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Midpoint circle: r=8, centre (-5,10)

Short answer

Use midpoint circle algorithm with p0=1-r=-7; octant points are (0,8), (1,8), (2,8), (3,7), (4,7), (5,6). Applying eight-way symmetry about (-5,10) yields 44 distinct pixels on the circle.

Calculate the points in the circumference of the circle having radius 8 units and center at (-5, 10) using the midpoint circle algorithm.

Given: radius r = 8, centre (-5,10).

Start at (x0, y0) = (0, 8). Initial parameter p0 = 1 − r = -7.

p < 0 : next point (x+1, y),     p_new = p + 2x_new + 1
p ≥ 0 : next point (x+1, y−1),   p_new = p + 2(x_new − y_new) + 1
Stop when x ≥ y

Decision parameter table (circle centred at the origin; p_k decides the next point):

kp_k(x_k, y_k)next (x, y)
0-7(0,8)(1,8)
1-4(1,8)(2,8)
21(2,8)(3,7)
3-6(3,7)(4,7)
43(4,7)(5,6)
52(5,6)(6,5)

Octant points about the origin: (0,8), (1,8), (2,8), (3,7), (4,7), (5,6).

Eight-way symmetry gives, for each octant point (x,y), the points (xc±x, yc±y) and (xc±y, yc±x):

(x,y)8 symmetric points
(0,8)(-5,18) (-5,18) (-5,2) (-5,2) (3,10) (-13,10) (3,10) (-13,10)
(1,8)(-4,18) (-6,18) (-4,2) (-6,2) (3,11) (-13,11) (3,9) (-13,9)
(2,8)(-3,18) (-7,18) (-3,2) (-7,2) (3,12) (-13,12) (3,8) (-13,8)
(3,7)(-2,17) (-8,17) (-2,3) (-8,3) (2,13) (-12,13) (2,7) (-12,7)
(4,7)(-1,17) (-9,17) (-1,3) (-9,3) (2,14) (-12,14) (2,6) (-12,6)
(5,6)(0,16) (-10,16) (0,4) (-10,4) (1,15) (-11,15) (1,5) (-11,5)

Answer: 44 distinct pixels on the whole circle, listed above.

✓ Answer checked by Claude Opus 5.5 (high effort)

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