Simplification
SelingerSimplification
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Meshes.SelingerSimplification — Type
SelingerSimplification(τ)Selinger’s simplification algorithm with tolerance τ in length units (default to meter).
The higher is the tolerance, the more aggressive is the simplification.
References
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SelingerSimplification, P. 2003. Potrace: A polygon-based tracing algorithm
poly = PolyArea([(0.22926679, 0.47329807), (0.23094065, 0.44913536), (0.2569517, 0.38217533),
(0.3072999, 0.272418), (0.34814754, 0.18421611), (0.37949452, 0.11756973),
(0.4013409, 0.07247882), (0.41368666, 0.048943404), (0.42597583, 0.031655528),
(0.4382084, 0.0206152), (0.45038435, 0.015822414), (0.4625037, 0.017277176),
(0.47175184, 0.02439156), (0.47812873, 0.03716557), (0.4816344, 0.055599205),
(0.48226887, 0.07969247), (0.48172843, 0.10446181), (0.4800131, 0.12990724),
(0.47712287, 0.15602873), (0.47305775, 0.18282633), (0.47093934, 0.20558843),
(0.47076762, 0.22431506), (0.47254258, 0.23900622), (0.47626427, 0.24966191),
(0.47768936, 0.25845313), (0.47681788, 0.26537988), (0.4736498, 0.27044216),
(0.46818516, 0.27363995), (0.4613889, 0.27232954), (0.45326096, 0.2665109),
(0.44380143, 0.256184), (0.43301025, 0.24134888), (0.4246466, 0.22978415),
(0.41871038, 0.22148979), (0.4152017, 0.21646582), (0.4141205, 0.21471222),
(0.41227448, 0.21589448), (0.40966362, 0.22001258), (0.40628797, 0.22706655),
(0.40214747, 0.23705636), (0.40200475, 0.24653101), (0.40585983, 0.25549048),
(0.41371268, 0.2639348), (0.4255633, 0.2718639), (0.4378565, 0.28495985),
(0.4505922, 0.30322257), (0.46377045, 0.32665208), (0.47739124, 0.35524836),
(0.5046394, 0.36442512), (0.5455148, 0.35418236), (0.60001767, 0.32452005),
(0.66814786, 0.27543822), (0.7186763, 0.24664374), (0.75160307, 0.23813659),
(0.76692814, 0.2499168), (0.7646515, 0.28198436), (0.7769703, 0.29925033),
(0.8038847, 0.3017147), (0.84539455, 0.28937748), (0.9015, 0.26223865),
(0.94408435, 0.24899776), (0.9731477, 0.24965483), (0.98869, 0.26420987),
(0.9907113, 0.29266283), (0.9849871, 0.31338844), (0.97151726, 0.32638666),
(0.950302, 0.3316575), (0.9213412, 0.32920095), (0.8798396, 0.34078467),
(0.8257972, 0.36640862), (0.7592141, 0.40607283), (0.6800901, 0.4597773),
(0.6450007, 0.49104902), (0.6539457, 0.49988794), (0.7069251, 0.48629412),
(0.803939, 0.45026752), (0.877913, 0.4226481), (0.9288472, 0.40343583),
(0.9567415, 0.39263073), (0.961596, 0.39023277), (0.9419039, 0.40523484),
(0.89766514, 0.43763688), (0.8288798, 0.48743892), (0.7355478, 0.55464095),
(0.6655121, 0.60063523), (0.6187727, 0.6254217), (0.5953296, 0.62900037),
(0.5951828, 0.6113712), (0.57516366, 0.60261106), (0.53527224, 0.6027198),
(0.4755085, 0.6116975), (0.3958725, 0.6295441), (0.33913234, 0.6398651),
(0.30528808, 0.6426605), (0.2943397, 0.6379303), (0.30628717, 0.6256744),
(0.32149008, 0.6093727), (0.33994842, 0.5890249), (0.36166218, 0.5646312),
(0.38663134, 0.5361916), (0.3919681, 0.520893), (0.3776725, 0.5187355),
(0.34374446, 0.52971905), (0.29018405, 0.5538437), (0.25439468, 0.5678829),
(0.2363764, 0.5718367), (0.23612918, 0.56570506), (0.25365302, 0.549488),
(0.2733971, 0.5246488), (0.29536137, 0.49118724), (0.3195459, 0.4491035),
(0.34595063, 0.39839754), (0.3647463, 0.3590396), (0.37593287, 0.33102974),
(0.37951034, 0.31436795), (0.37547874, 0.30905423), (0.36070493, 0.3204269),
(0.33518887, 0.348486), (0.29893062, 0.3932315), (0.25193012, 0.45466346)])
simp1 = simplify(poly, SelingerSimplification(0.01))
simp2 = simplify(poly, SelingerSimplification(0.05))
simp3 = simplify(poly, SelingerSimplification(0.10))
fig = Mke.Figure(size = (800, 800))
viz(fig[1,1], poly)
viz(fig[1,2], simp1)
viz(fig[2,1], simp2)
viz(fig[2,2], simp3)
fig
DouglasPeuckerSimplification
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Meshes.DouglasPeuckerSimplification — Type
DouglasPeuckerSimplification(τ)Douglas-Peucker’s simplification algorithm with tolerance τ in length units (default to meter).
The higher is the tolerance, the more aggressive is the simplification.
References
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Douglas, D. and Peucker, T. 1973. Algorithms for the Reduction of the Number of Points Required to Represent a Digitized Line or its Caricature
simp1 = simplify(poly, DouglasPeuckerSimplification(0.01))
simp2 = simplify(poly, DouglasPeuckerSimplification(0.05))
simp3 = simplify(poly, DouglasPeuckerSimplification(0.10))
fig = Mke.Figure(size = (800, 800))
viz(fig[1,1], poly)
viz(fig[1,2], simp1)
viz(fig[2,1], simp2)
viz(fig[2,2], simp3)
fig
MinMaxSimplification
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Meshes.MinMaxSimplification — Type
MinMaxSimplification(method; min=3, max=typemax(Int), maxiter=10)Simplify geometries with binary search algorithm and a parent simplification method.
The simplification is performed until the number of vertices is in the [min, max] range or until a maximum number of iterations maxiter is reached.
simp1 = simplify(poly, MinMaxSimplification(DouglasPeuckerSimplification, max=20))
simp2 = simplify(poly, MinMaxSimplification(DouglasPeuckerSimplification, max=10))
simp3 = simplify(poly, MinMaxSimplification(DouglasPeuckerSimplification, max=5))
fig = Mke.Figure(size = (800, 800))
viz(fig[1,1], poly)
viz(fig[1,2], simp1)
viz(fig[2,1], simp2)
viz(fig[2,2], simp3)
fig