Need help reducing an equation, math wiz's welcome. =)

This is a discussion on Need help reducing an equation, math wiz's welcome. =) within the C++ Programming forums, part of the General Programming Boards category; Heya guys, I've been busy! I've been cranking out simple 3D C++ apps that my girlfriend's kids love. I made ...

  1. #1
    C++ Enthusiast M.Richard Tober's Avatar
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    Need help reducing an equation, math wiz's welcome. =)

    Heya guys, I've been busy! I've been cranking out simple 3D C++ apps that my girlfriend's kids love. I made a pong clone and now I'm working on a maze game, etc etc. Lots of fun.
    Here's the trouble! 3D graphics = math. I'm a better programmer than arithmetician.

    Code:
    ((14 - (int)(13.8 - ((float)y / 35.217)))*50)+((int)(-25.0 + ((float)x / 34.7)) + 25)
    How can I reduce/simplify this?

    What it does? Takes the x and y coordinates from OpenGL's "glutMotionFunc" - and translates them to object space coordinates some -30Z units in the distance. The x and y are serialized into a linear one dimensional array of 1,400 3-float structures. This array can be saved and loaded from disk like lightning, which is hot... but then getting it back into X and Y (adjusted from two positive coordinates (gotten by a modulus 50, and a subsequent divide 50) into a 0,0 signed coored.... omg... I digress.

    I can always post some source. I'm NOT gonna do this way next time, and I learned alot. But man, 3 days to get this solution. The key was finally inverting the Y coord at the end of the process. Anyhow... relevant code for the sick freaks like me:

    Code Produced here: [Edited, wrecked, I'm tired, sorry]
    Code:
    static void motion(int x, int y)
    {
        cursorPosX = -25.0 + ((float)x / 34.7);
        cursorPosY = 13.8 - ((float)y / 35.217);
    
        clog << "Window Coordinates in Pixels with top left origin: ";
        clog << "x: " << x << " y: " << y << endl;
        clog << "Screen space coordinates with center origin: ";
        clog << "x: " << cursorPosX << " y: " << cursorPosY << endl;
        clog << "Formulation board coordinates from top-left: ";
        clog << "x:" << (int)cursorPosX + 25 << " y: " << 14 - (int)cursorPosY << endl;
    
        boardX = (int)cursorPosX + 25;
        boardY = 14 - (int)cursorPosY;
        int square = (boardY*50)+boardX;
    
        cout << boardX << " " << boardY << " " << square
        << " \\ " << (square % 50) << " " << (square / 50 )
        << "   [" << (square % 50)-25 << " " << -((square / 50 )-14) << "]" << endl;
    
        board[square] = colorTable(currentColor);
    }
    And here's the final, compact, Linus Torvalds would shoot me, over simplification, noob, product:
    Code:
    static void motion(int x, int y)
    {
        cursorPosX = (-25.0 + ((float)x / 34.7));
        cursorPosY = (13.8 - ((float)y / 35.217));
        board[((14 - (int)(13.8 - ((float)y / 35.217)))*50)+((int)(-25.0 + ((float)x / 34.7)) + 25)] = colorTable(currentColor);
    }
    Which is why I need help reducing that badboy on the last line.

    Thank you if any spare time or effort. You gurus inspire me.

    M. Richard Tober

  2. #2
    C++ Enthusiast M.Richard Tober's Avatar
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    By the way, I've actually improved in skill, not all my code is wierd and convoluted - here's a templated function that takes a one dimentional array, it's size in elements, and a string filename - and saves it to a file! And the read one too.

    Note: I use this in my custom *.hpp toolbox header, so the names are qualified.

    Code:
    template <class T> bool readArray(T *array, unsigned long arraySize, std::string fileName)
    {
        std::ifstream file(fileName.c_str(), std::ios::binary);
        if (!file.is_open()) {
            std::cerr << "Unable to open \"" << fileName << "\"." << std::endl;
            return false;
        } else {
            std::clog << "\"" << fileName << "\" opened successfully." << std::endl;
            std::clog << "Reading " << arraySize *sizeof(T) << " bytes." << std::endl;
            file.read((char*) array, arraySize * sizeof(T));
            if (file.fail()) {
                std::cerr << "Read operation failed." << std::endl;
                file.clear();
                return false;
            } else {
                std::clog << "Read " << file.gcount() << " bytes." << std::endl;
            }
            std::clog << "Closing \"" << fileName << "\"." << std::endl;
            file.close();
        }
        return true;
    }
    Code:
    template <class T> bool writeArray(T *array, unsigned long arraySize, std::string fileName)
    {
        std::ofstream file(fileName.c_str(), std::ios::binary);
        if (!file.is_open()) {
            std::cerr << "Unable to open \"" << fileName << "\"." << std::endl;
            return false;
        } else {
            std::clog << "\"" << fileName << "\" opened successfully." << std::endl;
            std::clog << "Writing " << arraySize *sizeof(T) << " bytes." << std::endl;
            file.write((char*)array, arraySize * sizeof(T));
            if (file.fail()) {
                std::cerr << "Write operation failed." << std::endl;
                file.clear();
                return false;
            } else {
                std::clog << "Wrote " << arraySize *sizeof(T) << " bytes." << std::endl;
            }
            std::clog << "Closing \"" << fileName << "\"." << std::endl;
            file.close();
        }
        return true;
    }

  3. #3
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    I have a couple of questons/observations about the following line of code:
    Code:
    board[((14 - (int)(13.8 - ((float)y / 35.217)))*50)+((int)(-25.0 + ((float)x / 34.7)) + 25)] = colorTable(currentColor);
    First how, where is board defined?

    Second I would move the calculation from inside the brackets [] to a separate variable, so this variable's value can be tested to insure you do not access the array out of bounds.

    Third you can probably remove the C-style float casts from the equation, you already have at least one floating point number in the calculation. I would probably break this calculation up into smaller equations, handling the x and y calculations separately. By breaking the equation up, if you have problems you can display these individual variables to insure that your calculations are correct. It also appears that the -25 and +25 cancel each other out and are not needed.

    This is about what I would do for your calculation. I would then test indexValue to insure that it is in bounds for your array. I would also consider changing these "magic" constants to constant variables with meaningful names to help explain what you are trying to accomplish in these calculations.

    Code:
       int yValue = (14.0 - (13.8 - (y / 35.217))) * 50.0;
       int xValue = x / 34.7;
       int indexValue = yValue + xValue;
    Also is there a reason you are using an array instead of a vector?


    Jim

  4. #4
    C++ Enthusiast M.Richard Tober's Avatar
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    Right! Sorry Jim, the board is an array of structures. Lemme dig it out:
    Code:
    struct mrtcolor {
        float r;
        float g;
        float b;
    };
    And the array:
    Code:
    mrtcolor board[1400];
    But, that aside, your simplification is very nice, and when you advise to get rid of the c-style casts, you mean go with like:
    [ reinterpret_cast <new_type> (expression) static_cast <new_type> (expression) const_cast <new_type> (expression) ]
    Your advice prompted me to learn about these, thank you!

    As for vector, I -had- a vector solution, but ran into trouble getting boost libraries to link to my project. Hence no boost::serialization, hence vectors are not so easy to get into binary files. That board[1400] array is saved to a binary file, and reloaded.

    Searializing vectors basically... was the stumbling block there.

  5. #5
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    In this case I was saying that you don't need the casts at all. However in C++ programs you should actually use the C++ style casts instead of the C style casts.

    Jim

  6. #6
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    Quote Originally Posted by jimblumberg View Post
    Code:
       int yValue = (14.0 - (13.8 - (y / 35.217))) * 50.0;
    (14.0 - 13.8)*50.0 is 1.0 .....
    Right 98% of the time, and don't care about the other 3%.

  7. #7
    Algorithm Dissector iMalc's Avatar
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    Quote Originally Posted by M.Richard Tober View Post
    And here's the final, compact, Linus Torvalds would shoot me, over simplification, noob, product:
    Linux Torvalds is a neanderthal who wouldn't understand the benefits of simplification if it shot him in the foot.

    Code is not oversimplified until it's just plain wrong.
    My homepage
    Advice: Take only as directed - If symptoms persist, please see your debugger

    Linus Torvalds: "But it clearly is the only right way. The fact that everybody else does it some other way only means that they are wrong"

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