Matthew M. ha scritto:
This week we’re going to keep it simple… very simple.
## ##
# #
specifies the aspect ratio (height divided by width).
ruby circle.rb 7 1.4
This should draw a circle of radius 7 with aspect ratio of 1.4. If done
correctly, your output will actually look like a circle (assuming 1.4 is an
accurate measure of the actual aspect ratio).
Here my solution. It is available on pastie:
http://pastie.org/215379
http://pastie.org/215380 (specs)
and it is also attached below:
Solution to Ruby Q. #166 - Circle Drawing
Usage:
Circle.new(5).to_s
or:
Circle.new(5, 2).to_s
or:
Circle.new(5, 2, ‘x’).to_s
Objects of class Circle draw circles on stdout. The aspect ratio
correction is actually made drawing an ellipse with semimajor axis
(a) equals to the given circle radius and semiminor axis (b) equals
to a / aspect_ratio.
Circle class is responsible to
* initialize a Circle object with the given radius, aspect ratio
and drawing char
* initialize a canvas
* draw the circle on its internal canvas
* convert the canvas to string for output on stdout
class Circle
cx, cy are the coordinates of the circle’s center.
attr_reader :cx, :cy
attr_reader :radius
w, h are width and height of the canvas
attr_reader :w, :h
canvas is a linear array that is initially filled with spaces
attr_reader :canvas
Initialize a Circle object passing a value for radius, aspect
ratio and drawing character.
def initialize(radius, aspect_ratio = 1.0, char = ‘#’)
@radius = radius.to_i
@aspect_ratio = aspect_ratio.to_f
@char = char
fail "Error: radius must be > 0" if @radius <= 0
fail "Error: aspect ratio must be > 0" if @aspect_ratio <= 0
# a is the semimajor axis of the ellipse and is equal to the given
# radius
@a = @radius
# b is the semiminor axis of the ellipse and is calculated from a
# and the given aspect ratio
@b = (@a / @aspect_ratio).ceil
# calculate the size of the canvas
@w, @h = (@a + 1) * 2, (@b + 1) * 2
# center coordinates correspond to the size of semiaxis.
@cx, @cy = @a, @b
# initialize the canvas with spaces
@canvas = Array.new(@w * @h, ' ')
# draw ellipse on canvas
draw_ellipse(@a, @b)
end
Print circle on stdout.
def to_s
result = “”
(0…@h - 1).each do |line|
result << @canvas[line * @w…line * @w + @w - 1].to_s << “\n”
end
result
end
private
Draw the given character on canvas to the given coordinates.
def point(x, y)
@canvas[y * @w + x] = @char
end
Translates and mirrors point (x, y) in the quadrants taking
advantage of the simmetries in the ellipse. Thus, for a given
point (x, y) the method plot three other points in the remaining
quadrants.
def plot_four_points(x, y)
point(@cx + x, @cy + y)
point(@cx - x, @cy + y)
point(@cx + x, @cy - y)
point(@cx - x, @cy - y)
end
Draw an ellipse on canvas. This method implements a Bresenham
based algorithm by John Kennedy
The method calculates two set of points in the first quadrant. The
first set starts on the positive x axis and wraps in a
counterclockwise direction until the tangent line slope is equal
to -1. The second set starts on the positive y axis and wraps in
a clockwise direction until the tangent line slope is equal to -1.
def draw_ellipse(a, b)
a_square = 2 * a2
b_square = 2 * b2
draw_first_set(a, b, a_square, b_square)
draw_second_set(a, b, a_square, b_square)
end
The method increments y and decides when to decrement x testing
the sign of a function. In this case, the decision function is
(2*ellipse_error+x_change) and its value is calculated
iteratively.
def draw_first_set(a, b, a_square, b_square)
x, y = a, 0
x_change, y_change = b**2 * (1 - 2 * a), a**2
stopping_x, stopping_y = b_square * a, 0
ellipse_error = 0
while(stopping_x >= stopping_y) do
plot_four_points(x, y)
y += 1
stopping_y += a_square
ellipse_error += y_change
y_change += a_square
if (2 * ellipse_error + x_change) > 0
x -= 1
stopping_x -= b_square
ellipse_error += x_change
x_change += b_square
end
end
end
The method increments x and decides when to decrement y testing
the sign of a function. In this case, the decision function is
(2*ellipse_error+y_change) and its value is calculated
iteratively.
def draw_second_set(a, b, a_square, b_square)
x, y = 0, b
x_change, y_change = b**2, a**2 * (1 - 2 * b)
stopping_x, stopping_y = 0, a_square * b
ellipse_error = 0
while stopping_x <= stopping_y do
plot_four_points(x, y)
x += 1
stopping_x += b_square
ellipse_error += x_change
x_change += b_square
if (2 * ellipse_error + y_change) > 0
y -= 1
stopping_y -= a_square
ellipse_error += y_change
y_change += a_square
end
end
end
end
Usage:
ruby circle.rb 7 #=> print out a circle of radius 7
ruby circle.rb 7 1.8 #=> print out a circle of radius 7 and aspect
ratio 1.8
ruby circle.rb 7 1.8 x #=> print out a circle of radius 7 and aspect
ratio 1.8
using the ascii char ‘x’
print Circle.new(ARGV[0], ARGV[1] || 1.0, ARGV[2] || ‘#’).to_s if $0 ==
FILE
