%% Partitioning Longitudinal Terminal States in Trajectory Generation
% This example shows how to partition the longitudinal terminal states in optimal trajectory planning using a trajectoryOptimalFrenet object.
%% Create and Assign Map to State Validator
% Create a state validator object for collision checking.

stateValidator = validatorOccupancyMap; 

% Create an obstacle grid map.

grid = zeros(50,100);
grid(25:27,28:33) = 1;
grid(16:18,37:42) = 1;
grid(29:31,72:77) = 1;

% Create a binaryOccupancyMap with the grid map.

map = binaryOccupancyMap(grid);

% Assign the map and the state bounds to the state validator.

stateValidator.Map = map;
stateValidator.StateSpace.StateBounds(1:2,:) = [map.XWorldLimits; map.YWorldLimits];

%% Plan and Visualize Trajectory
% Create a reference path for the planner to follow.

refPath = [0,25;30,30;75,20;100,25];

% Initialize the planner object with the reference path, and the state validator.

planner = trajectoryOptimalFrenet(refPath,stateValidator);

% Assign longitudinal terminal state, lateral deviation, and maximum acceleration values.

planner.TerminalStates.Longitudinal = 100;
planner.TerminalStates.Lateral = -5:5:5;
planner.FeasibilityParameters.MaxAcceleration = 10;

% Assign the number of partitions for the longitudinal terminal state.

planner.NumSegments = 3;

% Trajectory Planning
% Initial Frenet state of vehicle.

initFrenetState = zeros(1,6);

% Plan a trajectory from initial Frenet state.

plan(planner,initFrenetState);

% Trajectory Visualization
% Visualize the map and the trajectories.

show(map)
hold on
show(planner,'Trajectory','all')
hold on

% Generate Lane Boundaries
% Calculate end of reference path as Frenet state.

refPathEnd = cart2frenet(planner,[planner.Waypoints(end,:) 0 0 0 0]);

% Calculate lane offsets on both sides of the lateral terminal states with half lane width value.

laneOffsets = unique([planner.TerminalStates.Lateral+2.5 planner.TerminalStates.Lateral-2.5]);

% Calculate positions of lanes in Cartesian state.

numLaneOffsets = numel(laneOffsets);
xRefPathEnd = ceil(refPathEnd(1));
laneXY = zeros((numLaneOffsets*xRefPathEnd)+numLaneOffsets,2);
xIndex = 0;

for laneID = 1:numLaneOffsets
    for x = 1:xRefPathEnd
        laneCart = frenet2cart(planner,[x 0 0 laneOffsets(laneID) 0 0]);
        xIndex = xIndex + 1;
        laneXY(xIndex,:) = laneCart(1:2);
    end
    xIndex = xIndex + 1;
    laneXY(xIndex,:) = NaN(1,2);
end

% Plot lane boundaries.

plot(laneXY(:,1),laneXY(:,2),'LineWidth',0.5,'Color',[0.5 0.5 0.5],'DisplayName','Lane Boundaries','LineStyle','--')

% Copyright 2019 The MathWorks, Inc.