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MaxSea International Software editor for marine market MaxSea is distributed in 25 countries Available in 13 languages. 90.000 ships equiped

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Our group H OLDING B IDART - F RANCE S OFTWARE B IDART - F RANCE C OMMERCIAL, S ALES, M ARKETING, SUPPORT B ARCELONA - S PAIN S OFTWARE P ORTLAND - USA C HARTS B IDART - F RANCE 75 E MPLOYES T URNOVER 2012: 6.2 M€ (+10%)

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Radar Overlay Strong collaboration with FURUNO Japan (1st worldwide marine electronics manufacturer).

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Cameras FLIR (IR, night vision…)

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Isochrones for minimum time route optimization Wind polar Wave polar Set sail Weather prediction (wind, waves) Currents Optimal route

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DEMO

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Isochrone : Dynamic programming N Objective: Maximize distance for a given time interval ∆t DStep n →Isochrone at time ζ Reference : Knmi publicatie met nummer : 102.94 On minimal-time ship routing S.J. Bijlsma 1975

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N D Wind Polars Isochrone : Dynamic programming

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N D a d1d1 d2d2 d3d3 d4d4 What is the shorter path ? Isochrone : Dynamic programming

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N D Wind polar Direct construction of next point : normal to isochrone == normal to polar Isochrone : Dynamic programming

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N D Repeat for all isochrone point, you construct next isochrone. Isochrone : Dynamic programming

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Next isochrone (dash) Optimization becomes a geometrical optimization. Not easy to resolve, in good computational time, taking into account numerical precision. Multiple path for optimal route at intersection point. Isochrone : Dynamic programming

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Route optimization for motor boats Main goal: fuel consumption optimization. But also limit weather conditions. Several types of boats – Motor – Motor with sail assistance – Motor Sailing – Sailing

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3D Routing New problem : find best course (2d) and best motor speed (power) to minimize fuel consumption. Motor and MotorSail boats have round speed polars (motor always on) => isochrones are isodistance (shortest path).

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Fuel Consumption models Motor : – Hydro & areo dynamic forces + motor consumption curve. – Approximation 2 nd degree from speed inside speed limits (18-25kts) : Conso t/nm = 0.0036*V2 + 0.1015V + 0.8848 (not linear) Motor Sailing : mutilple Wind polar curves (for each motor power / sail %).

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Fast Marching Method Ordered Upwind Method We wanted a new method for 2D & 3D (more easy to implement than 3D geometric calculation). Differential equation : Consumption = f(x,y,t,course,motor power). Front propagation. Strong anisotropy : wind and wind polar (sailing) or waves.

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Ordered Upwind Method Considered are sorted according to cost. Reference : SIAM J. Numer. Anal., 41(1), 325–363. (39 pages) Ordered Upwind Methods for Static Hamilton--Jacobi Equations: Theory and Algorithms

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Ordered Upwind Method Smallest Considered is removed from Sorted Queue. It becomes the Last Accepted.

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Ordered Upwind Method All Neighbors of Last Accepted are updated. Cost and Arrival Time are computed.

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Ordered Upwind Method Again, smallest Considered => Last Accepted

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Ordered Upwind Method The Front advanced with 2 new Accepted. Loop until arrival point is reached.

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3D OUM

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OUM : 3 update methods Direct Cost : from a node to horizontal, vertical or diagonal node. Enumeration : minimise over 20 angles (original method from Vladimirsky) Gradiant : from downwind gradiant, select best speed vector in polar, use it to compute upwind.

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Enumeration Linear cost interpolation between U2 & U3. 20 angles tried for minimization.

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Gradiant, when 3 accepted neighboors

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DEMO

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Experience Difficult to validate results : reference solution. Gradiant was working during unit testing, we found problems during integration. Parallel algorithm is not evidence. Software optimization is needed for interactive simulations.

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