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| 1 | +unit PerspectiveCorrect; |
| 2 | + |
| 3 | +interface |
| 4 | + |
| 5 | +uses |
| 6 | + System.Math, |
| 7 | + SimpleSVD, |
| 8 | + GR32, |
| 9 | + GR32_Transforms, |
| 10 | + GR32_Math, |
| 11 | + GR32_Blend; |
| 12 | + |
| 13 | +type |
| 14 | + TMyProjectiveTransformation = class(T3x3Transformation) |
| 15 | + private |
| 16 | + FDestHeight: TFloat; |
| 17 | + FDestWidth: TFloat; |
| 18 | + FQuadX: array [0..3] of TFloat; |
| 19 | + FQuadY: array [0..3] of TFloat; |
| 20 | + function GetDestHeight: TFloat; |
| 21 | + function GetDestWidth: TFloat; |
| 22 | + procedure SetX0(Value: TFloat); {$IFDEF UseInlining} inline; {$ENDIF} |
| 23 | + procedure SetX1(Value: TFloat); {$IFDEF UseInlining} inline; {$ENDIF} |
| 24 | + procedure SetX2(Value: TFloat); {$IFDEF UseInlining} inline; {$ENDIF} |
| 25 | + procedure SetX3(Value: TFloat); {$IFDEF UseInlining} inline; {$ENDIF} |
| 26 | + procedure SetY0(Value: TFloat); {$IFDEF UseInlining} inline; {$ENDIF} |
| 27 | + procedure SetY1(Value: TFloat); {$IFDEF UseInlining} inline; {$ENDIF} |
| 28 | + procedure SetY2(Value: TFloat); {$IFDEF UseInlining} inline; {$ENDIF} |
| 29 | + procedure SetY3(Value: TFloat); {$IFDEF UseInlining} inline; {$ENDIF} |
| 30 | + protected |
| 31 | + procedure PrepareTransform; override; |
| 32 | + procedure ReverseTransformFixed(DstX, DstY: TFixed; out SrcX, SrcY: TFixed); override; |
| 33 | + procedure ReverseTransformFloat(DstX, DstY: TFloat; out SrcX, SrcY: TFloat); override; |
| 34 | + procedure TransformFixed(SrcX, SrcY: TFixed; out DstX, DstY: TFixed); override; |
| 35 | + procedure TransformFloat(SrcX, SrcY: TFloat; out DstX, DstY: TFloat); override; |
| 36 | + public |
| 37 | + function GetTransformedBounds(const ASrcRect: TFloatRect): TFloatRect; override; |
| 38 | + property DestWidth: TFloat read GetDestWidth; |
| 39 | + property DestHeight: TFloat read GetDestHeight; |
| 40 | + published |
| 41 | + property X0: TFloat read FQuadX[0] write SetX0; |
| 42 | + property X1: TFloat read FQuadX[1] write SetX1; |
| 43 | + property X2: TFloat read FQuadX[2] write SetX2; |
| 44 | + property X3: TFloat read FQuadX[3] write SetX3; |
| 45 | + property Y0: TFloat read FQuadY[0] write SetY0; |
| 46 | + property Y1: TFloat read FQuadY[1] write SetY1; |
| 47 | + property Y2: TFloat read FQuadY[2] write SetY2; |
| 48 | + property Y3: TFloat read FQuadY[3] write SetY3; |
| 49 | + end; |
| 50 | + |
| 51 | +function getPerspectiveTransform(const src, |
| 52 | + dst: TArray<TFloatPoint>): TFloatMatrix; |
| 53 | +implementation |
| 54 | + |
| 55 | +function getPerspectiveTransform(const src, |
| 56 | + dst: TArray<TFloatPoint>): TFloatMatrix; |
| 57 | +const |
| 58 | + DECOMP_SVD = 1; |
| 59 | + |
| 60 | +var |
| 61 | + A, b, c: TMatrix; |
| 62 | + M, N, i: Integer; |
| 63 | + svd_deomposition: TSVD; |
| 64 | + A_pinv: TMatrix; |
| 65 | + Mat: TFloatMatrix; |
| 66 | +begin |
| 67 | + M := 8; |
| 68 | + N := 8; |
| 69 | + A := TMatrix.Create(M, N, 'A', TMatrix.AS_MATRIX); |
| 70 | + b := TMatrix.Create(M, 1, 'b', TMatrix.AS_VECTOR); |
| 71 | + c := TMatrix.Create(N, 1, 'c', TMatrix.AS_VECTOR); |
| 72 | + |
| 73 | + for i := 0 to 3 do |
| 74 | + begin |
| 75 | + A[i,0] := src[i].X; |
| 76 | + A[i+4,3] := src[i].X; |
| 77 | + A[i,1] := src[i].Y; |
| 78 | + a[i+4,4] := src[i].Y; |
| 79 | + A[i,2] := 1; |
| 80 | + A[i+4,5] := 1; |
| 81 | + A[i,3] := 0; |
| 82 | + A[i,4] := 0; |
| 83 | + A[i,5] := 0; |
| 84 | + A[i+4,0] := 0; |
| 85 | + A[i+4,1] := 0; |
| 86 | + A[i+4,2] := 0; |
| 87 | + A[i,6] := -src[i].x*dst[i].x; |
| 88 | + A[i,7] := -src[i].y*dst[i].x; |
| 89 | + A[i+4,6] := -src[i].x*dst[i].y; |
| 90 | + A[i+4,7] := -src[i].y*dst[i].y; |
| 91 | + B.Mat[i] := dst[i].x; |
| 92 | + B.Mat[i+4] := dst[i].y; |
| 93 | + end; |
| 94 | + svd_deomposition := TSVD.Create; |
| 95 | + A_pinv := nil; |
| 96 | + try |
| 97 | + A_pinv := svd_deomposition.PinvCompute(A, A.Rows, A.Cols); |
| 98 | + svd_deomposition.multiply(A_pinv, b, c); |
| 99 | + Mat[0][0] := c.Mat[0]; |
| 100 | + Mat[1][0] := c.Mat[1]; |
| 101 | + Mat[2][0] := c.Mat[2]; |
| 102 | + Mat[0][1] := c.Mat[3]; |
| 103 | + Mat[1][1] := c.Mat[4]; |
| 104 | + Mat[2][1] := c.Mat[5]; |
| 105 | + Mat[0][2] := c.Mat[6]; |
| 106 | + Mat[1][2] := c.Mat[7]; |
| 107 | + Mat[2][2] := 1; |
| 108 | + Result := Mat; |
| 109 | + finally |
| 110 | + A_pinv.Free; |
| 111 | + svd_deomposition.Free; |
| 112 | + end; |
| 113 | +end; |
| 114 | + |
| 115 | +{ TMyProjectiveTransformation } |
| 116 | + |
| 117 | +function TMyProjectiveTransformation.GetDestHeight: TFloat; |
| 118 | +begin |
| 119 | + if not TransformValid then PrepareTransform; |
| 120 | + Result := FDestHeight; |
| 121 | +end; |
| 122 | + |
| 123 | +function TMyProjectiveTransformation.GetDestWidth: TFloat; |
| 124 | +begin |
| 125 | + if not TransformValid then PrepareTransform; |
| 126 | + Result := FDestWidth; |
| 127 | +end; |
| 128 | + |
| 129 | +function TMyProjectiveTransformation.GetTransformedBounds( |
| 130 | + const ASrcRect: TFloatRect): TFloatRect; |
| 131 | +var |
| 132 | + p0, p1, p2, p3: TFloatPoint; |
| 133 | +begin |
| 134 | + p0 := Transform(FloatPoint(X0, Y0)); |
| 135 | + p1 := Transform(FloatPoint(X1, Y1)); |
| 136 | + p2 := Transform(FloatPoint(X2, Y2)); |
| 137 | + p3 := Transform(FloatPoint(X3, Y3)); |
| 138 | + |
| 139 | +// p0 := (FloatPoint(X0, Y0)); |
| 140 | +// p1 := (FloatPoint(X1, Y1)); |
| 141 | +// p2 := (FloatPoint(X2, Y2)); |
| 142 | +// p3 := (FloatPoint(X3, Y3)); |
| 143 | + |
| 144 | + Result.Left := Min(Min(p0.X, p1.X), Min(p2.X, p3.X)); |
| 145 | + Result.Right := Max(Max(p0.X, p1.X), Max(p2.X, p3.X)); |
| 146 | + Result.Top := Min(Min(p0.Y, p1.Y), Min(p2.Y, p3.Y)); |
| 147 | + Result.Bottom := Max(Max(p0.Y, p1.Y), Max(p2.Y, p3.Y)); |
| 148 | +end; |
| 149 | + |
| 150 | +function Distance(P1, P2: TFloatPoint): Single; |
| 151 | +begin |
| 152 | + Result := Sqrt(Sqr(P1.X - P2.X) + Sqr(P1.Y - P2.Y)); |
| 153 | +end; |
| 154 | + |
| 155 | +procedure TMyProjectiveTransformation.PrepareTransform; |
| 156 | +var |
| 157 | + widthA, widthB, heightA, heightB: TFloat; |
| 158 | + src, dst: TArray<TFloatPoint>; |
| 159 | +begin |
| 160 | + src := TArray<TFloatPoint>.Create( |
| 161 | + FloatPoint(X0, Y0), |
| 162 | + FloatPoint(X1, Y1), |
| 163 | + FloatPoint(X2, Y2), |
| 164 | + FloatPoint(X3, Y3) |
| 165 | + ); |
| 166 | + widthA := Distance(src[2], src[3]); |
| 167 | + widthB := Distance(src[1], src[0]); |
| 168 | + FDestWidth := Max(widthA, widthB); |
| 169 | + |
| 170 | + heightA := Distance(src[1], src[2]); |
| 171 | + heightB := Distance(src[0], src[3]); |
| 172 | + FDestHeight := Max(heightA, heightB); |
| 173 | + |
| 174 | + dst := TArray<TFloatPoint>.Create( |
| 175 | + FloatPoint(0, 0), |
| 176 | + FloatPoint(FDestWidth, 0), |
| 177 | + FloatPoint(FDestWidth, FDestHeight), |
| 178 | + FloatPoint(0, FDestHeight) |
| 179 | + ); |
| 180 | + |
| 181 | + FMatrix := getPerspectiveTransform(src, dst); |
| 182 | +// Invert(FMatrix); |
| 183 | + inherited; |
| 184 | +end; |
| 185 | + |
| 186 | +procedure TMyProjectiveTransformation.ReverseTransformFixed(DstX, DstY: TFixed; |
| 187 | + out SrcX, SrcY: TFixed); |
| 188 | +var |
| 189 | + Z: TFixed; |
| 190 | + Zf: TFloat; |
| 191 | +begin |
| 192 | + Z := FixedMul(FInverseFixedMatrix[0, 2], DstX) + |
| 193 | + FixedMul(FInverseFixedMatrix[1, 2], DstY) + FInverseFixedMatrix[2, 2]; |
| 194 | + |
| 195 | + if Z = 0 then Exit; |
| 196 | + |
| 197 | + {$IFDEF UseInlining} |
| 198 | + SrcX := FixedMul(DstX, FInverseFixedMatrix[0, 0]) + |
| 199 | + FixedMul(DstY, FInverseFixedMatrix[1, 0]) + FInverseFixedMatrix[2, 0]; |
| 200 | + SrcY := FixedMul(DstX, FInverseFixedMatrix[0,1]) + |
| 201 | + FixedMul(DstY, FInverseFixedMatrix[1, 1]) + FInverseFixedMatrix[2, 1]; |
| 202 | + {$ELSE} |
| 203 | + inherited; |
| 204 | + {$ENDIF} |
| 205 | + |
| 206 | + if Z <> FixedOne then |
| 207 | + begin |
| 208 | + EMMS; |
| 209 | + Zf := FixedOne / Z; |
| 210 | + SrcX := Round(SrcX * Zf); |
| 211 | + SrcY := Round(SrcY * Zf); |
| 212 | + end; |
| 213 | +end; |
| 214 | + |
| 215 | +procedure TMyProjectiveTransformation.ReverseTransformFloat(DstX, DstY: TFloat; |
| 216 | + out SrcX, SrcY: TFloat); |
| 217 | +var |
| 218 | + Z: TFloat; |
| 219 | +begin |
| 220 | + EMMS; |
| 221 | + Z := FInverseMatrix[0, 2] * DstX + FInverseMatrix[1, 2] * DstY + |
| 222 | + FInverseMatrix[2, 2]; |
| 223 | + |
| 224 | + if Z = 0 then Exit; |
| 225 | + |
| 226 | + {$IFDEF UseInlining} |
| 227 | + SrcX := DstX * FInverseMatrix[0, 0] + DstY * FInverseMatrix[1, 0] + |
| 228 | + FInverseMatrix[2, 0]; |
| 229 | + SrcY := DstX * FInverseMatrix[0, 1] + DstY * FInverseMatrix[1, 1] + |
| 230 | + FInverseMatrix[2, 1]; |
| 231 | + {$ELSE} |
| 232 | + inherited; |
| 233 | + {$ENDIF} |
| 234 | + |
| 235 | + if Z <> 1 then |
| 236 | + begin |
| 237 | + Z := 1 / Z; |
| 238 | + SrcX := SrcX * Z; |
| 239 | + SrcY := SrcY * Z; |
| 240 | + end; |
| 241 | +end; |
| 242 | + |
| 243 | +procedure TMyProjectiveTransformation.SetX0(Value: TFloat); |
| 244 | +begin |
| 245 | + FQuadX[0] := Value; |
| 246 | + Changed; |
| 247 | +end; |
| 248 | + |
| 249 | +procedure TMyProjectiveTransformation.SetX1(Value: TFloat); |
| 250 | +begin |
| 251 | + FQuadX[1] := Value; |
| 252 | + Changed; |
| 253 | +end; |
| 254 | + |
| 255 | +procedure TMyProjectiveTransformation.SetX2(Value: TFloat); |
| 256 | +begin |
| 257 | + FQuadX[2] := Value; |
| 258 | + Changed; |
| 259 | +end; |
| 260 | + |
| 261 | +procedure TMyProjectiveTransformation.SetX3(Value: TFloat); |
| 262 | +begin |
| 263 | + FQuadX[3] := Value; |
| 264 | + Changed; |
| 265 | +end; |
| 266 | + |
| 267 | +procedure TMyProjectiveTransformation.SetY0(Value: TFloat); |
| 268 | +begin |
| 269 | + FQuadY[0] := Value; |
| 270 | + Changed; |
| 271 | +end; |
| 272 | + |
| 273 | +procedure TMyProjectiveTransformation.SetY1(Value: TFloat); |
| 274 | +begin |
| 275 | + FQuadY[1] := Value; |
| 276 | + Changed; |
| 277 | +end; |
| 278 | + |
| 279 | +procedure TMyProjectiveTransformation.SetY2(Value: TFloat); |
| 280 | +begin |
| 281 | + FQuadY[2] := Value; |
| 282 | + Changed; |
| 283 | +end; |
| 284 | + |
| 285 | +procedure TMyProjectiveTransformation.SetY3(Value: TFloat); |
| 286 | +begin |
| 287 | + FQuadY[3] := Value; |
| 288 | + Changed; |
| 289 | +end; |
| 290 | + |
| 291 | + |
| 292 | +procedure TMyProjectiveTransformation.TransformFixed(SrcX, SrcY: TFixed; |
| 293 | + out DstX, DstY: TFixed); |
| 294 | +var |
| 295 | + Z: TFixed; |
| 296 | + Zf: TFloat; |
| 297 | +begin |
| 298 | + Z := FixedMul(FFixedMatrix[0, 2], SrcX) + |
| 299 | + FixedMul(FFixedMatrix[1, 2], SrcY) + FFixedMatrix[2, 2]; |
| 300 | + |
| 301 | + if Z = 0 then Exit; |
| 302 | + |
| 303 | + {$IFDEF UseInlining} |
| 304 | + DstX := FixedMul(SrcX, FFixedMatrix[0, 0]) + |
| 305 | + FixedMul(SrcY, FFixedMatrix[1, 0]) + FFixedMatrix[2, 0]; |
| 306 | + DstY := FixedMul(SrcX, FFixedMatrix[0, 1]) + |
| 307 | + FixedMul(SrcY, FFixedMatrix[1, 1]) + FFixedMatrix[2, 1]; |
| 308 | + {$ELSE} |
| 309 | + inherited; |
| 310 | + {$ENDIF} |
| 311 | + |
| 312 | + if Z <> FixedOne then |
| 313 | + begin |
| 314 | + EMMS; |
| 315 | + Zf := FixedOne / Z; |
| 316 | + DstX := Round(DstX * Zf); |
| 317 | + DstY := Round(DstY * Zf); |
| 318 | + end; |
| 319 | +end; |
| 320 | + |
| 321 | +procedure TMyProjectiveTransformation.TransformFloat(SrcX, SrcY: TFloat; |
| 322 | + out DstX, DstY: TFloat); |
| 323 | +var |
| 324 | + Z: TFloat; |
| 325 | +begin |
| 326 | + EMMS; |
| 327 | + Z := FMatrix[0, 2] * SrcX + FMatrix[1, 2] * SrcY + FMatrix[2, 2]; |
| 328 | + |
| 329 | + if Z = 0 then Exit; |
| 330 | + |
| 331 | + {$IFDEF UseInlining} |
| 332 | + DstX := SrcX * Matrix[0, 0] + SrcY * Matrix[1, 0] + Matrix[2, 0]; |
| 333 | + DstY := SrcX * Matrix[0, 1] + SrcY * Matrix[1, 1] + Matrix[2, 1]; |
| 334 | + {$ELSE} |
| 335 | + inherited; |
| 336 | + {$ENDIF} |
| 337 | + |
| 338 | + if Z <> 1 then |
| 339 | + begin |
| 340 | + Z := 1 / Z; |
| 341 | + DstX := DstX * Z; |
| 342 | + DstY := DstY * Z; |
| 343 | + end; |
| 344 | +end; |
| 345 | + |
| 346 | +end. |
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