Simplification

Meshes.simplify — Function

simplify(object, method)

Simplify geometric object with given method.

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Meshes.SimplificationMethod — Type

SimplificationMethod

A method for simplifying geometric objects.

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SelingerSimplification

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

SelingerSimplification, P. 2003. Potrace: A polygon-based tracing algorithm

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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

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

Douglas, D. and Peucker, T. 1973. Algorithms for the Reduction of the Number of Points Required to Represent a Digitized Line or its Caricature

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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

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.

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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