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Calculate the affine transform matrix from 3 point correspondance in Objective-C (with Accelerate framework for LAPACK matrix inverse)
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// | |
// 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; | |
} |
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// | |
// 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 |
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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... |
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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 ?