273 lines
6.6 KiB
Ruby
273 lines
6.6 KiB
Ruby
require "pp"
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# A tiny ruby script to design and test the implementation of the arc-support
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class Numeric
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# -1 if the number < 0, 1 if number >= 0
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def sign
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return 0 if self == 0
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(self < 0) ? -1 : 1
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end
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end
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class CircleTest
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include Math
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def init
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@pixels = []
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@tool_position = [14,14]
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40.times { @pixels << '.'*40 }
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end
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def plot_pixel(x,y, c)
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return if x<0 || y<0 || x>39 || y > 39
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@pixels[y] = @pixels[y][0..x][0..-2]+c+@pixels[y][(x+1)..-1]
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end
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def show
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@pixels.each do |line|
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puts line.gsub('.','. ').gsub('0','0 ').gsub('1','1 ').gsub('2','2 ').gsub('X','X ').gsub('o','o ')
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end
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end
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# dP[x+1,y]: 1 + 2 x
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# dP[x-1,y]: 1 - 2 x
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# dP[x, y+1]: 1 + 2 y
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# dP[x, y-1]: 1 - 2 y
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# dP[x+1, y+1]: 2 (1 + x + y) 1+2x+1+2y
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# dP[x+1, y-1]: 2 (1 + x - y) 1+2x+1-2y
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# dP[x-1, y-1]: 2 (1 - x - y) 2-2x-2y
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# dP[x-1, y+1]: 2 (1 - x + y) 2-2x+2x
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# dP[x+a, y+b]: |dx| - 2*dx*x + |dy| + 2*dy*y
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# Algorithm from the wikipedia aricle on the Midpoint circle algorithm.
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def raster_circle(radius)
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f = 1-radius
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ddF_x = 1
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ddF_y = -2*radius
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x = 0
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y = radius
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while x<=y
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if f>0
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y -= 1
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ddF_y += 2
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f += ddF_y
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end
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x += 1
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ddF_x += 2
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f += ddF_x
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plot_pixel(x+14,-y+14,'X')
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end
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x += 1
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ddF_x += 2
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f += ddF_x
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while y>0
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if f<0
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x += 1
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ddF_x += 2
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f += ddF_x
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end
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y -= 1
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ddF_y += 2
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f += ddF_y
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plot_pixel(x+14,-y+14,'o')
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end
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end
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# An "ideal" arc. Computationally expensive, but always pure
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def pure_arc(theta, segment, angular_direction, radius)
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var = [(sin(theta)*(radius)), (cos(theta)*(radius))]
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error_sum = 0.0
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error_count = 0.0
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max_error = 0.0
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(PI*2*radius).ceil.times do
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if var[0].abs<var[1].abs
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major_axis = 0
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minor_axis = 1
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else
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major_axis = 1
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minor_axis = 0
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end
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delta = [var[1].sign*angular_direction, -var[0].sign*angular_direction]
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delta[0] = angular_direction if delta[0] == 0
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delta[1] = angular_direction if delta[1] == 0
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var[major_axis] += delta[major_axis]
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var[minor_axis] = (sqrt((radius**2-var[major_axis]**2))*var[minor_axis].sign).round
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error_count += 1
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error = (var[minor_axis].abs-(sqrt((radius**2)-var[major_axis]**2)).abs).abs
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max_error = [max_error,error].max
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error_sum += error
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plot_pixel(var[0]+14, -var[1]+14, 'X')
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end
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puts "Average error: #{error_sum/error_count} Maximum eror: #{max_error}"
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end
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# A DDA-direct search circle interpolator. Optimal and impure
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def arc_clean(theta, angular_travel, radius)
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radius = radius
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x = (sin(theta)*radius).round
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y = (cos(theta)*radius).round
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angular_direction = angular_travel.sign
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tx = (sin(theta+angular_travel)*radius).round
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ty = (cos(theta+angular_travel)*radius).round
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f = (x**2 + y**2 - radius**2).round
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min_x = 0
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max_x = 0
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i = 0
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pp [x,y]
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while true
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if i > 0
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plot_pixel(x+14, -y+14, "012"[i%3].chr)
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else
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plot_pixel(x+14, -y+14, "X")
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end
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dx = (y==0) ? -x.sign : y.sign*angular_direction
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dy = (x==0) ? -y.sign : -x.sign*angular_direction
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pp [[x,y],[dx,dy]]
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if x.abs<y.abs
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f_straight = f + 1+2*x*dx
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f_diagonal = f_straight + 1+2*y*dy
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x += dx
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if (f_straight.abs < f_diagonal.abs)
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f = f_straight
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else
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y += dy
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f = f_diagonal
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end
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else
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f_straight = f + 1+2*y*dy
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f_diagonal = f_straight + 1+2*x*dx
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y += dy
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if (f_straight.abs < f_diagonal.abs)
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f = f_straight
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else
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x += dx
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f = f_diagonal
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end
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end
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f_should_be = (x**2+y**2-radius**2)
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if f.round != f_should_be.round
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raise "f out of range. Is #{f}, should be #{f_should_be}"
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end
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min_x = [x,min_x].min
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max_x = [x,max_x].max
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break if (x.sign == tx.sign && y.sign == ty.sign) && (x.abs>=tx.abs) && (y.abs>=ty.abs)
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i += 1
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end
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puts "Target #{[tx,ty].inspect}"
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plot_pixel(tx+14, -ty+14, "o")
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pp [x,y]
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puts "Diameter: #{max_x-min_x}"
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end
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# A DDA-direct search circle interpolator. Optimal and impure
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def arc_supaoptimal(theta, angular_travel, radius)
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radius = radius
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x = (sin(theta)*radius).round
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y = (cos(theta)*radius).round
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angular_direction = angular_travel.sign
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tx = (sin(theta+angular_travel)*(radius-0.5)).floor
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ty = (cos(theta+angular_travel)*(radius-0.5)).floor
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f = (x**2 + y**2 - radius**2).round
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x2 = 2*x
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y2 = 2*y
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dx = (y==0) ? -x.sign : y.sign*angular_direction
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dy = (x==0) ? -y.sign : -x.sign*angular_direction
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max_steps = (angular_travel.abs*radius*2).floor
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# dP[x+1,y]: 1 + 2 x
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# dP[x, y+1]: 1 + 2 y
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max_steps.times do |i|
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if i > 0
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plot_pixel(x+20, -y+20, "012"[i%3].chr)
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else
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plot_pixel(x+20, -y+20, "X")
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end
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raise "x2 out of range" unless x2 == 2*x
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raise "y2 out of range" unless y2 == 2*y
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f_should_be = (x**2+y**2-radius**2)
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if f.round != f_should_be.round
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show
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raise "f out of range. Is #{f}, should be #{f_should_be}"
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end
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if x.abs<y.abs
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x += dx
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f += 1+x2*dx
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x2 += 2*dx
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f_diagonal = f + 1 + y2*dy
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if (f.abs >= f_diagonal.abs)
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y += dy
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dx = y.sign*angular_direction unless y == 0
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y2 += 2*dy
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f = f_diagonal
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end
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dy = -x.sign*angular_direction unless x == 0
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else
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y += dy
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f += 1+y2*dy
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y2 += 2*dy
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f_diagonal = f + 1 + x2*dx
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if (f.abs >= f_diagonal.abs)
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x += dx
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dy = -x.sign*angular_direction unless x == 0
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x2 += 2*dx
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f = f_diagonal
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end
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dx = y.sign*angular_direction unless y == 0
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end
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break if x*ty.sign*angular_direction>=tx*ty.sign*angular_direction &&
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y*tx.sign*angular_direction<=ty*tx.sign*angular_direction
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end
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plot_pixel(tx+20, -ty+20, "o")
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return {:tx => tx, :ty => ty, :x => x, :y => y}
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end
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end
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test = CircleTest.new
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test.init
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test.arc_clean(0, Math::PI*2, 3)
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# (1..10000).each do |r|
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# test.init
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# data = test.arc_supaoptimal(2.9, Math::PI*1, r)
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# if (data[:tx]-data[:x]).abs > 1 || (data[:ty]-data[:y]).abs > 1
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# puts "r=#{r} fails target control"
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# pp data
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# puts
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# end
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# end
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# test.init
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# data = test.arc_supaoptimal(1.1, -Math::PI, 19)
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# pp data
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#test.pure_arc(0,1,1,4)
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test.show
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