Tag: algorithms

Entries for tag "algorithms", ordered from most recent. Entry count: 62.

Warning! Some information on this page is older than 3 years now. I keep it for reference, but it probably doesn't reflect my current knowledge and beliefs.

Pages: 1 2 3 ... 8 >

Jan 2013

How to Flip Triangles in Triangle Mesh

Given triangle mesh, as we use it in real-time rendering of 3D graphics, we say that each triangle have two sides, depending on whether its vertices are oriented clockwise or counterclockwise from particular point of view. In Direct3D, by default, triangles oriented clockwise are considered front-facing and they are visible, while triangles oriented counterclockwise are invisible because they are discarded by the API feature called backface culling.

When we have backface culling enabled and we convert mesh between coordinate systems, we sometimes need to "flip triangles". When vertices of each triangle are separate, an algorithm for this is easy. We just need to swap first with third vertex of each triangle (or any other two vertices). So we can start implementing the flipping method like this:

class CMesh
    D3D11_PRIMITIVE_TOPOLOGY m_Topology;
    bool m_HasIndices;
    std::vector<SVertex> m_Vertices;
    std::vector<uint32_t> m_Indices;

void CMesh::FlipTriangles()

Where the function template for flipping triangles in a vector is:

template<typename T>
void CMesh::FlipTriangleListInArray(std::vector<T>& values)
    for(size_t i = 0, count = values.size(); i < count - 2; i += 3)
        std::swap(values[i], values[i + 2]);

Simple reversing all elements in the vector with std::reverse would also do the job. But things get complicated when we consider triangle strip topology. (I assume here that you know how graphics API-s generate orientation of triangles in a triangle strip.) Reversing vertices works, but only when number of vertices in the strip is odd. When it's even, triangles stay oriented in the same way.

I asked question about this on forum.warsztat.gd (in Polish). User albiero proposed following solution: just duplicate first vertex. It will generate additional degenerate (invisible) triangle, but thanks to this all following triangles will be flipped. It seems to work!

I also wanted to handle strip-cut index (a special value -1 which starts new triangle strip), so the rest of my fully-featured algorithm for triangle flipping is:

            size_t begIndex = 0;
            while(begIndex < m_Indices.size())
                const size_t indexCount = m_Indices.size();
                while(begIndex < indexCount && m_Indices[begIndex] == UINT_MAX)
                if(begIndex == indexCount)
                size_t endIndex = begIndex + 1;
                while(endIndex < indexCount && m_Indices[endIndex] != UINT_MAX)
                // m_Indices.size() can change here!
                FlipTriangleStripInArray<uint32_t>(m_Indices, begIndex, endIndex);
                begIndex = endIndex + 1;
            FlipTriangleStripInArray<SVertex>(m_Vertices, 0, m_Vertices.size());

Where function template for flipping triangles in selected part of a vector is:

template<typename T>
void CMesh::FlipTriangleStripInArray(std::vector<T>& values, size_t begIndex, size_t endIndex)
    const size_t count = endIndex - begIndex;
    if(count < 3) return;
    // Number of elements (and triangles) is odd: Reverse elements.
    if(count % 2)
        std::reverse(values.begin() + begIndex, values.begin() + endIndex);
    // Number of elements (and triangles) is even: Repeat first element.
        values.insert(values.begin() + begIndex, values[begIndex]);

Comments (1) | Tags: directx rendering algorithms | Author: Adam Sawicki | Share

Mar 2012

Iterating Backward using Unsigned Numbers

I've had a discussion recently with my colleagues about what is the best way of writing a loop in C++ that would iterate backward: Count-1, Count-2, ..., 0, using unsigned integer numbers. I'd like to share all possible solutions I managed to gather.

Iterating forward is simple:

unsigned count = 10;
// Forward: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
for(unsigned i = 0; i < count; ++i)
    printf("%d ", i);

Iterating backward is equally simple and looks similar, if you use signed integers:

// Backward: 9, 8, 7, 6, 5, 4, 3, 2, 1, 0
// Using signed integer
for(int i = count - 1; i >= 0; --i)
    printf("%d ", i);

Same code cannot be used with unsigned integers, because it creates infinite loop, as unsigned number is always >= 0 and just wraps around to maximum value 0xFFFFFFFF:

// WRONG: Inifinte loop, unsigned int wraps around and is always >= 0.
for(unsigned i = count - 1; i >= 0; --i)
    printf("%d ", i);

Changing condition to i > 0 is also invalid, because then loop is not executed for i == 0:

// WRONG: Not executed for i == 0.
for(unsigned i = count - 1; i > 0; --i)
    printf("%d ", i);

Here comes a bunch of possible valid solutions. My favourite is following for loop:

for(unsigned i = count; i--; )
    printf("%d ", i);

Following while loop does same thing. Some people say that it looks more clear. I don't think so, while I believe the for loop is better because it creates local scope for variable i, while the following code does not:

unsigned i = count;
    printf("%d ", i);

Another way of implementing exactly same logic is to write the condition like this. It may look like C++ had the "goes to zero" arrow operator -->, but it is actually just (i-- > 0) :)

unsigned i = count;
while(i --> 0)
    printf("%d ", i);

Another possible solution of loop condition (a one that does not use the postdecrementation operator) is to compare i with maximum integer value. One disadvantage of it is that you have to carefully match the value of the max constant with type of your iterator - whether it is unsigned int, unsigned short etc.

for(unsigned i = count - 1; i != UINT_MAX; --i)
    printf("%d ", i);

Another way of doing this, without using maximum value, is:

for(unsigned i = count - 1; i < count; --i)
    printf("%d ", i);

Finally there are solutions possible that introduce second iterator:

// Option 1 using second iterator:
// i goes 0...9, j is inverted i.
for(unsigned i = 0; i < count; ++i)
    unsigned j = count - i - 1;
    printf("%d ", j);

// Option 2 using second iterator:
// i goes 10...1, j is decramented i.
for(unsigned i = count; i > 0; --i)
    unsigned j = i - 1;
    printf("%d ", j);

Which is your favorite loop? Please leave a comment :)

Comments (2) | Tags: algorithms c++ | Author: Adam Sawicki | Share

Feb 2012

Algorithms for Managing Tree Structure

What are the ways of storing a tree data structure in memory? I mean a tree with arbitrary number of child nodes. Probably first thing that comes to our minds - as high level programmers - is to dynamically allocate each node as object of some class that would store its data and a collection of pointers to its children. Opposite approach would be to store all nodes in some array - a continuous piece of memory, where each node would refer to other nodes by index or something. Third approach - something in between in terms of sophistication, as well as efficiency - is to have dynamically allocated nodes, but not to store a collection of all child nodes. It is a good idea to employ kind of linked list here. I'd like to describe such data structure and basic algorithms for manipulating it.

The idea is that each node stores - besides its data - 5 pointers (possibly null) to some other nodes: parent, previous sibling, next sibling, first child and last child. It could be seen as equivalent to doubly linked list. It has much more pointers that is needed to be able to traverse whole tree, but thanks to this you can traverse such tree in any order, as well as insert and remove nodes at any point, with best possible time complexity. A node with Parent == null is considered a tree root. Here is a picture of a single node and example tree:

Read full entry > | Comments (4) | Tags: algorithms .net | Author: Adam Sawicki | Share

Jan 2012

Resizing Images to Generate Thumbnails in PHP

Some time ago I came across a problem of calculating an image size for automatically generated thumbnail for gallery script coded in PHP. It required a moment's thought, so I'd like to share this algorithm. In fact there will be two algorithms.

First code scales the image down with following rules: Destination size will not exceed given thumbnail size, but the width or height can be smaller to always preserve aspect ratio. Images smaller than thumbnail size are not magnified.

$src_size_x, $src_size_y - Source image size.
THUMBNAIL_SIZE_X, THUMBNAIL_SIZE_Y - Constants defining thumbnail size.

$dst_size_x, $dst_size_y - Destination thumbnail size.

if( $src_size_x <= THUMBNAIL_SIZE_X && $src_size_y <= THUMBNAIL_SIZE_Y )
  $dst_size_x = $src_size_x;
  $dst_size_y = $src_size_y;
  $dst_size_x = THUMBNAIL_SIZE_X;
  $dst_size_y = (int)( $src_size_y * THUMBNAIL_SIZE_X / $src_size_x );
  if( $dst_size_y > THUMBNAIL_SIZE_Y )
    $dst_size_x = (int)( $src_size_x * THUMBNAIL_SIZE_Y / $src_size_y );
    $dst_size_y = THUMBNAIL_SIZE_Y;

Second algorithm also helps with generating image thumbnails, but works differently. It assumes that destination image will always be of size (THUMBNAIL_SIZE_X, THUMBNAIL_SIZE_Y), while source iamge can be cropped to select only the center of the image if it has different aspect ratio than the thumbnail.

Inputs to this algorithm are the same, while outputs are:

$src_x, $src_y - Offset in the source image to begin copying from.
$src_w, $src_h - Size of the rectangle to select from cropped source image.

The code that uses this algorithm should then select from the source image a rectangle with left-top position ($src_x, $src_y), size ($src_w, $src_h) and copy it, with scaling and resampling, to the destination image with the size exactly (THUMBNAIL_SIZE_X, THUMBNAIL_SIZE_Y). That's what imagecopyresampled function from GD library can do. This algorithm does not handle cases where source image is smaller than thumbnail.

$src_h = $src_size_y;
$src_w = (int)( $src_h * THUMBNAIL_SIZE_X / THUMBNAIL_SIZE_Y );

if( $src_w <= $src_size_x )
  $src_x = ( $src_size_x - $src_w ) / 2;
  $src_y = 0;
  $src_w = $src_size_x;
  $src_h = (int)( $src_w * THUMBNAIL_SIZE_Y / THUMBNAIL_SIZE_X );
  $src_x = 0;
  $src_y = ( $src_size_y - $src_h ) / 2;

Comments (1) | Tags: webdev algorithms php | Author: Adam Sawicki | Share

Jan 2012

Fast, Heuristic Disk Search

In March 2007 I've written an algorithm which I called "Fast, heuristic disk search" and published it in my article Szybkie, heurystyczne przeszukiwanie dysku (in Polish) on codeguru.pl. Today I went back to it, improved it a bit and I think it is a good opportunity to present it once again, this time in English :)

The problem is about searching hard disk, looking for a file or directory with particular name. Naive approach, which is used by file searching functions in programs like Total Commander, uses depth-first search, so it enters C:\, then C:\Program Files, then C:\Program Files\Adobe etc., spending lots of time in places where it probably won't find the file we are looking for.

Game developers know that searching algorithm can be significantly improved by using some heuristics that will drive algorithm towards (probably) right direction. We do it in A* pathfinding. Does a similar principle could be used also when searching for a file?

My particular problem was configuring a program with path to a console tool, let's say fxc.exe shader compiler from DirectX SDK. We could present a textbox where user has to enter path to this tool. We could also make "Browse" button with an open file dialog to simplify locating it. But wouldn't be great if program tried to locate it automatically on first run? Some installed programs store path in a registry key, but if it doesn't, we have no idea where could it be if we don't look for it among files and directories on hard disk.

My algorithm tries to locate given file or directory in given time limit by searching all given directories and their subdirectories. The improvement I propose here is inteligent management of the order in which we process these directories.

The algorithm uses two collections: a queue of directories to process and a set of already visisted directories. Here is the code in C#:

Read full entry > | Comments (0) | Tags: algorithms .net | Author: Adam Sawicki | Share

Oct 2011

Circular Buffer of Raw Binary Data in C++

Circular Buffer, Cyclic Buffer or Ring Buffer is a data structure that effectively manages a queue of some items. Items can be added at the back and removed from the front. It has limited capacity because it is based on preallocated array. Functionality is implemented using two pointers or indices - pointing to the first and past the last valid element. The Begin pointer is incremented whenever an item is popped from the front so that it "chases" the End pointer, which is incremented whenever a new item is pushed to the back. They can both wrap around the size of the array. Both operations are done very effectively - in constant time O(1) and no reallocations are needed. This makes circular buffers perfect solution for queues of some data streams, like video or audio.

It's not very sophisticated data structure, but there is one problem. Sample codes of circular buffers you can find on the Internet, just like for many other data structures, operate usually on a single object of some user-defined type. What if we need a buffer for raw binary data, stored as array of bytes? We can treat single bytes as data items, but enqueueing and dequeueing single bytes with separate function calls would not be efficient. We can, on the other hand, define some block of data (like 4096 bytes) as the type of item, but this limits us to operating on on such block at a time.

Best solution would be to write an implementation that operates on binary data in form of (const char *bytes, size_t byte_count) and allows writing and reading arbitrary amount of data in a single call, just like functions for writing and reading files do. The only problem that arises in such code is that sometimes the block of data you want to write to or read from the buffer is not in a continuous region of memory, but wraps around to the beginning of the array so we have to process it on two parts - first at the end of the array and the second at the beginning.

Here is my C++ implementation of a circular buffer for raw binary data:

#include <algorithm> // for std::min

class CircularBuffer
  CircularBuffer(size_t capacity);

  size_t size() const { return size_; }
  size_t capacity() const { return capacity_; }
  // Return number of bytes written.
  size_t write(const char *data, size_t bytes);
  // Return number of bytes read.
  size_t read(char *data, size_t bytes);

  size_t beg_index_, end_index_, size_, capacity_;
  char *data_;

CircularBuffer::CircularBuffer(size_t capacity)
  : beg_index_(0)
  , end_index_(0)
  , size_(0)
  , capacity_(capacity)
  data_ = new char[capacity];

  delete [] data_;

size_t CircularBuffer::write(const char *data, size_t bytes)
  if (bytes == 0) return 0;

  size_t capacity = capacity_;
  size_t bytes_to_write = std::min(bytes, capacity - size_);

  // Write in a single step
  if (bytes_to_write <= capacity - end_index_)
    memcpy(data_ + end_index_, data, bytes_to_write);
    end_index_ += bytes_to_write;
    if (end_index_ == capacity) end_index_ = 0;
  // Write in two steps
    size_t size_1 = capacity - end_index_;
    memcpy(data_ + end_index_, data, size_1);
    size_t size_2 = bytes_to_write - size_1;
    memcpy(data_, data + size_1, size_2);
    end_index_ = size_2;

  size_ += bytes_to_write;
  return bytes_to_write;

size_t CircularBuffer::read(char *data, size_t bytes)
  if (bytes == 0) return 0;

  size_t capacity = capacity_;
  size_t bytes_to_read = std::min(bytes, size_);

  // Read in a single step
  if (bytes_to_read <= capacity - beg_index_)
    memcpy(data, data_ + beg_index_, bytes_to_read);
    beg_index_ += bytes_to_read;
    if (beg_index_ == capacity) beg_index_ = 0;
  // Read in two steps
    size_t size_1 = capacity - beg_index_;
    memcpy(data, data_ + beg_index_, size_1);
    size_t size_2 = bytes_to_read - size_1;
    memcpy(data + size_1, data_, size_2);
    beg_index_ = size_2;

  size_ -= bytes_to_read;
  return bytes_to_read;

Similar phenomenon can be observed in API of the FMOD sound library. Just like graphical textures in DirectX, sound samples in FMOD can also be "locked" to get pointer to a raw memory we can read or fill. But DirectX textures lie in the continuous memory region, so we get a single pointer. The only difficult thing in understanding locking textures is the concept of "stride", which can be greater than the width of a single row. Here in FMOD the Sound::lock() method returns two pointers and two lengths, probably because the locked region can wrap over end of internally used circular buffer like the one shown above.

Comments (0) | Tags: c++ algorithms | Author: Adam Sawicki | Share

Nov 2010

My Implementation of Diff Algorithm

Algorithm for comparing two sequences of some data is very useful. For example, version control systems like SVN or Git use it to highlight differences between two versions of a text file. But what if you need to code such algorithm from scratch? Today it was my task and it turned out to be not so simple, so I want to share my sample implementation in C++ which I came up with based on some readings from the Internet and my previous experiences with calculating Levenshtein distance.

What we need to compare is sometimes just lines of text files that are equal or not, but I needed something more complex, so let's say an item is defined as follows:

struct Item
  unsigned ID;
  const char *Text;

For items from opposite sides to be comparable they must have same ID values. Text may be different, but I'd prefer to match items with same Text (treated as NULL-terminated string) or at least same Text length.

Here are sample data:

const Item items1[] = {
  { 1, "Foo" },
  { 1, "Foo" },
  { 2, "Bar" },
  { 4, "Foobar" },
const Item items2[] = {
  { 1, "Foo" },
  { 1, "Firefox" },
  { 1, "Another one" },
  { 2, "Boo" },
  { 5, "Last one" },
const unsigned count1 = _countof(items1);
const unsigned count2 = _countof(items2);

The final result may look like this:

1              Foo   <->   1              Foo
--                   <->   1          Firefox
1              Foo   <->   1      Another one
2              Bar   <->   2              Boo
4           Foobar   <->   --
--                   <->   5         Last one

Read full entry > | Comments (0) | Tags: algorithms | Author: Adam Sawicki | Share

Jul 2010

Music Analysis - Spectrogram

I've started learning about sound analysis. I have some deficiencies in education when it comes to digital signal processing (greetings for the professor who taught this subject at our university ;) but Wikipedia comes to the rescue. As a starting point, here is a spectrogram I've made from one of my recent favourite songs: Sarge Devant feat. Emma Hewitt - Take Me With You.

Now I'm going to exaplain in details how I've done this by showing some C++ code. First I had to figure out how to decode an MP3, OGG or other compressed sound format. FMOD is my favourite sound library and I knew it can play many file formats. It took me some time though to find functions for fast decoding uncompressed PCM data from a song without actually playing it for all 3 minutes. I've found on the FMOD forum that Sound::seekData and Sound::readData can do the job. Finally I've finished with this code (all code shown here is stripped from error checking which I actually do everywhere):

Read full entry > | Comments (1) | Tags: math libraries music rendering dsp algorithms | Author: Adam Sawicki | Share

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