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SplineLibBilinear.pas
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SplineLibBilinear.pas
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(*************************************************************************
Copyright (c) 2007, Sergey Bochkanov (ALGLIB project).
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are
met:
- Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
- Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer listed
in this license in the documentation and/or other materials
provided with the distribution.
- Neither the name of the copyright holders nor the names of its
contributors may be used to endorse or promote products derived from
this software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*************************************************************************)
{*******************************************************}
{ Modify and Adaptive by Simkin A.V. }
{ to }
{ Image Library for Bachelor Diploma Project }
{ MSTU n.a. Bauman, ICS-1 }
{ GNU GPL 2009, Simkin A.V. }
{ }
{*******************************************************}
{ 24.04.2009 }
{*******************************************************}
unit SplineLibBilinear;
interface
uses Math, SplineLibLinear, ImgLibTypes;
procedure BuildBilinearSpline(X : TDDoubleArray;
Y : TDDoubleArray;
F : TDDouble2Array;
M : Integer;
N : Integer;
var C : TDDoubleArray);
procedure BuildBicubicSpline(X : TDDoubleArray;
Y : TDDoubleArray;
F : TDDouble2Array;
M : Integer;
N : Integer;
var C : TDDoubleArray);
function SplineInterpolation2D(const C : TDDoubleArray;
X : Double;
Y : Double):Double;
procedure SplineDifferentiation2D(const C : TDDoubleArray;
X : Double;
Y : Double;
var F : Double;
var FX : Double;
var FY : Double;
var FXY : Double);
procedure SplineUnpack2D(const C : TDDoubleArray;
var M : Integer;
var N : Integer;
var Tbl : TDDouble2Array);
procedure Spline2DLinTransXY(var C : TDDoubleArray;
AX : Double;
BX : Double;
AY : Double;
BY : Double);
procedure Spline2DLinTransF(var C : TDDoubleArray; A : Double; B : Double);
procedure Spline2DCopy(const C : TDDoubleArray; var CC : TDDoubleArray);
procedure BicubicResampleCartesian(const A : TDDouble2Array;
OldHeight : Integer;
OldWidth : Integer;
var B : TDDouble2Array;
NewHeight : Integer;
NewWidth : Integer);
procedure BilinearResampleCartesian(const A : TDDouble2Array;
OldHeight : Integer;
OldWidth : Integer;
var B : TDDouble2Array;
NewHeight : Integer;
NewWidth : Integer);
procedure BiakimaResampleCartesian(const A : TDDouble2Array;
OldHeight : Integer;
OldWidth : Integer;
var B : TDDouble2Array;
NewHeight : Integer;
NewWidth : Integer);
procedure BicubicResample(OldWidth : Integer;
OldHeight : Integer;
NewWidth : Integer;
NewHeight : Integer;
const A : TDDouble2Array;
var B : TDDouble2Array);
procedure BilinearResample(OldWidth : Integer;
OldHeight : Integer;
NewWidth : Integer;
NewHeight : Integer;
const A : TDDouble2Array;
var B : TDDouble2Array);
implementation
uses ImgLibArrayExt;
procedure BicubicCalcDerivatives(const A : TDDouble2Array;
const X : TDDoubleArray;
const Y : TDDoubleArray;
M : Integer;
N : Integer;
var DX : TDDouble2Array;
var DY : TDDouble2Array;
var DXY : TDDouble2Array);forward;
(*************************************************************************
Построение билинейного интерполирующего сплайна
Входные параметры:
X - массив абсцисс прямоугольной сетки на которой строится сплайн.
Нумерация элементов: [0..N-1]
Y - массив ординат прямоугольной сетки на которой строится сплайн.
Нумерация элементов: [0..M-1]
F - матрица значений функции в узлах сетки.
Нумерация элементов: [0..M-1, 0..N-1]
M - размер сетки по оси Y, M>=2
N - размер сетки по оси X, N>=2
Выходные параметры:
C - таблица коэффициентов для использования в подпрограмме
SplineInterpolation2D.
-- ALGLIB PROJECT --
Copyright 05.07.2007 by Bochkanov Sergey
*************************************************************************)
procedure BuildBilinearSpline(X : TDDoubleArray;
Y : TDDoubleArray;
F : TDDouble2Array;
M : Integer;
N : Integer;
var C : TDDoubleArray);
var
I : Integer;
J : Integer;
K : Integer;
TblSize : Integer;
Shift : Integer;
T : Double;
//DX : TDDouble2Array;
//DY : TDDouble2Array;
//DXY : TDDouble2Array;
begin
X := aDynamicArrayCopy(X);
Y := aDynamicArrayCopy(Y);
F := aDynamicArrayCopy(F);
Assert((N>=2) and (M>=2), 'BuildBilinearSpline: N<2 or M<2!');
//
// Sort points
//
J:=0;
while J<=N-1 do
begin
K := J;
I:=J+1;
while I<=N-1 do
begin
if X[I]<X[K] then
begin
K := I;
end;
Inc(I);
end;
if K<>J then
begin
I:=0;
while I<=M-1 do
begin
T := F[I,J];
F[I,J] := F[I,K];
F[I,K] := T;
Inc(I);
end;
T := X[J];
X[J] := X[K];
X[K] := T;
end;
Inc(J);
end;
I:=0;
while I<=M-1 do
begin
K := I;
J:=I+1;
while J<=M-1 do
begin
if Y[J]<Y[K] then
begin
K := J;
end;
Inc(J);
end;
if K<>I then
begin
J:=0;
while J<=N-1 do
begin
T := F[I,J];
F[I,J] := F[K,J];
F[K,J] := T;
Inc(J);
end;
T := Y[I];
Y[I] := Y[K];
Y[K] := T;
end;
Inc(I);
end;
//
// Fill C:
// C[0] - length(C)
// C[1] - type(C):
// -1 = bilinear interpolant
// -3 = general cubic spline
// (see BuildBicubicSpline)
// C[2]:
// N (x count)
// C[3]:
// M (y count)
// C[4]...C[4+N-1]:
// x[i], i = 0...N-1
// C[4+N]...C[4+N+M-1]:
// y[i], i = 0...M-1
// C[4+N+M]...C[4+N+M+(N*M-1)]:
// f(i,j) table. f(0,0), f(0, 1), f(0,2) and so on...
//
TblSize := 4+N+M+N*M;
SetLength(C, TblSize-1+1);
C[0] := TblSize;
C[1] := -1;
C[2] := N;
C[3] := M;
I:=0;
while I<=N-1 do
begin
C[4+I] := X[I];
Inc(I);
end;
I:=0;
while I<=M-1 do
begin
C[4+N+I] := Y[I];
Inc(I);
end;
I:=0;
while I<=M-1 do
begin
J:=0;
while J<=N-1 do
begin
Shift := I*N+J;
C[4+N+M+Shift] := F[I,J];
Inc(J);
end;
Inc(I);
end;
end;
(*************************************************************************
Построение бикубического интерполирующего сплайна
Входные параметры:
X - массив абсцисс прямоугольной сетки на которой строится сплайн.
Нумерация элементов: [0..N-1]
Y - массив ординат прямоугольной сетки на которой строится сплайн.
Нумерация элементов: [0..M-1]
F - матрица значений функции в узлах сетки.
Нумерация элементов: [0..M-1, 0..N-1]
M - размер сетки по оси Y
N - размер сетки по оси X
Выходные параметры:
C - таблица коэффициентов для использования в подпрограмме
SplineInterpolation2D.
-- ALGLIB PROJECT --
Copyright 05.07.2007 by Bochkanov Sergey
*************************************************************************)
procedure BuildBicubicSpline(X : TDDoubleArray;
Y : TDDoubleArray;
F : TDDouble2Array;
M : Integer;
N : Integer;
var C : TDDoubleArray);
var
I : Integer;
J : Integer;
K : Integer;
TblSize : Integer;
Shift : Integer;
T : Double;
DX : TDDouble2Array;
DY : TDDouble2Array;
DXY : TDDouble2Array;
begin
X := aDynamicArrayCopy(X);
Y := aDynamicArrayCopy(Y);
F := aDynamicArrayCopy(F);
Assert((N>=2) and (M>=2), 'BuildBicubicSpline: N<2 or M<2!');
//
// Sort points
//
J:=0;
while J<=N-1 do
begin
K := J;
I:=J+1;
while I<=N-1 do
begin
if X[I]<X[K] then
begin
K := I;
end;
Inc(I);
end;
if K<>J then
begin
I:=0;
while I<=M-1 do
begin
T := F[I,J];
F[I,J] := F[I,K];
F[I,K] := T;
Inc(I);
end;
T := X[J];
X[J] := X[K];
X[K] := T;
end;
Inc(J);
end;
I:=0;
while I<=M-1 do
begin
K := I;
J:=I+1;
while J<=M-1 do
begin
if Y[J]<Y[K] then
begin
K := J;
end;
Inc(J);
end;
if K<>I then
begin
J:=0;
while J<=N-1 do
begin
T := F[I,J];
F[I,J] := F[K,J];
F[K,J] := T;
Inc(J);
end;
T := Y[I];
Y[I] := Y[K];
Y[K] := T;
end;
Inc(I);
end;
//
// Fill C:
// C[0] - length(C)
// C[1] - type(C):
// -1 = bilinear interpolant
// (see BuildBilinearInterpolant)
// -3 = general cubic spline
// C[2]:
// N (x count)
// C[3]:
// M (y count)
// C[4]...C[4+N-1]:
// x[i], i = 0...N-1
// C[4+N]...C[4+N+M-1]:
// y[i], i = 0...M-1
// C[4+N+M]...C[4+N+M+(N*M-1)]:
// f(i,j) table. f(0,0), f(0, 1), f(0,2) and so on...
// C[4+N+M+N*M]...C[4+N+M+(2*N*M-1)]:
// df(i,j)/dx table.
// C[4+N+M+2*N*M]...C[4+N+M+(3*N*M-1)]:
// df(i,j)/dy table.
// C[4+N+M+3*N*M]...C[4+N+M+(4*N*M-1)]:
// d2f(i,j)/dxdy table.
//
TblSize := 4+N+M+4*N*M;
SetLength(C, TblSize-1+1);
C[0] := TblSize;
C[1] := -3;
C[2] := N;
C[3] := M;
I:=0;
while I<=N-1 do
begin
C[4+I] := X[I];
Inc(I);
end;
I:=0;
while I<=M-1 do
begin
C[4+N+I] := Y[I];
Inc(I);
end;
BicubicCalcDerivatives(F, X, Y, M, N, DX, DY, DXY);
I:=0;
while I<=M-1 do
begin
J:=0;
while J<=N-1 do
begin
Shift := I*N+J;
C[4+N+M+Shift] := F[I,J];
C[4+N+M+N*M+Shift] := DX[I,J];
C[4+N+M+2*N*M+Shift] := DY[I,J];
C[4+N+M+3*N*M+Shift] := DXY[I,J];
Inc(J);
end;
Inc(I);
end;
end;
(*************************************************************************
Интерполяция двухмерным (билинейным или бикубическим) сплайном
Входные параметры:
C - таблица коэффициентов, рассчитанная подпрограммой построения
сплайна.
X, Y- точка, в которой вычисляется значение сплайна
Результат:
Значение интерполирующего сплайна в точке (X,Y)
-- ALGLIB PROJECT --
Copyright 05.07.2007 by Bochkanov Sergey
*************************************************************************)
function SplineInterpolation2D(const C : TDDoubleArray;
X : Double;
Y : Double):Double;
var
V : Double;
VX : Double;
VY : Double;
VXY : Double;
begin
SplineDifferentiation2D(C, X, Y, V, VX, VY, VXY);
Result := V;
end;
(*************************************************************************
Интерполяция двухмерным (билинейным или бикубическим) сплайном.
Также осуществлятся вычисление градиента и перекрестной производной.
Входные параметры:
C - таблица коэффициентов, рассчитанная подпрограммой построения
сплайна.
X, Y- точка, в которой вычисляется значение сплайна
Результат:
F - значение интерполирующего сплайна
FX - dF/dX
FY - dF/dY
FXY - d2F/dXdY
-- ALGLIB PROJECT --
Copyright 05.07.2007 by Bochkanov Sergey
*************************************************************************)
procedure SplineDifferentiation2D(const C : TDDoubleArray;
X : Double;
Y : Double;
var F : Double;
var FX : Double;
var FY : Double;
var FXY : Double);
var
N : Integer;
M : Integer;
T : Double;
DT : Double;
U : Double;
DU : Double;
I : Integer;
J : Integer;
IX : Integer;
IY : Integer;
L : Integer;
R : Integer;
H : Integer;
Shift1 : Integer;
S1 : Integer;
S2 : Integer;
S3 : Integer;
S4 : Integer;
SF : Integer;
SFX : Integer;
SFY : Integer;
SFXY : Integer;
Y1 : Double;
Y2 : Double;
Y3 : Double;
Y4 : Double;
V : Double;
T0 : Double;
T1 : Double;
T2 : Double;
T3 : Double;
U0 : Double;
U1 : Double;
U2 : Double;
U3 : Double;
begin
Assert((Round(C[1])=-1) or (Round(C[1])=-3), 'TwoDimensionalInterpolation: incorrect C!');
N := Round(C[2]);
M := Round(C[3]);
//
// Binary search in the [ x[0], ..., x[n-2] ] (x[n-1] is not included)
//
L := 4;
R := 4+N-2+1;
while L<>R-1 do
begin
H := (L+R) div 2;
if C[H]>=X then
begin
R := H;
end
else
begin
L := H;
end;
end;
T := (X-C[L])/(C[L+1]-C[L]);
DT := 1.0/(C[L+1]-C[L]);
IX := L-4;
//
// Binary search in the [ y[0], ..., y[m-2] ] (y[m-1] is not included)
//
L := 4+N;
R := 4+N+(M-2)+1;
while L<>R-1 do
begin
H := (L+R) div 2;
if C[H]>=Y then
begin
R := H;
end
else
begin
L := H;
end;
end;
U := (Y-C[L])/(C[L+1]-C[L]);
DU := 1.0/(C[L+1]-C[L]);
IY := L-(4+N);
//
// Prepare F, dF/dX, dF/dY, d2F/dXdY
//
F := 0;
FX := 0;
FY := 0;
FXY := 0;
//
// Bilinear interpolation
//
if Round(C[1])=-1 then
begin
Shift1 := 4+N+M;
Y1 := C[Shift1+N*IY+IX];
Y2 := C[Shift1+N*IY+(IX+1)];
Y3 := C[Shift1+N*(IY+1)+(IX+1)];
Y4 := C[Shift1+N*(IY+1)+IX];
F := (1-T)*(1-U)*Y1+T*(1-U)*Y2+T*U*Y3+(1-T)*U*Y4;
FX := (-(1-U)*Y1+(1-U)*Y2+U*Y3-U*Y4)*DT;
FY := (-(1-T)*Y1-T*Y2+T*Y3+(1-T)*Y4)*DU;
FXY := (Y1-Y2+Y3-Y4)*DU*DT;
Exit;
end;
//
// Bicubic interpolation
//
if Round(C[1])=-3 then
begin
//
// Prepare info
//
T0 := 1;
T1 := T;
T2 := Sqr(T);
T3 := T*T2;
U0 := 1;
U1 := U;
U2 := Sqr(U);
U3 := U*U2;
SF := 4+N+M;
SFX := 4+N+M+N*M;
SFY := 4+N+M+2*N*M;
SFXY := 4+N+M+3*N*M;
S1 := N*IY+IX;
S2 := N*IY+(IX+1);
S3 := N*(IY+1)+(IX+1);
S4 := N*(IY+1)+IX;
//
// Calculate
//
V := +1*C[SF+S1];
F := F+V*T0*U0;
V := +1*C[SFY+S1]/DU;
F := F+V*T0*U1;
FY := FY+1*V*T0*U0*DU;
V := -3*C[SF+S1]+3*C[SF+S4]-2*C[SFY+S1]/DU-1*C[SFY+S4]/DU;
F := F+V*T0*U2;
FY := FY+2*V*T0*U1*DU;
V := +2*C[SF+S1]-2*C[SF+S4]+1*C[SFY+S1]/DU+1*C[SFY+S4]/DU;
F := F+V*T0*U3;
FY := FY+3*V*T0*U2*DU;
V := +1*C[SFX+S1]/DT;
F := F+V*T1*U0;
FX := FX+1*V*T0*U0*DT;
V := +1*C[SFXY+S1]/(DT*DU);
F := F+V*T1*U1;
FX := FX+1*V*T0*U1*DT;
FY := FY+1*V*T1*U0*DU;
FXY := FXY+1*V*T0*U0*DT*DU;
V := -3*C[SFX+S1]/DT+3*C[SFX+S4]/DT-2*C[SFXY+S1]/(DT*DU)-1*C[SFXY+S4]/(DT*DU);
F := F+V*T1*U2;
FX := FX+1*V*T0*U2*DT;
FY := FY+2*V*T1*U1*DU;
FXY := FXY+2*V*T0*U1*DT*DU;
V := +2*C[SFX+S1]/DT-2*C[SFX+S4]/DT+1*C[SFXY+S1]/(DT*DU)+1*C[SFXY+S4]/(DT*DU);
F := F+V*T1*U3;
FX := FX+1*V*T0*U3*DT;
FY := FY+3*V*T1*U2*DU;
FXY := FXY+3*V*T0*U2*DT*DU;
V := -3*C[SF+S1]+3*C[SF+S2]-2*C[SFX+S1]/DT-1*C[SFX+S2]/DT;
F := F+V*T2*U0;
FX := FX+2*V*T1*U0*DT;
V := -3*C[SFY+S1]/DU+3*C[SFY+S2]/DU-2*C[SFXY+S1]/(DT*DU)-1*C[SFXY+S2]/(DT*DU);
F := F+V*T2*U1;
FX := FX+2*V*T1*U1*DT;
FY := FY+1*V*T2*U0*DU;
FXY := FXY+2*V*T1*U0*DT*DU;
V := +9*C[SF+S1]-9*C[SF+S2]+9*C[SF+S3]-9*C[SF+S4]+6*C[SFX+S1]/DT+3*C[SFX+S2]/DT-3*C[SFX+S3]/DT-6*C[SFX+S4]/DT+6*C[SFY+S1]/DU-6*C[SFY+S2]/DU-3*C[SFY+S3]/DU+3*C[SFY+S4]/DU+4*C[SFXY+S1]/(DT*DU)+2*C[SFXY+S2]/(DT*DU)+1*C[SFXY+S3]/(DT*DU)+2*C[SFXY+S4]/(DT*DU);
F := F+V*T2*U2;
FX := FX+2*V*T1*U2*DT;
FY := FY+2*V*T2*U1*DU;
FXY := FXY+4*V*T1*U1*DT*DU;
V := -6*C[SF+S1]+6*C[SF+S2]-6*C[SF+S3]+6*C[SF+S4]-4*C[SFX+S1]/DT-2*C[SFX+S2]/DT+2*C[SFX+S3]/DT+4*C[SFX+S4]/DT-3*C[SFY+S1]/DU+3*C[SFY+S2]/DU+3*C[SFY+S3]/DU-3*C[SFY+S4]/DU-2*C[SFXY+S1]/(DT*DU)-1*C[SFXY+S2]/(DT*DU)-1*C[SFXY+S3]/(DT*DU)-2*C[SFXY+S4]/(DT*DU);
F := F+V*T2*U3;
FX := FX+2*V*T1*U3*DT;
FY := FY+3*V*T2*U2*DU;
FXY := FXY+6*V*T1*U2*DT*DU;
V := +2*C[SF+S1]-2*C[SF+S2]+1*C[SFX+S1]/DT+1*C[SFX+S2]/DT;
F := F+V*T3*U0;
FX := FX+3*V*T2*U0*DT;
V := +2*C[SFY+S1]/DU-2*C[SFY+S2]/DU+1*C[SFXY+S1]/(DT*DU)+1*C[SFXY+S2]/(DT*DU);
F := F+V*T3*U1;
FX := FX+3*V*T2*U1*DT;
FY := FY+1*V*T3*U0*DU;
FXY := FXY+3*V*T2*U0*DT*DU;
V := -6*C[SF+S1]+6*C[SF+S2]-6*C[SF+S3]+6*C[SF+S4]-3*C[SFX+S1]/DT-3*C[SFX+S2]/DT+3*C[SFX+S3]/DT+3*C[SFX+S4]/DT-4*C[SFY+S1]/DU+4*C[SFY+S2]/DU+2*C[SFY+S3]/DU-2*C[SFY+S4]/DU-2*C[SFXY+S1]/(DT*DU)-2*C[SFXY+S2]/(DT*DU)-1*C[SFXY+S3]/(DT*DU)-1*C[SFXY+S4]/(DT*DU);
F := F+V*T3*U2;
FX := FX+3*V*T2*U2*DT;
FY := FY+2*V*T3*U1*DU;
FXY := FXY+6*V*T2*U1*DT*DU;
V := +4*C[SF+S1]-4*C[SF+S2]+4*C[SF+S3]-4*C[SF+S4]+2*C[SFX+S1]/DT+2*C[SFX+S2]/DT-2*C[SFX+S3]/DT-2*C[SFX+S4]/DT+2*C[SFY+S1]/DU-2*C[SFY+S2]/DU-2*C[SFY+S3]/DU+2*C[SFY+S4]/DU+1*C[SFXY+S1]/(DT*DU)+1*C[SFXY+S2]/(DT*DU)+1*C[SFXY+S3]/(DT*DU)+1*C[SFXY+S4]/(DT*DU);
F := F+V*T3*U3;
FX := FX+3*V*T2*U3*DT;
FY := FY+3*V*T3*U2*DU;
FXY := FXY+9*V*T2*U2*DT*DU;
Exit;
end;
end;
(*************************************************************************
Распаковка сплайна
Входные параметры:
C - массив коэффициентов, вычисленный подпрограммой для
построения билинейного или бикубического сплайна.
Выходные параметры:
M - размер сетки по оси Y
N - размер сетки по оси X
Tbl - таблица коэффициентов сплайна. Массив с нумерацией элементов
[0..(N-1)*(M-1)-1, 0..19]. Каждая строка матрицы соответствует
одной ячейке сетки. Сетка обходится сначала слева направо (т.е.
в порядке возрастания X), затем снизу вверх (т.е. в порядке
возрастания Y).
Формат матрицы:
For I = 0...M-2, J=0..N-2:
K = I*(N-1)+J
Tbl[K,0] = X[j]
Tbl[K,1] = X[j+1]
Tbl[K,2] = Y[i]
Tbl[K,3] = Y[i+1]
Tbl[K,4] = C00
Tbl[K,5] = C01
Tbl[K,6] = C02
Tbl[K,7] = C03
Tbl[K,8] = C10
Tbl[K,9] = C11
...
Tbl[K,19] = C33
На каждой из ячеек сетки сплайн имеет вид:
t = x-x[j]
u = y-y[i]
S(x) = SUM(c[i,j]*(x^i)*(y^j), i=0..3, j=0..3)
-- ALGLIB PROJECT --
Copyright 29.06.2007 by Bochkanov Sergey
*************************************************************************)
procedure SplineUnpack2D(const C : TDDoubleArray;
var M : Integer;
var N : Integer;
var Tbl : TDDouble2Array);
var
I : Integer;
J : Integer;
CI : Integer;
CJ : Integer;
K : Integer;
P : Integer;
Shift : Integer;
S1 : Integer;
S2 : Integer;
S3 : Integer;
S4 : Integer;
SF : Integer;
SFX : Integer;
SFY : Integer;
SFXY : Integer;
Y1 : Double;
Y2 : Double;
Y3 : Double;
Y4 : Double;
DT : Double;
DU : Double;
begin
Assert((Round(C[1])=-3) or (Round(C[1])=-1), 'SplineUnpack2D: incorrect C!');
N := Round(C[2]);
M := Round(C[3]);
SetLength(Tbl, (N-1)*(M-1)-1+1, 19+1);
//
// Fill
//
I:=0;
while I<=M-2 do
begin
J:=0;
while J<=N-2 do
begin
P := I*(N-1)+J;
Tbl[P,0] := C[4+J];
Tbl[P,1] := C[4+J+1];
Tbl[P,2] := C[4+N+I];
Tbl[P,3] := C[4+N+I+1];
DT := 1/(Tbl[P,1]-Tbl[P,0]);
DU := 1/(Tbl[P,3]-Tbl[P,2]);
//
// Bilinear interpolation
//
if Round(C[1])=-1 then
begin
K:=4;
while K<=19 do
begin
Tbl[P,K] := 0;
Inc(K);
end;
Shift := 4+N+M;
Y1 := C[Shift+N*I+J];
Y2 := C[Shift+N*I+(J+1)];
Y3 := C[Shift+N*(I+1)+(J+1)];
Y4 := C[Shift+N*(I+1)+J];
Tbl[P,4] := Y1;
Tbl[P,4+1*4+0] := Y2-Y1;
Tbl[P,4+0*4+1] := Y4-Y1;
Tbl[P,4+1*4+1] := Y3-Y2-Y4+Y1;
end;
//
// Bicubic interpolation
//
if Round(C[1])=-3 then
begin
SF := 4+N+M;
SFX := 4+N+M+N*M;
SFY := 4+N+M+2*N*M;
SFXY := 4+N+M+3*N*M;
S1 := N*I+J;
S2 := N*I+(J+1);
S3 := N*(I+1)+(J+1);
S4 := N*(I+1)+J;
Tbl[P,4+0*4+0] := +1*C[SF+S1];
Tbl[P,4+0*4+1] := +1*C[SFY+S1]/DU;
Tbl[P,4+0*4+2] := -3*C[SF+S1]+3*C[SF+S4]-2*C[SFY+S1]/DU-1*C[SFY+S4]/DU;
Tbl[P,4+0*4+3] := +2*C[SF+S1]-2*C[SF+S4]+1*C[SFY+S1]/DU+1*C[SFY+S4]/DU;
Tbl[P,4+1*4+0] := +1*C[SFX+S1]/DT;
Tbl[P,4+1*4+1] := +1*C[SFXY+S1]/(DT*DU);
Tbl[P,4+1*4+2] := -3*C[SFX+S1]/DT+3*C[SFX+S4]/DT-2*C[SFXY+S1]/(DT*DU)-1*C[SFXY+S4]/(DT*DU);
Tbl[P,4+1*4+3] := +2*C[SFX+S1]/DT-2*C[SFX+S4]/DT+1*C[SFXY+S1]/(DT*DU)+1*C[SFXY+S4]/(DT*DU);
Tbl[P,4+2*4+0] := -3*C[SF+S1]+3*C[SF+S2]-2*C[SFX+S1]/DT-1*C[SFX+S2]/DT;
Tbl[P,4+2*4+1] := -3*C[SFY+S1]/DU+3*C[SFY+S2]/DU-2*C[SFXY+S1]/(DT*DU)-1*C[SFXY+S2]/(DT*DU);
Tbl[P,4+2*4+2] := +9*C[SF+S1]-9*C[SF+S2]+9*C[SF+S3]-9*C[SF+S4]+6*C[SFX+S1]/DT+3*C[SFX+S2]/DT-3*C[SFX+S3]/DT-6*C[SFX+S4]/DT+6*C[SFY+S1]/DU-6*C[SFY+S2]/DU-3*C[SFY+S3]/DU+3*C[SFY+S4]/DU+4*C[SFXY+S1]/(DT*DU)+2*C[SFXY+S2]/(DT*DU)+1*C[SFXY+S3]/(DT*DU)+2*C[SFXY+S4]/(DT*DU);
Tbl[P,4+2*4+3] := -6*C[SF+S1]+6*C[SF+S2]-6*C[SF+S3]+6*C[SF+S4]-4*C[SFX+S1]/DT-2*C[SFX+S2]/DT+2*C[SFX+S3]/DT+4*C[SFX+S4]/DT-3*C[SFY+S1]/DU+3*C[SFY+S2]/DU+3*C[SFY+S3]/DU-3*C[SFY+S4]/DU-2*C[SFXY+S1]/(DT*DU)-1*C[SFXY+S2]/(DT*DU)-1*C[SFXY+S3]/(DT*DU)-2*C[SFXY+S4]/(DT*DU);
Tbl[P,4+3*4+0] := +2*C[SF+S1]-2*C[SF+S2]+1*C[SFX+S1]/DT+1*C[SFX+S2]/DT;
Tbl[P,4+3*4+1] := +2*C[SFY+S1]/DU-2*C[SFY+S2]/DU+1*C[SFXY+S1]/(DT*DU)+1*C[SFXY+S2]/(DT*DU);
Tbl[P,4+3*4+2] := -6*C[SF+S1]+6*C[SF+S2]-6*C[SF+S3]+6*C[SF+S4]-3*C[SFX+S1]/DT-3*C[SFX+S2]/DT+3*C[SFX+S3]/DT+3*C[SFX+S4]/DT-4*C[SFY+S1]/DU+4*C[SFY+S2]/DU+2*C[SFY+S3]/DU-2*C[SFY+S4]/DU-2*C[SFXY+S1]/(DT*DU)-2*C[SFXY+S2]/(DT*DU)-1*C[SFXY+S3]/(DT*DU)-1*C[SFXY+S4]/(DT*DU);
Tbl[P,4+3*4+3] := +4*C[SF+S1]-4*C[SF+S2]+4*C[SF+S3]-4*C[SF+S4]+2*C[SFX+S1]/DT+2*C[SFX+S2]/DT-2*C[SFX+S3]/DT-2*C[SFX+S4]/DT+2*C[SFY+S1]/DU-2*C[SFY+S2]/DU-2*C[SFY+S3]/DU+2*C[SFY+S4]/DU+1*C[SFXY+S1]/(DT*DU)+1*C[SFXY+S2]/(DT*DU)+1*C[SFXY+S3]/(DT*DU)+1*C[SFXY+S4]/(DT*DU);
end;
//
// Rescale Cij
//
CI:=0;
while CI<=3 do
begin
CJ:=0;
while CJ<=3 do
begin
Tbl[P,4+CI*4+CJ] := Tbl[P,4+CI*4+CJ]*Power(DT, CI)*Power(DU, CJ);
Inc(CJ);
end;
Inc(CI);
end;
Inc(J);
end;
Inc(I);
end;
end;
(*************************************************************************
Линейная замена аргумента двухмерного сплайна
Входные параметры:
C - массив коэффициентов, вычисленный подпрограммой для
построения сплайна S(x).
AX, BX - коэффициенты преобразования x = A*t + B
AY, BY - коэффициенты преобразования y = A*u + B
Выходные параметры:
C - преобразованный сплайн
-- ALGLIB PROJECT --
Copyright 30.06.2007 by Bochkanov Sergey
*************************************************************************)
procedure Spline2DLinTransXY(var C : TDDoubleArray;
AX : Double;
BX : Double;
AY : Double;
BY : Double);
var
I : Integer;
J : Integer;
N : Integer;
M : Integer;
V : Double;
X : TDDoubleArray;
Y : TDDoubleArray;
F : TDDouble2Array;
TypeC : Integer;
begin
TypeC := Round(C[1]);
Assert((TypeC=-3) or (TypeC=-1), 'Spline2DLinTransXY: incorrect C!');
N := Round(C[2]);
M := Round(C[3]);
SetLength(X, N-1+1);
SetLength(Y, M-1+1);
SetLength(F, M-1+1, N-1+1);
J:=0;
while J<=N-1 do
begin
X[J] := C[4+J];
Inc(J);
end;
I:=0;
while I<=M-1 do
begin
Y[I] := C[4+N+I];
Inc(I);
end;
I:=0;
while I<=M-1 do
begin
J:=0;
while J<=N-1 do
begin
F[I,J] := C[4+N+M+I*N+J];
Inc(J);
end;
Inc(I);
end;
//
// Special case: AX=0 or AY=0
//
if AX=0 then
begin
I:=0;
while I<=M-1 do
begin
V := SplineInterpolation2D(C, BX, Y[I]);
J:=0;
while J<=N-1 do
begin
F[I,J] := V;
Inc(J);
end;
Inc(I);
end;
if TypeC=-3 then
begin
BuildBicubicSpline(X, Y, F, M, N, C);
end;
if TypeC=-1 then
begin
BuildBilinearSpline(X, Y, F, M, N, C);
end;
AX := 1;
BX := 0;
end;
if AY=0 then
begin
J:=0;
while J<=N-1 do
begin
V := SplineInterpolation2D(C, X[J], BY);
I:=0;
while I<=M-1 do
begin
F[I,J] := V;
Inc(I);
end;
Inc(J);
end;
if TypeC=-3 then
begin
BuildBicubicSpline(X, Y, F, M, N, C);
end;
if TypeC=-1 then
begin
BuildBilinearSpline(X, Y, F, M, N, C);
end;
AY := 1;
BY := 0;
end;
//
// General case: AX<>0, AY<>0
// Unpack, scale and pack again.
//
J:=0;
while J<=N-1 do
begin
X[J] := (X[J]-BX)/AX;
Inc(J);
end;
I:=0;
while I<=M-1 do
begin
Y[I] := (Y[I]-BY)/AY;
Inc(I);
end;
if TypeC=-3 then
begin
BuildBicubicSpline(X, Y, F, M, N, C);
end;