Convert Mat to Array/Vector in OpenCV - c++

I am novice in OpenCV. Recently, I have troubles finding OpenCV functions to convert from Mat to Array. I researched with .ptr and .at methods available in OpenCV APIs, but I could not get proper data. I would like to have direct conversion from Mat to Array(if available, if not to Vector). I need OpenCV functions because the code has to be undergo high level synthesis in Vivado HLS. Please help.

If the memory of the Mat mat is continuous (all its data is continuous), you can directly get its data to a 1D array:
std::vector<uchar> array(mat.rows*mat.cols*mat.channels());
if (mat.isContinuous())
array = mat.data;
Otherwise, you have to get its data row by row, e.g. to a 2D array:
uchar **array = new uchar*[mat.rows];
for (int i=0; i<mat.rows; ++i)
array[i] = new uchar[mat.cols*mat.channels()];
for (int i=0; i<mat.rows; ++i)
array[i] = mat.ptr<uchar>(i);
UPDATE: It will be easier if you're using std::vector, where you can do like this:
std::vector<uchar> array;
if (mat.isContinuous()) {
// array.assign(mat.datastart, mat.dataend); // <- has problems for sub-matrix like mat = big_mat.row(i)
array.assign(mat.data, mat.data + mat.total()*mat.channels());
} else {
for (int i = 0; i < mat.rows; ++i) {
array.insert(array.end(), mat.ptr<uchar>(i), mat.ptr<uchar>(i)+mat.cols*mat.channels());
}
}
p.s.: For cv::Mats of other types, like CV_32F, you should do like this:
std::vector<float> array;
if (mat.isContinuous()) {
// array.assign((float*)mat.datastart, (float*)mat.dataend); // <- has problems for sub-matrix like mat = big_mat.row(i)
array.assign((float*)mat.data, (float*)mat.data + mat.total()*mat.channels());
} else {
for (int i = 0; i < mat.rows; ++i) {
array.insert(array.end(), mat.ptr<float>(i), mat.ptr<float>(i)+mat.cols*mat.channels());
}
}
UPDATE2: For OpenCV Mat data continuity, it can be summarized as follows:
Matrices created by imread(), clone(), or a constructor will always be continuous.
The only time a matrix will not be continuous is when it borrows data (except the data borrowed is continuous in the big matrix, e.g. 1. single row; 2. multiple rows with full original width) from an existing matrix (i.e. created out of an ROI of a big mat).
Please check out this code snippet for demonstration.

Can be done in two lines :)
Mat to array
uchar * arr = image.isContinuous()? image.data: image.clone().data;
uint length = image.total()*image.channels();
Mat to vector
cv::Mat flat = image.reshape(1, image.total()*image.channels());
std::vector<uchar> vec = image.isContinuous()? flat : flat.clone();
Both work for any general cv::Mat.
Explanation with a working example
cv::Mat image;
image = cv::imread(argv[1], cv::IMREAD_UNCHANGED); // Read the file
cv::namedWindow("cvmat", cv::WINDOW_AUTOSIZE );// Create a window for display.
cv::imshow("cvmat", image ); // Show our image inside it.
// flatten the mat.
uint totalElements = image.total()*image.channels(); // Note: image.total() == rows*cols.
cv::Mat flat = image.reshape(1, totalElements); // 1xN mat of 1 channel, O(1) operation
if(!image.isContinuous()) {
flat = flat.clone(); // O(N),
}
// flat.data is your array pointer
auto * ptr = flat.data; // usually, its uchar*
// You have your array, its length is flat.total() [rows=1, cols=totalElements]
// Converting to vector
std::vector<uchar> vec(flat.data, flat.data + flat.total());
// Testing by reconstruction of cvMat
cv::Mat restored = cv::Mat(image.rows, image.cols, image.type(), ptr); // OR vec.data() instead of ptr
cv::namedWindow("reconstructed", cv::WINDOW_AUTOSIZE);
cv::imshow("reconstructed", restored);
cv::waitKey(0);
Extended explanation:
Mat is stored as a contiguous block of memory, if created using one of its constructors or when copied to another Mat using clone() or similar methods. To convert to an array or vector we need the address of its first block and array/vector length.
Pointer to internal memory block
Mat::data is a public uchar pointer to its memory.
But this memory may not be contiguous. As explained in other answers, we can check if mat.data is pointing to contiguous memory or not using mat.isContinous(). Unless you need extreme efficiency, you can obtain a continuous version of the mat using mat.clone() in O(N) time. (N = number of elements from all channels). However, when dealing images read by cv::imread() we will rarely ever encounter a non-continous mat.
Length of array/vector
Q: Should be row*cols*channels right?
A: Not always. It can be rows*cols*x*y*channels.
Q: Should be equal to mat.total()?
A: True for single channel mat. But not for multi-channel mat
Length of the array/vector is slightly tricky because of poor documentation of OpenCV. We have Mat::size public member which stores only the dimensions of single Mat without channels. For RGB image, Mat.size = [rows, cols] and not [rows, cols, channels]. Mat.total() returns total elements in a single channel of the mat which is equal to product of values in mat.size. For RGB image, total() = rows*cols. Thus, for any general Mat, length of continuous memory block would be mat.total()*mat.channels().
Reconstructing Mat from array/vector
Apart from array/vector we also need the original Mat's mat.size [array like] and mat.type() [int]. Then using one of the constructors that take data's pointer, we can obtain original Mat. The optional step argument is not required because our data pointer points to continuous memory. I used this method to pass Mat as Uint8Array between nodejs and C++. This avoided writing C++ bindings for cv::Mat with node-addon-api.
References:
Create memory continuous Mat
OpenCV Mat data layout
Mat from array

Here is another possible solution assuming matrix have one column( you can reshape original Mat to one column Mat via reshape):
Mat matrix= Mat::zeros(20, 1, CV_32FC1);
vector<float> vec;
matrix.col(0).copyTo(vec);

None of the provided examples here work for the generic case, which are N dimensional matrices. Anything using "rows" assumes theres columns and rows only, a 4 dimensional matrix might have more.
Here is some example code copying a non-continuous N-dimensional matrix into a continuous memory stream - then converts it back into a Cv::Mat
#include <iostream>
#include <cstdint>
#include <cstring>
#include <opencv2/opencv.hpp>
int main(int argc, char**argv)
{
if ( argc != 2 )
{
std::cerr << "Usage: " << argv[0] << " <Image_Path>\n";
return -1;
}
cv::Mat origSource = cv::imread(argv[1],1);
if (!origSource.data) {
std::cerr << "Can't read image";
return -1;
}
// this will select a subsection of the original source image - WITHOUT copying the data
// (the header will point to a region of interest, adjusting data pointers and row step sizes)
cv::Mat sourceMat = origSource(cv::Range(origSource.size[0]/4,(3*origSource.size[0])/4),cv::Range(origSource.size[1]/4,(3*origSource.size[1])/4));
// correctly copy the contents of an N dimensional cv::Mat
// works just as fast as copying a 2D mat, but has much more difficult to read code :)
// see http://stackoverflow.com/questions/18882242/how-do-i-get-the-size-of-a-multi-dimensional-cvmat-mat-or-matnd
// copy this code in your own cvMat_To_Char_Array() function which really OpenCV should provide somehow...
// keep in mind that even Mat::clone() aligns each row at a 4 byte boundary, so uneven sized images always have stepgaps
size_t totalsize = sourceMat.step[sourceMat.dims-1];
const size_t rowsize = sourceMat.step[sourceMat.dims-1] * sourceMat.size[sourceMat.dims-1];
size_t coordinates[sourceMat.dims-1] = {0};
std::cout << "Image dimensions: ";
for (int t=0;t<sourceMat.dims;t++)
{
// calculate total size of multi dimensional matrix by multiplying dimensions
totalsize*=sourceMat.size[t];
std::cout << (t>0?" X ":"") << sourceMat.size[t];
}
// Allocate destination image buffer
uint8_t * imagebuffer = new uint8_t[totalsize];
size_t srcptr=0,dptr=0;
std::cout << std::endl;
std::cout << "One pixel in image has " << sourceMat.step[sourceMat.dims-1] << " bytes" <<std::endl;
std::cout << "Copying data in blocks of " << rowsize << " bytes" << std::endl ;
std::cout << "Total size is " << totalsize << " bytes" << std::endl;
while (dptr<totalsize) {
// we copy entire rows at once, so lowest iterator is always [dims-2]
// this is legal since OpenCV does not use 1 dimensional matrices internally (a 1D matrix is a 2d matrix with only 1 row)
std::memcpy(&imagebuffer[dptr],&(((uint8_t*)sourceMat.data)[srcptr]),rowsize);
// destination matrix has no gaps so rows follow each other directly
dptr += rowsize;
// src matrix can have gaps so we need to calculate the address of the start of the next row the hard way
// see *brief* text in opencv2/core/mat.hpp for address calculation
coordinates[sourceMat.dims-2]++;
srcptr = 0;
for (int t=sourceMat.dims-2;t>=0;t--) {
if (coordinates[t]>=sourceMat.size[t]) {
if (t==0) break;
coordinates[t]=0;
coordinates[t-1]++;
}
srcptr += sourceMat.step[t]*coordinates[t];
}
}
// this constructor assumes that imagebuffer is gap-less (if not, a complete array of step sizes must be given, too)
cv::Mat destination=cv::Mat(sourceMat.dims, sourceMat.size, sourceMat.type(), (void*)imagebuffer);
// and just to proof that sourceImage points to the same memory as origSource, we strike it through
cv::line(sourceMat,cv::Point(0,0),cv::Point(sourceMat.size[1],sourceMat.size[0]),CV_RGB(255,0,0),3);
cv::imshow("original image",origSource);
cv::imshow("partial image",sourceMat);
cv::imshow("copied image",destination);
while (cv::waitKey(60)!='q');
}

Instead of getting image row by row, you can put it directly to an array. For CV_8U type image, you can use byte array, for other types check here.
Mat img; // Should be CV_8U for using byte[]
int size = (int)img.total() * img.channels();
byte[] data = new byte[size];
img.get(0, 0, data); // Gets all pixels

byte * matToBytes(Mat image)
{
int size = image.total() * image.elemSize();
byte * bytes = new byte[size]; //delete[] later
std::memcpy(bytes,image.data,size * sizeof(byte));
}

You can use iterators:
Mat matrix = ...;
std::vector<float> vec(matrix.begin<float>(), matrix.end<float>());

cv::Mat m;
m.create(10, 10, CV_32FC3);
float *array = (float *)malloc( 3*sizeof(float)*10*10 );
cv::MatConstIterator_<cv::Vec3f> it = m.begin<cv::Vec3f>();
for (unsigned i = 0; it != m.end<cv::Vec3f>(); it++ ) {
for ( unsigned j = 0; j < 3; j++ ) {
*(array + i ) = (*it)[j];
i++;
}
}
Now you have a float array. In case of 8 bit, simply change float to uchar, Vec3f to Vec3b and CV_32FC3 to CV_8UC3.

If you know that your img is 3 channel, than you can try this code
Vec3b* dados = new Vec3b[img.rows*img.cols];
for (int i = 0; i < img.rows; i++)
for(int j=0;j<img.cols; j++)
dados[3*i*img.cols+j] =img.at<Vec3b>(i,j);
If you wanna check the (i,j) vec3b you can write
std::cout << (Vec3b)img.at<Vec3b>(i,j) << std::endl;
std::cout << (Vec3b)dados[3*i*img.cols+j] << std::endl;

Since answer above is not very accurate as mentioned in its comments but its "edit queue is full", I have to add correct one-liners.
Mat(uchar, 1 channel) to vector(uchar):
std::vector<uchar> vec = (image.isContinuous() ? image : image.clone()).reshape(1, 1); // data copy here
vector(any type) to Mat(the same type):
Mat m(vec, false); // false(by default) -- do not copy data

Related

Read a 3D Dicom image with DCMTK and convert it to OpenCV Mat

I have a dicom 3D image which is [512,512,5] (rows, cols, slices). I want to read it with DCMTK toolkit and convert it to a OpenCV Mat object. The image is 16 bits unsigned int.
My question is: Does anyone know the correct way to convert this dicom image into a Mat object? How to properly read all the slices with the method getOutputData?
Based on the comments of #Alan Birtles, there is the possibility to specify the frame you want to read on the getOutputData method. After reading each frame, you simply merge the Mat objects into a single Mat.
I wrote this code to get the whole volume:
DicomImage *image = new DicomImage(file);
// Get the information
unsigned int nRows = image->getHeight();
unsigned int nCols = image->getWidth();
unsigned int nImgs = image->getFrameCount();
vector <Mat> slices(nImgs);
// Loop for each slice
for(int k = 0; k<nImgs; k++){
(Uint16 *) pixelData = (Uint16 *)(image->getOutputData(16 /* bits */,k /* slice */));
slices[k] = Mat(nRows, nCols, CV_16U, pixelData).clone();
}
Mat img;
// Merge the slices in a single img
merge(slices,img);
cout << img.size() << endl;
cout << img.channels() << endl;
// Output:
// [512 x 512]
// 5

OpenCV reduce() Array to vector average

Using OpenCV 3.4.1 in C++ I have a 2 dimensional Mat array object. These first few lines just explain essentially how the data are obtained to fill this Mat object ("dat")
int rows=NUMBER_OF_ROWS;
int cols=NUMBER_OF_COLS;
float* rawdata;
rawdata = new float[rows*cols];
fits_read_img(FP, TFLOAT, firstpixel, npixels, &nullval, rawdata, &anynull, &status);
Then creation of the Mat object from the raw data looks like this:
cv::Mat dat = cv::Mat(rows, cols, CV_32FC1, rawdata);
So far, so good, and I've used this Mat object "dat" for many things. But now I want to create a row average of the data. That should give me a rows x 1 vector, with every column of each row reduced into a single value, the average of all the values in that row. Something like this:
So OpenCV has a reduce() function. Here is how I've tried calling it:
std::vector<float> vec(rows);
cv::reduce(dat, vec, 1, cv::REDUCE_AVG, CV_32FC1);
which segfaults. If I go the other direction, I.E.
cv::reduce(dat, vec, 0, cv::REDUCE_AVG, CV_32FC1);
then I get a 1 x cols vector containing a column average. In fact, it gives me the exact equivalent of this:
int r, c;
float sum;
for (c=0; c<cols; c++) {
sum=0;
for (r=0; r<rows; r++) {
sum += dat.at<float>(r,c);
}
std::cout << "sum=" << ss << " avg=" << ss/r << std::endl;
}
So I could certainly use a brute-force method like this to get the row average that I want, but it seems I ought to be able to get it with a single cv::reduce() call.
What am I missing?

OpenCV 3 C++ Mat fetching with pointer goes random

I'm quite new to OpenCV and I'm now using version 3.4.1 with C++ implementation. I'm still exploring, so this question is not specific to a project, but is more of a "try to understand how it works". Please consider, with the same idea in mind, that I know that I'm somehow "reinventing the will" with this code, but I wrote this example to understand "HOW IT WORKS".
The idea is:
Read an RGB image
Make it binary
Find Connected areas
Colour each area differently
As an example I'm using a 5x5 pixel RGB image saved as BMP. The image is a white box with black pixels all around it's contour.
Up to the point where I get the ConnectedComponents matrix, named Mat::Labels, it all goes fine. If I print the Matrix I see exactly what I expect:
11111
10001
10001
10001
11111
Remember that I've inverted the threshold so it is correct to get 1 on the edges...
I then create a Mat with same size of Mat::Labels but 3 channels to colour it with RGB. This is named Mat::ColoredLabels.
Next step is to instanciate a pointer that runs through the Mat::Labels and for each position in the Mat::Labels where the value is 1 fill the corresponding Mat:.ColoredLabels position with a color.
HERE THINGS GOT VERY WRONG ! The pointer does not fetch the Mat::Labels row byt row as I would expect but follows some other order.
Questions:
Am I doing something wrong or it is "obvious" that the pointer fetching follows some "umpredictable" order ?
How could I set values of a Matrix (Mat::ColoredLabels) based on the values of another matrix (Mat::Labels) ?
.
#include "opencv2\highgui.hpp"
#include "opencv2\opencv.hpp"
#include <stdio.h>
using namespace cv;
int main(int argc, char *argv[]) {
char* FilePath = "";
Mat Img;
Mat ImgGray;
Mat ImgBinary;
Mat Labels;
uchar *P;
uchar *CP;
// Image acquisition
if (argc < 2) {
printf("Missing argument");
return -1;
}
FilePath = argv[1];
Img = imread(FilePath, CV_LOAD_IMAGE_COLOR);
if (Img.empty()) {
printf("Invalid image");
return -1;
}
// Convert to Gray...I know I could convert it right away while loading....
cvtColor(Img, ImgGray, CV_RGB2GRAY);
// Threshold (inverted) to obtain black background and white blobs-> it works
threshold(ImgGray, ImgBinary, 170, 255, CV_THRESH_BINARY_INV);
// Find Connected Components and put the 1/0 result in Mat::Labels
int BlobsNum = connectedComponents(ImgBinary, Labels, 8, CV_16U);
// Just to see what comes out with a 5x5 image. I get:
// 11111
// 10001
// 10001
// 10001
// 11111
std::cout << Labels << "\n";
// Prepare to fetch the Mat(s) with pointer to be fast
int nRows = Labels.rows;
int nCols = Labels.cols * Labels.channels();
if (Labels.isContinuous()) {
nCols *= nRows;
nRows = 1;
}
// Prepare a Mat as big as LAbels but with 3 channels to color different blobs
Mat ColoredLabels(Img.rows, Img.cols, CV_8UC3, cv::Scalar(127, 127, 127));
int ColoredLabelsNumChannels = ColoredLabels.channels();
// Fetch Mat::Labels and Mat::ColoredLabes with the same for cycle...
for (int i = 0; i < nRows; i++) {
// !!! HERE SOMETHING GOES WRONG !!!!
P = Labels.ptr<uchar>(i);
CP = ColoredLabels.ptr<uchar>(i);
for (int j = 0; j < nCols; j++) {
// The coloring operation does not work
if (P[j] > 0) {
CP[j*ColoredLabelsNumChannels] = 0;
CP[j*ColoredLabelsNumChannels + 1] = 0;
CP[j*ColoredLabelsNumChannels + 2] = 255;
}
}
}
std::cout << "\n" << ColoredLabels << "\n";
namedWindow("ColoredLabels", CV_WINDOW_NORMAL);
imshow("ColoredLabels", ColoredLabels);
waitKey(0);
printf("Execution completed succesfully");
return 0;
}
You used connectedComponents function with CV_16U parameter. This means that the single element of the image will consist of 16 bits (hence '16') and you have to interpret them as unsigned integer (hence 'U'). And since ptr returns a pointer, you have to dereference it to get the value.
Therefore you should access label image elements in the following way:
unsigned short val = *Labels.ptr<unsigned short>(i) // or uint16_t
unsigned short val = Labels.at<unsigned short>.at(y, x);
Regarding your second question, it is as simple as that, but of course you have to understand which type casts result in loss of precisions or overflows and which ones not.
mat0.at<int>(y, x) = mat1.at<int>(y, x); // both matrices have CV_32S types
mat2.at<int>(y, x) = mat3.at<char>(y,x); // CV_32S and CV_8S
// Implicit cast occurs. Possible information loss: assigning 32-bit integer values to 8-bit ints
// mat4.at<unsigned char>(y, x) = mat5.at<unsigned int>(y, x); // CV_8U and CV_32U

Getting the difference between two frames in opencv

I'm trying to get the the difference between two cv::Mat frames in OpenCv. So here is what I tried,
#include<opencv2\opencv.hpp>
#include<opencv2\calib3d\calib3d.hpp>
#include<opencv2\core\core.hpp>
#include <opencv2\highgui\highgui.hpp>
int main ()
{
cv::VideoCapture cap(0);
cv::Mat frame, frame1,frame2;
int key=0;
while(key!=27){
cap >> frame;
if(key=='c'){
frame1 = frame;
key = 0;
}
if(key =='x'){
cv::absdiff(frame, frame1, frame2); // I also tried frame2= (frame -frame1)*255;
cv::imshow("difference ",frame2);
key =0;
}
cv::imshow("stream",frame);
key = cv::waitKey(10);
}
}
the result is always the same a 0 Matrix, any idea what I'm doing wrong here?
thanks in advance for your help.
Mat objects are pointer typed. After setting frame1 to frame directly using frame1 = frame, both matrices show the same point and same frame also. You have to copy frame value using "copyTo" method of Mat.
OpenCV Matrixes use pointers internally
The documentation of the Mat type states:
Mat is basically a class with two data parts: the matrix header and a pointer to the matrix containing the pixel values.
[...]
Whenever somebody copies a header of a Mat object, a counter is increased for the matrix. Whenever a header is cleaned this counter is decreased. When the counter reaches zero the matrix too is freed. Sometimes you will want to copy the matrix itself too, so OpenCV provides the clone() and copyTo() functions.
cv::Mat F = A.clone();
cv::Mat G;
A.copyTo(G);
OpenCV overloads the affectation operator on cv::Mat objects so that the line mat1 = mat2 only affects the pointer to the data in mat1 (that points to the same data as mat2). This avoids time consuming copies of all the image data.
If you want to save the data of a matrix, you have to write mat1 = mat2.clone() or mat2.copyTo(mat1).
I was looking for a similar program and I came across your post, here is a sample I have written for frameDifferencing, hope this helps, the below function will give you the difference between two frames
/** #function differenceFrame */
Mat differenceFrame( Mat prev_frame, Mat curr_frame )
{
Mat image = prev_frame.clone();
printf("frame rows %d Cols %d\n" , image.rows, image.cols);
for (int rows = 0; rows < image.rows; rows++)
{
for (int cols = 0; cols < image.cols; cols++)
{
/* printf("BGR value %lf %lf %lf\n" , abs(prev_frame.at<cv::Vec3b>(rows,cols)[0] -
curr_frame.at<cv::Vec3b>(rows,cols)[0]),
abs(prev_frame.at<cv::Vec3b>(rows,cols)[1] -
curr_frame.at<cv::Vec3b>(rows,cols)[0]),
abs(prev_frame.at<cv::Vec3b>(rows,cols)[2] -
curr_frame.at<cv::Vec3b>(rows,cols)[0]));
*/
image.at<cv::Vec3b>(rows,cols)[0] = abs(prev_frame.at<cv::Vec3b>(rows,cols)[0] -
curr_frame.at<cv::Vec3b>(rows,cols)[0]);
image.at<cv::Vec3b>(rows,cols)[1] = abs(prev_frame.at<cv::Vec3b>(rows,cols)[1] -
curr_frame.at<cv::Vec3b>(rows,cols)[1]);
image.at<cv::Vec3b>(rows,cols)[2] = abs(prev_frame.at<cv::Vec3b>(rows,cols)[2] -
curr_frame.at<cv::Vec3b>(rows,cols)[2]);
}
}
return image;
}

How do you force the type of data in a cv::Mat to be float upon creation?

When iterating through a cv::Mat to output all of its values, you could do the following:
for (int r = 0; r < t.rows; r++)
{
for (int c = 0; c < t.cols; c++)
{
std::cout << t.at<float>(r,c) << ", ";
}
std::cout << std::endl << std::endl;
}
However, if the information stored in that array is not of type float, this will crash. How do you enforce the type of this matrix?
for 2 Mats nonFloatMat and floatMat when the first is the source matrix and the last is the destination matrix do
nonFloatMat.convertTo(floatMat, CV_32F); //if its a color image use CV_32FC3, or
// CV_32FC4 if its RGBA
convertTo's reference can be found here.
Edit:
and by the way, the code will work if you'll change the float to the correct concrete type of the matrix ie if the mat is a CV_8U you can do t.at<char>(r,c) etc.
While Boaz correctly answers your questions, converting your matrix adds a new problem Your function will allocate some new memory, will convert data, and then will perform calculations.
This adds a significant overhead for your function. The solution is to make a branch for every data type you suppose to support. This is the way OpenCV handles multiple data types (of course, it's a bit smarter than if-else)
if(mat.type()==CV_32FC1)
{
}
else if(mat.type()==CV_32FC3)
{
}
else if(mat.type()==CV_8UC3)
{
}
...
another solution, if your only aim is to print the matrix is
cout << myMat << endl;
Isn't it great?
You can also do this with the template wrapper class called Mat_.
So, to "force" the type of the matrix to float you could do the following:
Mat_<float> A(100, 100);
Also, another way to ensure a matrix is of a certain type (this is done quite a bit in the OpenCV source) is to use an assertion.
Like this:
void functionOnlyUsesFloatMats(const Mat& src)
{
CV_Assert( src.type() == CV_32FC1 );
// now you can be assured that only single-channel float matrices reach this code...
}
Or, you could check the type before proceeding, and convert if needed:
Mat floatMat;
if(src.type() != CV_32FC1)
{
src.convertTo(floatMat, CV_32F);
}
else
{
floatMat = src;
}
// proceed with float calculations...