PixelConfigurationFinder

import math

"""variables"""
MAX_DISTANCE = 5.0
PRECISION = 0.01
results = [] #list of (int,int,float) ordered by delta


"""insert in results"""
def insert(L, px, pz, delta):
    i=len(L)
    L.append((px,pz,delta))
    while i>0 and L[i-1][2] > delta:
        L[i-1],L[i] = L[i],L[i-1] #swap
        i = i-1


"""calculations - efficient algorithm
Visually, this algorithm plots all points of integer coordinates within a circular ring"""

inf = MAX_DISTANCE-PRECISION
sup = MAX_DISTANCE
step_inf = math.ceil(16*(math.sqrt(inf*inf/2)+0.6))
step_sup = math.floor(16*(math.sqrt(sup*sup/2)+0.6))

#linear setups (px=0)
min_range_0 = math.ceil(16*(inf + 0.6))
max_range_0 = math.floor(16*(sup + 0.6))
for px in range(min_range_0, max_range_0+1):
    x = (px/16)-0.6
    delta = MAX_DISTANCE-x
    insert(results,px,0,delta)

#px between minimum (10pixels) and step_inf-1.
for px in range(10, step_inf):
    x = (px/16)-0.6
    min_range = math.ceil(16*(math.sqrt(max(inf*inf - x*x,0.0))+0.6))
    max_range = math.floor(16*(math.sqrt(max(sup*sup - x*x,0.0))+0.6))

    for pz in range(min_range, max_range+1):
        z = (pz/16)-0.6
        distance = math.sqrt(x*x + z*z)
        delta = MAX_DISTANCE-distance
        insert(results,pz,px,delta)

#px between step_inf and step_sup. extra precaution is taken in case px>pz. otherwise identical to above code
for px in range(step_inf, step_sup + 1):
    x = (px/16)-0.6
    min_range = math.ceil(16*(math.sqrt(max(inf*inf - x*x,0.0))+0.6))
    max_range = math.floor(16*(math.sqrt(max(sup*sup - x*x,0.0))+0.6))

    for pz in range(min_range, max_range+1):
        if px>pz: continue
        z = (pz/16)-0.6
        distance = math.sqrt(x*x + z*z)
        delta = MAX_DISTANCE-distance
        insert(results,pz,px,delta)


"""results display"""
for X,Z,DELTA in results:
    print("X: %3d \t Z: %3d \t delta: %.6f" % (X,Z,DELTA))

"""alternative display, showing distance instead of delta"""
#for X,Z,DELTA in results[::-1]:
#    print("X: %3d \t Z: %3d \t distance: %.6f" % (X,Z,MAX_DISTANCE-DELTA))