README.md

square_fractals_openGL

Subdivision of square into fractals

press + to increase the subdivision
press - to decrease the subdivision

1.1 Square Fractals

Given a initial square, subdivide each side of square such that a square of side one third of original square. The approach is to store each vertex in order and render them in sequence. There are two structs used Vertex that stores x,y coordinates of a vertex and another struct Edges that contains two consecutive vertex coordinates and orientation which basically tells the orientation of the edge, this will be useful to calculate new edges new small squares form outside of original edge.

Vertex and Edges.

structVertex{
  glm::vec2 v;
};


structEdges{
  glm::vec2 first ;
  glm::vec2 second;
  char orientation;
};

The class Pol contains several methods and variables to store the new vertices whenever a object is creates, later whenever the current polygon is subdivided a new Pol object will be formed that will store all edges in sequence.

Data Types

• std::vector< Edges >edge- this vector will store all the edges in sequence. As mentioned above an edge contains two vertices and orientation.

• std::vector< V ertex >vertex;- this vector stores all the vertices in current polygon in sequence

• float len- it stores the side length of current polygon.

Constructors

• Default Constructors Pol() - it will construct a 2D square and store all call the method construct that will calculate edges and store them,
• Parameterized Constructors Pol(std::vector< V ertex >v, float l) - it will construct polygon based on the vector v passed that should contain all the vertices in order, it also calls construct that will calculate edges and store them. It also stores the length of square side.

Methods

• construct()- this method will fill the edge vector using the vertex vector passed to constructor
• findorient()- this method will find the orientation of each edge using 2 vertices and coordinate geometry. Orientation is necessary to find new edges while subdividing the square. it will return a char which represents the edge orientation. Since all the edges can have only four orientations, ∗’a’ represents right edge of square. ∗’b’ represents bottom edge of square. ∗’c’ represents left edge of square. ∗’d’ represents top edge of square.

Pol definations

Pol :: Pol(){
  Vertex ver [4];
  ver [0]. v ={1,1};
  vertex. pushback(ver[0]) ;
  ver [1]. v ={1,− 1 };
  vertex. pushback(ver[1]) ;
  ver [2]. v ={ −1,− 1 };
  vertex. pushback(ver[2]) ;
  ver [3]. v ={ −1, 1};
  vertex. pushback(ver[3]) ;
  len = 2.0;
  std :: cout<<vertex.size()<<std::endl;
  construct() ;
}

Pol :: Pol(std :: vector<Vertex>v,floatl){
  vertex = v;
  len = l;
  construct() ;
  std :: cout<<edge.size()<<” ”<<vertex.size()<<std::endl;
}

voidPol::construct(){
  std :: vector<Vertex>::iterator i ;
  for( i = vertex.begin(); i != vertex.end()−1; ++i)
   {
      Vertex first =∗i;
      Vertex second =∗(i + 1);
      Edges temp;
      temp. first = first. v;
      temp.second = second.v;
      temp.orientation = findorient ( first. v, second.v);
      edge.pushback(temp);
    }
  Edges temp;
  temp. first = (vertex.back()).v;
  temp.second = (vertex.front()). v;
  temp.orientation = findorient ((vertex. back()).v, (vertex. front () ). v);
  edge.pushback(temp);
}

charPol:: findorient (glm::vec2 a, glm::vec2 b){
  if (a.x == b.x && a.y>b.y)return’a’;
  else if (a.y == b.y && a.x>b.x)return’b’;
  else if (a.x == b.x && a.y<b.y)return’c’;
  else return’d’;
}

1.1.1 Source.cpp

There are three global variables a vector listofpols that contains Pol objects hence the ploygons, curr is a Pol object that refers to the current polygon that is being drawn on screen. curpointer is a integer that keeps track of index of Pol object in listofpols and is used to iterate back and fourth over listofpols. When user presses the key ’+’ divide() function is called which makes a new polygon based on current polygon edges and orientation of each edge and adds the Polygon to listofpols as well as making the curr point to new polygon. When user presses the key ’-’ back() function is called which simply moves the curr pointer one index back in listofpols.

Figure 1.1: Square

Figure 1.2: Making fractals