det
ty := (g.c*g.tx + -(g.a_1+1)*g.ty) / det
g.a_1 = a - 1
g.b = b
g.c = c
g.d_1 = d - 1
g.tx = tx
g.ty = ty
}
// SetElement sets an element at (i, j).
func (g *GeoM) SetElement(i, j int, element float64) {
e := float32(element)
switch {
case i == 0 && j == 0:
g.a_1 = e - 1
case i == 0 && j == 1:
g.b = e
case i == 0 && j == 2:
g.tx = e
case i == 1 && j == 0:
g.c = e
case i == 1 && j == 1:
g.d_1 = e - 1
case i == 1 && j == 2:
g.ty = e
default:
panic("ebiten: i or j is out of index")
}
}
// ScaleGeo is deprecated as of 1.2.0-alpha. Use Scale instead.
func ScaleGeo(x, y float64) GeoM {
g := GeoM{}
g.Scale(x, y)
return g
}
// TranslateGeo is deprecated as of 1.2.0-alpha. Use Translate instead.
func TranslateGeo(tx, ty float64) GeoM {
g := GeoM{}
g.Translate(tx, ty)
return g
}
// RotateGeo is deprecated as of 1.2.0-alpha. Use Rotate instead.
func RotateGeo(theta float64) GeoM {
g := GeoM{}
g.Rotate(theta)
return g
}
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