CS 111
Computer Science I

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This is a collection of recursive drawing methods. At a high level they are similar to examples done in class/homework.

If you do not understand completely the given method computePoint you could instead think about the general structure of the solution without writing any code.

Preliminaries

Create a new app called FractalsApp that has the methods described below.

The following method is given:

double[] computePoint( double x1, double y1, double x2, double y2, double distAlong, double distAway)
{
    double dx = x2 - x1;
    double dy = y2 - y1;

    //       start   walk to x2  turn90+walk away
    double x = x1 + distAlong*dx + dy*distAway;
    double y = y1 + distAlong*dy - dx*distAway;
        
    double[] point = { x, y };
    return point;
}

This method computes a new point relative to the line segment defined by the points (x1,y1) and (x2,y2).

Imagine a bug located at point (x1,y1):

1. the bug first walks along the segment the given distAlong towards point (x2,y2)
2. next the bug turns left 90 degrees and walks distAway from the line segment
3. the method returns the final location of the bug

Note that:

• the parameters distAlong and distAway should be fractions in terms of the length of the segment (this makes things easier)
• when calling the method the two points must be given in the correct order (this depends on the problem) since the bug always starts at the location specified by (x1,y1)

• distAway could be 0, so to compute the midpoint of a segment we could write:

  double[] midXY = computePoint( x1, y1, x2, y2, .5, 0 );  // half-way forward with no turning

Here is a possible use of the method:

void demo() { double x1 = 100; double x2 = 300; double y = 150; // the line segment canvas.drawLine( x1, y, x2, y, "red" ); // a few points double[] p1 = computePoint( x1, y, x2, y, 0.5, 0 ); // (blue) half along, does not move away double[] p2 = computePoint( x1, y, x2, y, 0.5, 0.5 ); // (green) half along, moves half away double[] p3 = computePoint( x1, y, x2, y, 0.75, 0.25 ); // (purple) 3/4 along, moves 1/4 away canvas.drawSquare( x1, y, 8, "white(black)" ); // (black) starting point as square canvas.drawCircle( p1[0], p1[1], 4, "white(blue)" ); canvas.drawCircle( p2[0], p2[1], 4, "white(green)" ); canvas.drawCircle( p3[0], p3[1], 4, "white(purple)" ); x1 = 300; x2 = 100; double y1 = 300; double y2 = 500; // the line segment canvas.drawLine( x1, y1, x2, y2, "red" ); p1 = computePoint( x1, y1, x2, y2, 0.5, 0 ); // (blue) half along, does not move away p2 = computePoint( x1, y1, x2, y2, 0.5, 0.5 ); // (green) half along, moves half away p3 = computePoint( x1, y1, x2, y2, 0.75, 0.25 ); // (purple) 3/4 along, moves 1/4 away canvas.drawSquare( x1, y1, 8, "white(black)" ); // (black) starting point as square canvas.drawCircle( p1[0], p1[1], 4, "white(blue)" ); canvas.drawCircle( p2[0], p2[1], 4, "white(green)" ); canvas.drawCircle( p3[0], p3[1], 4, "white(purple)" ); }

(click to enlarge)

Hint

Click Me! if you want to to see a general hint that applies to some of the methods below

Tree

Write a recursive method that produces the given drawing. Note that since the square is tilted it needs be drawn as a polygon, so all four points of the square need to be computed.

canvas.drawPolygon( the-color, x1, y1, x2, y2, ..., xN, yN )

• drawTree( x1, y1, x2, y2, depth ) where the given points (x1,y1) and (x2,y2) specify the base of the tree from left to right

  depth 1	depth 2	depth 3	depth 4	depth 10	depth 15

Click Me! if you want to to see a hint for the values for distAway but keep in mind that reasonable guesses might work too

Snowflake

Write a recursive method that produces the given drawing.

• drawSnowflake( x1, y1, x2, y2, depth ) where the given points (x1,y1) and (x2,y2) specify the where the snowflake begins and ends for the given depth

  depth 1	depth 2	depth 3	depth 4	depth 15

Click Me! if you want to to see a hint for the values for distAway but keep in mind that reasonable guesses might work too

Green Dragon

Write a recursive method that produces the given drawing.

• drawGreenDragon( x1, y1, x2, y2, depth ) where the given points (x1,y1) and (x2,y2) specify the where the dragon begins and ends for the given depth

  depth 1	depth 2	depth 3	depth 4	depth 15

Click Me! if you want to to see a hint for the values for distAway but keep in mind that reasonable guesses might work too

Red Dragon

Write a recursive method that produces the given drawing.

• drawRedDragon( x1, y1, x2, y2, depth ) where the given points (x1,y1) and (x2,y2) specify the where the dragon begins and ends for the given depth

  depth 1	depth 2	depth 3	depth 4	depth 15

Click Me! if you want to to see a hint for the values for distAway but keep in mind that reasonable guesses might work too

Exploration

Change gradually the values for distAlong and distAway and see the effect.