Calculate the affine transform matrix from 3 point correspondance in Objective-C (with Accelerate framework for LAPACK matrix inverse)

matrix_invert.c

//
//  matrix_invert.c
//  
//
//  Created by Xiaochao Yang on 6/11/13.
//  Copyright (c) 2013 Xiaochao Yang. All rights reserved.
//

#import <Accelerate/Accelerate.h>
#include <stdlib.h>

int matrix_invert(long N, double *matrix) {
    long error=0;
    long *pivot = malloc(N*N*sizeof(long));
    double *workspace = malloc(N*sizeof(double));
    
    dgetrf_(&N, &N, matrix, &N, pivot, &error);
    
    if (error == 0) {
        dgetri_(&N, matrix, &N, pivot, workspace, &N, &error);
    }
    
    free(pivot);
    free(workspace);
    return error;
}

matrix_invert.h

//
//  matrix_invert.h
//  
//
//  Created by Xiaochao Yang on 6/11/13.
//  Copyright (c) 2013 Xiaochao Yang. All rights reserved.
//

#ifndef TMC_matrix_invert_h
#define TMC_matrix_invert_h

int matrix_invert(long N, double *matrix)

#endif

TransformFromPointCorrespondence.m

CGPoint p1, p2, p3, q1, q2, q3;

// TODO: initialize points

double A[36];

A[ 0] = p1.x; A[ 1] = p1.y; A[ 2] = 0; A[ 3] = 0; A[ 4] = 1; A[ 5] = 0;
A[ 6] = 0; A[ 7] = 0; A[ 8] = p1.x; A[ 9] = p1.y; A[10] = 0; A[11] = 1;
A[12] = p2.x; A[13] = p2.y; A[14] = 0; A[15] = 0; A[16] = 1; A[17] = 0;
A[18] = 0; A[19] = 0; A[20] = p2.x; A[21] = p2.y; A[22] = 0; A[23] = 1;
A[24] = p3.x; A[25] = p3.y; A[26] = 0; A[27] = 0; A[28] = 1; A[29] = 0;
A[30] = 0; A[31] = 0; A[32] = p3.x; A[33] = p3.y; A[34] = 0; A[35] = 1;

int err = matrix_invert(6, A);
assert(err == 0);

double B[6];

B[0] = q1.x; B[1] = q1.y; B[2] = q2.x; B[3] = q2.y; B[4] = q3.x; B[5] = q3.y;

double M[6];

M[0] = A[ 0] * B[0] + A[ 1] * B[1] + A[ 2] * B[2] + A[ 3] * B[3] + A[ 4] * B[4] + A[ 5] * B[5];
M[1] = A[ 6] * B[0] + A[ 7] * B[1] + A[ 8] * B[2] + A[ 9] * B[3] + A[10] * B[4] + A[11] * B[5];
M[2] = A[12] * B[0] + A[13] * B[1] + A[14] * B[2] + A[15] * B[3] + A[16] * B[4] + A[17] * B[5];
M[3] = A[18] * B[0] + A[19] * B[1] + A[20] * B[2] + A[21] * B[3] + A[22] * B[4] + A[23] * B[5];
M[4] = A[24] * B[0] + A[25] * B[1] + A[26] * B[2] + A[27] * B[3] + A[28] * B[4] + A[29] * B[5];
M[5] = A[30] * B[0] + A[31] * B[1] + A[32] * B[2] + A[33] * B[3] + A[34] * B[4] + A[35] * B[5];

NSLog(@"%f, %f, %f, %f, %f, %f", M[0], M[1], M[2], M[3], M[4], M[5]);

CGAffineTransform transform = CGAffineTransformMake(M[0], M[2], M[1], M[3], M[4], M[5]); // Order is correct...

Many thanks for sharing..
it's seems that images get "warped" with this functions... for three points I guess we should get done with rotation, translation and scaling without getting any warp effect ?