1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
|
// Copyright 2010 The draw2d Authors. All rights reserved.
// created: 21/11/2010 by Laurent Le Goff
package draw2d
import (
"code.google.com/p/freetype-go/freetype/raster"
"math"
)
type MatrixTransform [6]float64
const (
epsilon = 1e-6
)
func (tr MatrixTransform) Determinant() float64 {
return tr[0]*tr[3] - tr[1]*tr[2]
}
func (tr MatrixTransform) Transform(points ...*float64) {
for i, j := 0, 1; j < len(points); i, j = i+2, j+2 {
x := *points[i]
y := *points[j]
*points[i] = x*tr[0] + y*tr[2] + tr[4]
*points[j] = x*tr[1] + y*tr[3] + tr[5]
}
}
func (tr MatrixTransform) TransformArray(points []float64) {
for i, j := 0, 1; j < len(points); i, j = i+2, j+2 {
x := points[i]
y := points[j]
points[i] = x*tr[0] + y*tr[2] + tr[4]
points[j] = x*tr[1] + y*tr[3] + tr[5]
}
}
func (tr MatrixTransform) TransformRectangle(x0, y0, x2, y2 *float64) {
x1 := *x2
y1 := *y0
x3 := *x0
y3 := *y2
tr.Transform(x0, y0, &x1, &y1, x2, y2, &x3, &y3)
*x0, x1 = minMax(*x0, x1)
*x2, x3 = minMax(*x2, x3)
*y0, y1 = minMax(*y0, y1)
*y2, y3 = minMax(*y2, y3)
*x0 = min(*x0, *x2)
*y0 = min(*y0, *y2)
*x2 = max(x1, x3)
*y2 = max(y1, y3)
}
func (tr MatrixTransform) TransformRasterPoint(points ...*raster.Point) {
for _, point := range points {
x := float64(point.X) / 256
y := float64(point.Y) / 256
point.X = raster.Fix32((x*tr[0] + y*tr[2] + tr[4]) * 256)
point.Y = raster.Fix32((x*tr[1] + y*tr[3] + tr[5]) * 256)
}
}
func (tr MatrixTransform) InverseTransform(points ...*float64) {
d := tr.Determinant() // matrix determinant
for i, j := 0, 1; j < len(points); i, j = i+2, j+2 {
x := *points[i]
y := *points[j]
*points[i] = ((x-tr[4])*tr[3] - (y-tr[5])*tr[2]) / d
*points[j] = ((y-tr[5])*tr[0] - (x-tr[4])*tr[1]) / d
}
}
// ******************** Vector transformations ********************
func (tr MatrixTransform) VectorTransform(points ...*float64) {
for i, j := 0, 1; j < len(points); i, j = i+2, j+2 {
x := *points[i]
y := *points[j]
*points[i] = x*tr[0] + y*tr[2]
*points[j] = x*tr[1] + y*tr[3]
}
}
// ******************** Transformations creation ********************
/** Creates an identity transformation. */
func NewIdentityMatrix() MatrixTransform {
return [6]float64{1, 0, 0, 1, 0, 0}
}
/**
* Creates a transformation with a translation, that,
* transform point1 into point2.
*/
func NewTranslationMatrix(tx, ty float64) MatrixTransform {
return [6]float64{1, 0, 0, 1, tx, ty}
}
/**
* Creates a transformation with a sx, sy scale factor
*/
func NewScaleMatrix(sx, sy float64) MatrixTransform {
return [6]float64{sx, 0, 0, sy, 0, 0}
}
/**
* Creates a rotation transformation.
*/
func NewRotationMatrix(angle float64) MatrixTransform {
c := math.Cos(angle)
s := math.Sin(angle)
return [6]float64{c, s, -s, c, 0, 0}
}
/**
* Creates a transformation, combining a scale and a translation, that transform rectangle1 into rectangle2.
*/
func NewMatrixTransform(rectangle1, rectangle2 [4]float64) MatrixTransform {
xScale := (rectangle2[2] - rectangle2[0]) / (rectangle1[2] - rectangle1[0])
yScale := (rectangle2[3] - rectangle2[1]) / (rectangle1[3] - rectangle1[1])
xOffset := rectangle2[0] - (rectangle1[0] * xScale)
yOffset := rectangle2[1] - (rectangle1[1] * yScale)
return [6]float64{xScale, 0, 0, yScale, xOffset, yOffset}
}
// ******************** Transformations operations ********************
/**
* Returns a transformation that is the inverse of the given transformation.
*/
func (tr MatrixTransform) GetInverseTransformation() MatrixTransform {
d := tr.Determinant() // matrix determinant
return [6]float64{
tr[3] / d,
-tr[1] / d,
-tr[2] / d,
tr[0] / d,
(tr[2]*tr[5] - tr[3]*tr[4]) / d,
(tr[1]*tr[4] - tr[0]*tr[5]) / d}
}
func (tr1 MatrixTransform) Multiply(tr2 MatrixTransform) MatrixTransform {
return [6]float64{
tr1[0]*tr2[0] + tr1[1]*tr2[2],
tr1[1]*tr2[3] + tr1[0]*tr2[1],
tr1[2]*tr2[0] + tr1[3]*tr2[2],
tr1[3]*tr2[3] + tr1[2]*tr2[1],
tr1[4]*tr2[0] + tr1[5]*tr2[2] + tr2[4],
tr1[5]*tr2[3] + tr1[4]*tr2[1] + tr2[5]}
}
func (tr *MatrixTransform) Scale(sx, sy float64) *MatrixTransform {
tr[0] = sx * tr[0]
tr[1] = sx * tr[1]
tr[2] = sy * tr[2]
tr[3] = sy * tr[3]
return tr
}
func (tr *MatrixTransform) Translate(tx, ty float64) *MatrixTransform {
tr[4] = tx*tr[0] + ty*tr[2] + tr[4]
tr[5] = ty*tr[3] + tx*tr[1] + tr[5]
return tr
}
func (tr *MatrixTransform) Rotate(angle float64) *MatrixTransform {
c := math.Cos(angle)
s := math.Sin(angle)
t0 := c*tr[0] + s*tr[2]
t1 := s*tr[3] + c*tr[1]
t2 := c*tr[2] - s*tr[0]
t3 := c*tr[3] - s*tr[1]
tr[0] = t0
tr[1] = t1
tr[2] = t2
tr[3] = t3
return tr
}
func (tr MatrixTransform) GetTranslation() (x, y float64) {
return tr[4], tr[5]
}
func (tr MatrixTransform) GetScaling() (x, y float64) {
return tr[0], tr[3]
}
func (tr MatrixTransform) GetScale() float64 {
x := 0.707106781*tr[0] + 0.707106781*tr[1]
y := 0.707106781*tr[2] + 0.707106781*tr[3]
return math.Sqrt(x*x + y*y)
}
func (tr MatrixTransform) GetMaxAbsScaling() (s float64) {
sx := math.Abs(tr[0])
sy := math.Abs(tr[3])
if sx > sy {
return sx
}
return sy
}
func (tr MatrixTransform) GetMinAbsScaling() (s float64) {
sx := math.Abs(tr[0])
sy := math.Abs(tr[3])
if sx > sy {
return sy
}
return sx
}
// ******************** Testing ********************
/**
* Tests if a two transformation are equal. A tolerance is applied when
* comparing matrix elements.
*/
func (tr1 MatrixTransform) Equals(tr2 MatrixTransform) bool {
for i := 0; i < 6; i = i + 1 {
if !fequals(tr1[i], tr2[i]) {
return false
}
}
return true
}
/**
* Tests if a transformation is the identity transformation. A tolerance
* is applied when comparing matrix elements.
*/
func (tr MatrixTransform) IsIdentity() bool {
return fequals(tr[4], 0) && fequals(tr[5], 0) && tr.IsTranslation()
}
/**
* Tests if a transformation is is a pure translation. A tolerance
* is applied when comparing matrix elements.
*/
func (tr MatrixTransform) IsTranslation() bool {
return fequals(tr[0], 1) && fequals(tr[1], 0) && fequals(tr[2], 0) && fequals(tr[3], 1)
}
/**
* Compares two floats.
* return true if the distance between the two floats is less than epsilon, false otherwise
*/
func fequals(float1, float2 float64) bool {
return math.Abs(float1-float2) <= epsilon
}
// this VertexConverter apply the Matrix transformation tr
type VertexMatrixTransform struct {
tr MatrixTransform
Next VertexConverter
}
func NewVertexMatrixTransform(tr MatrixTransform, converter VertexConverter) *VertexMatrixTransform {
return &VertexMatrixTransform{tr, converter}
}
// Vertex Matrix Transform
func (vmt *VertexMatrixTransform) NextCommand(command VertexCommand) {
vmt.Next.NextCommand(command)
}
func (vmt *VertexMatrixTransform) Vertex(x, y float64) {
u := x*vmt.tr[0] + y*vmt.tr[2] + vmt.tr[4]
v := x*vmt.tr[1] + y*vmt.tr[3] + vmt.tr[5]
vmt.Next.Vertex(u, v)
}
// this adder apply a Matrix transformation to points
type MatrixTransformAdder struct {
tr MatrixTransform
next raster.Adder
}
func NewMatrixTransformAdder(tr MatrixTransform, adder raster.Adder) *MatrixTransformAdder {
return &MatrixTransformAdder{tr, adder}
}
// Start starts a new curve at the given point.
func (mta MatrixTransformAdder) Start(a raster.Point) {
mta.tr.TransformRasterPoint(&a)
mta.next.Start(a)
}
// Add1 adds a linear segment to the current curve.
func (mta MatrixTransformAdder) Add1(b raster.Point) {
mta.tr.TransformRasterPoint(&b)
mta.next.Add1(b)
}
// Add2 adds a quadratic segment to the current curve.
func (mta MatrixTransformAdder) Add2(b, c raster.Point) {
mta.tr.TransformRasterPoint(&b, &c)
mta.next.Add2(b, c)
}
// Add3 adds a cubic segment to the current curve.
func (mta MatrixTransformAdder) Add3(b, c, d raster.Point) {
mta.tr.TransformRasterPoint(&b, &c, &d)
mta.next.Add3(b, c, d)
}
|
