Interpolating/moving an object along a path in Python

Question

I'm trying to move an object along a path with constant velocity. I have a set of nodes using networkx, and have gotten the shortest path between these nodes. The shortest path is not smooth or dependent on time. I want to interpolate or move through the path so that the object moves through the path with a dt = 1/3600 and constant velocity, updating the position along the path. I have some example/pseudo code:

def func(self):
    distance = 0

    for i in range(len(nodes)-1):
        shortest_path = nx.shortest_path(G_full, source=nodes[i], target=nodes[i+1], weight='weight')
        
        node_dist = 0

        for j in range(len(shortest_path)-1):
            node_dist += geodesic(shortest_path[j], shortest_path[j+1]).kilometers
            distance += geodesic(shortest_path[j], shortest_path[j+1]).kilometers
    return node_dist, distance

This gives me the shortest path between a list of nodes, for example the nodes: [(47.6835508, 6.4912519), (47.9078655, 6.3314071), (48.0126858, 6.6045816)]

I've tried iterating over the shortest path for each node, but get stuck on how I should set up the path updating.

Answer 1

To achieve smooth interpolation and move an object along the path with a constant velocity, you can use linear interpolation between consecutive nodes. You'll need to calculate the total distance of the path and then determine the intermediate positions based on the desired time step (dt) and constant velocity.

Here's an example/pseudo code to help you achieve this:

from geopy.distance import geodesic

class PathInterpolator: def init(self, nodes, G_full): self.nodes = nodes self.G_full = G_full self.distance, self.total_distance = self.calculate_distances()

def calculate_distances(self):
    distance = 0
    total_distance = 0

    for i in range(len(self.nodes) - 1):
        shortest_path = nx.shortest_path(
            self.G_full, source=self.nodes[i], target=self.nodes[i + 1], weight="weight"
        )

        for j in range(len(shortest_path) - 1):
            total_distance += geodesic(
                shortest_path[j], shortest_path[j + 1]
            ).kilometers

    return distance, total_distance

def interpolate_path(self, dt=1/3600, constant_velocity=10):
    current_distance = 0

    while current_distance < self.total_distance:
        current_distance += constant_velocity * dt
        current_position = self.get_position_at_distance(current_distance)
        print("Current Position:", current_position)
        # You can do something with the current_position, such as updating the object's position.

def get_position_at_distance(self, target_distance):
    current_distance = 0

    for i in range(len(self.nodes) - 1):
        shortest_path = nx.shortest_path(
            self.G_full, source=self.nodes[i], target=self.nodes[i + 1], weight="weight"
        )

        for j in range(len(shortest_path) - 1):
            segment_distance = geodesic(
                shortest_path[j], shortest_path[j + 1]
            ).kilometers

            if current_distance + segment_distance >= target_distance:
                ratio = (target_distance - current_distance) / segment_distance
                lat = shortest_path[j][0] + ratio * (
                    shortest_path[j + 1][0] - shortest_path[j][0]
                )
                lon = shortest_path[j][1] + ratio * (
                    shortest_path[j + 1][1] - shortest_path[j][1]
                )
                return lat, lon

            current_distance += segment_distance

Example usage:

nodes = [(47.6835508, 6.4912519), (47.9078655, 6.3314071), (48.0126858, 6.6045816)] G_full = your_networkx_graph # Replace with your actual graph

path_interpolator = PathInterpolator(nodes, G_full) path_interpolator.interpolate_path()

This code defines a `PathInterpolator` class that calculates the total distance of the path and provides a method for interpolating the path at a given time step (`dt`) with a constant velocity. The `get_position_at_distance` method is responsible for returning the interpolated position based on the current distance along the path.