added buffered stepping support and the rudiments of the arc-interpolator
This commit is contained in:
Simen Svale Skogsrud
@ -15,11 +15,11 @@ class CircleTest
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def init
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@pixels = []
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@tool_position = [14,14]
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30.times { @pixels << '.'*30 }
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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>29 || y > 29
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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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@ -34,11 +34,11 @@ class CircleTest
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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)
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# dP[x+1, y-1]: 2 (1 + x - y)
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# dP[x-1, y-1]: 2 (1 - x - y)
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# dP[x-1, y+1]: 2 (1 - x + 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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@ -111,6 +111,7 @@ class CircleTest
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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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@ -130,8 +131,10 @@ class CircleTest
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plot_pixel(x+14, -y+14, "X")
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end
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dx = (y==0) ? angular_direction : y.sign*angular_direction
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dy = (x==0) ? angular_direction : -x.sign*angular_direction
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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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@ -173,12 +176,250 @@ class CircleTest
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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 && 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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# A DDA-direct search circle interpolator unrolled for each octant. Optimal and impure
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def arc_unrolled(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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# Quandrants of the circls
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# \ 1|2 /
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# 8\ | / 3
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# \|/
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# ---------|-----------
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# 7 /|\ 4
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# / | \
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# / 6 | 5 \
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#
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#
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#
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if angular_direction>0 # clockwise
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if x.abs<y.abs # quad 1,2,6,5
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if y>0 # quad 1,2
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while x<0 # quad 1 x+,y+
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x += 1
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f += 1+x2
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x2 += 2
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f_diagonal = f + 1 + y2
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if (f.abs >= f_diagonal.abs)
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y += 1
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y2 += 2
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f = f_diagonal
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end
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end
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while x>=0 # quad 2, x+, y-
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x += 1
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f += 1+x2
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x2 += 2
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f_diagonal = f + 1 - y2
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if (f.abs >= f_diagonal.abs)
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y -= 1
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y2 -= 2
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f = f_diagonal
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end
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end
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end
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if y<=0 # quad 6, 5
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while x<0 # quad 6 x-, y+
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x -= 1
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f += 1-x2
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x2 -= 2
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f_diagonal = f + 1 + y2
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if (f.abs >= f_diagonal.abs)
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y += 1
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y2 += 2
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f = f_diagonal
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end
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end
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while x>=0 # quad 5 x-, y-
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x -= 1
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f += 1-x2
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x2 -= 2
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f_diagonal = f + 1 - y2
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if (f.abs >= f_diagonal.abs)
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y -= 1
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y2 -= 2
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f = f_diagonal
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end
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end
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end
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# Quandrants of the circls
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# \ 1|2 /
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# 8\ | / 3
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# \|/
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# ---------|-----------
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# 7 /|\ 4
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# / | \
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# / 6 | 5 \
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else 3 # quad 3,4,7,8
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if x>0 # quad 3,4
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while y>0 # quad 3 x+,y+
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x += 1
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f += 1+x2
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x2 += 2
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f_diagonal = f + 1 + y2
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if (f.abs >= f_diagonal.abs)
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y += 1
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y2 += 2
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f = f_diagonal
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end
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end
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while x>=0 # quad 2, x+, y-
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x += 1
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f += 1+x2
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x2 += 2
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f_diagonal = f + 1 - y2
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if (f.abs >= f_diagonal.abs)
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y -= 1
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y2 -= 2
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f = f_diagonal
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end
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end
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end
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if y<=0 # quad 6, 5
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while x<0 # quad 6 x-, y+
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x -= 1
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f += 1-x2
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x2 -= 2
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f_diagonal = f + 1 + y2
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if (f.abs >= f_diagonal.abs)
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y += 1
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y2 += 2
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f = f_diagonal
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end
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end
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while x>=0 # quad 5 x-, y-
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x -= 1
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f += 1-x2
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x2 -= 2
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f_diagonal = f + 1 - y2
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if (f.abs >= f_diagonal.abs)
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y -= 1
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y2 -= 2
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f = f_diagonal
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end
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end
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end
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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 && 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, 5)
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#test.arc_clean(0, Math::PI*2, 5)
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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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