void drawSierpinskiTriangleHelper(GWindow& gw, double x, double y, int size, int order){
if(order > 0)
gw.drawLine(x, y, x + size, y);
gw.drawLine(x, y, x + size/2, y - size*sqrt(3)/2);
gw.drawLine(x + size, y, x + size/2, y - size*sqrt(3)/2);
drawSierpinskiTriangleHelper(gw, x - size/4, y - size*sqrt(3)/4, size/2, order-1);
drawSierpinskiTriangleHelper(gw, x + 3*size/4, y - size*sqrt(3)/4, size/2, order-1);
drawSierpinskiTriangleHelper(gw, x + size/4, y + size*sqrt(3)/4, size/2, order-1);
}
/*
* Display ChessBoard in graphics window
*/
void draw_ChessBoard(Grid<bool> &ChessBoard, GWindow &gw)
{
int row = ChessBoard.numRows();
int col = ChessBoard.numCols();
double width = gw.getWidth();
double height = gw.getHeight();
double cell_width = width/col;
double cell_height = height/row;
for(int i = 0; i < row; i++)
{
gw.drawLine(0, i*cell_height, width, i*cell_height);
gw.drawLine(i*cell_width, 0, i*cell_width, height);
}
}
pair<double, double> drawCoordinateSystem(GWindow &graphicsWindow, int scale) {
pair<double, double> result;
result.first = graphicsWindow.getWidth() / 2;
result.second = graphicsWindow.getHeight() / 2;
graphicsWindow.drawLine(result.first, 0, result.first, result.second * 2);
graphicsWindow.drawLine(0, result.second, result.first * 2, result.second);
for (int x = -result.first / scale + 1; x <= result.first / scale - 1; x++)
graphicsWindow.drawLine(result.first + x * scale, result.second - 5,
result.first + x * scale, result.second + 5);
for (int y = -result.second / scale + 1; y <= result.second / scale - 1; y++)
graphicsWindow.drawLine(result.first - 5, result.second + y * scale,
result.first + 5, result.second + y * scale);
GLabel* xMark = new GLabel("x", result.first * 2 - 20, result.second + 15);
graphicsWindow.add(xMark);
GLabel* yMark = new GLabel("y", result.first + 10, 20);
graphicsWindow.add(yMark);
return result;
}
void drawSierpinskiTriangle(GWindow& gw, double x, double y, double size, int order) {
// TODO: write this function
//gw.drawLine(20,20,30,80);
if (order <= 0) return;
if (order == 1) {
gw.drawLine(x,y,x+size,y);
gw.drawLine(x+size,y,x+0.5*size,y+sqrt(3)/2.0*size);
gw.drawLine(x,y,x+0.5*size,y+sqrt(3)/2.0*size);
}
else
{
drawSierpinskiTriangle(gw, x, y, 0.5*size, order - 1);
drawSierpinskiTriangle(gw, x + 0.5*size, y, 0.5*size, order - 1);
drawSierpinskiTriangle(gw, x + 0.25*size, y + sqrt(3)/4.0*size, 0.5*size, order - 1);
}
}
/*
* Function: drawSierpinskiTriangle();
* --------------------
* Draw a Sierpinski Triangle of a given order
*
* Preconditions: valid x,y values, order >=0
*
* @param: Start position, size of sides, order of sierpinski triangle
* @return: Nothing, but does draw something
*/
void drawSierpinskiTriangle(GWindow& gw, double x, double y, int size, int order) {
// If the order is >0, draw the first triangle (this case is a little different than rest)
// If not, do nothing, as we should
// Check to make sure out parameters are valid
checkSierpinskiParams(gw, x, y, size, order);
if(order>0) {
//determine the new midpoints
double x2=x+size*cos(PI/3);
double y2=y+size*sin(PI/3);
double x3=x+size;
double y3=y;
// Draw outer triangle
gw.drawLine(x,y,x2,y2);
gw.drawLine(x,y,x3,y3);
gw.drawLine(x2,y2,x3,y3);
}
// Start the recursive process
drawSierpinskiHelp(gw,x,y,size,order);
}
/*
* Function: drawSierpinskiHelp();
* --------------------
* Helper function that does the actual recursion
*
* Preconditions: valid x,y values, order >=0
*
* @param: Start position, size of sides, order of sierpinski triangle
* @return: Nothing, but does draw something
*/
void drawSierpinskiHelp(GWindow& gw, double x, double y, int size, int order) {
// As long as the order is large enough we will start recursing
if(order>1){
// Determine the new midpoints
double x2=x+size*cos(PI/3);
double y2=y+size*sin(PI/3);
double x3=x+size;
double y3=y;
// Draw the triangle connecting the midpoints
gw.drawLine((x2+x)/2,(y2+y)/2,(x3+x2)/2,(y2+y3)/2);
gw.drawLine((x3+x2)/2,(y2+y3)/2,(x+x3)/2,(y3+y)/2);
gw.drawLine((x3+x)/2,(y+y3)/2,(x2+x)/2,(y2+y)/2);
/* Repeat this process with 3 recursive calls */
// Make starting point the top left corner
drawSierpinskiTriangle(gw,x,y,size/2,order-1);
// Make starting point middle of left edge
drawSierpinskiTriangle(gw,(x2+x)/2,(y+y2)/2,size/2,order-1);
// make starting point middle of top edge
drawSierpinskiTriangle(gw,(x3+x)/2,(y+y3)/2,size/2,order-1);
}
}
//builds two lines from each of two gotten vertex and calls itself recursively until the depth of recursion becomes zero
void drawPythagoreanTree(GWindow &gw, GPoint endPoint1, GPoint endPoint2, double input_length, double theta, int recursion_depth){
double theta_one = theta - THETA;
double theta_two = theta + THETA;
double length = input_length * cos(THETA_RADIAN);
GPoint branch1_1 = gw.drawPolarLine(endPoint1, length*2, theta_one);
GPoint branch1_2 = gw.drawPolarLine(endPoint2, length, theta_one);
gw.setColor("YELLOW");
gw.drawLine(branch1_1, branch1_2);
GPoint branch2_1 = gw.drawPolarLine(endPoint1, length, theta_two);
GPoint branch2_2 = gw.drawPolarLine(endPoint2, length*2, theta_two);
gw.setColor("GREEN");
gw.drawLine(branch2_1, branch2_2);
recursion_depth--;
if(recursion_depth == 0){
return;
}
drawPythagoreanTree(gw, branch1_1, branch1_2, length, theta_one, recursion_depth);
drawPythagoreanTree(gw, branch2_1, branch2_2, length, theta_two, recursion_depth);
}
void drawSierpinkiTriangle(GPoint & top,int edge,int order,GWindow & gw) {
int triangleHeight = (int)sqrt(pow((double)edge,2) - pow((double)edge/2,2));
GPoint ptA = top;
GPoint ptB((top.getX() - (triangleHeight/2)),(top.getY()+triangleHeight));
GPoint ptC((top.getX() + (triangleHeight/2)),(top.getY()+triangleHeight));
gw.drawLine(ptA,ptB);
gw.drawLine(ptB,ptC);
gw.drawLine(ptC,ptA);
if(order != 0) {
order -= 1;
edge = edge / 2;
if(edge != 0) {
triangleHeight = triangleHeight / 2;
GPoint ptAb = top;
GPoint ptBb((top.getX()-(triangleHeight/2)),(top.getY()+triangleHeight));
GPoint ptCb((top.getX() + (triangleHeight / 2)), (top.getY() + triangleHeight));
drawSierpinkiTriangle(ptAb, edge, order, gw);
drawSierpinkiTriangle(ptBb, edge, order, gw);
drawSierpinkiTriangle(ptCb, edge, order, gw);
}
}
}