How to randomly replace a given line vector multiple times within a polygon?

Question

I have this line vector that represents the movement trajectory of a given animal. I would like to randomly replace this vector line within a polygon, multiple times, changing its position and orientation, but without changing the trajectory itself. Is this possible? It is OK if random trajectories intersect each other, as long as they don't fall outside the polygon. Here is an example:

The black square is the polygon, the continuous blue line is the real trajectory, and the three dotted blue lines are examples of three random placements of the trajectory within the polygon.

How can I do this on QGIS or R?

I don't have any experience with Python.

Answer 1

Following PyQGIS code is one of possible approach:

import random

registry = QgsMapLayerRegistry.instance()

trajectory = registry.mapLayersByName('trajectory')
extent_trajectory = registry.mapLayersByName('extent_trajectory')

feat_extent_trajectory = extent_trajectory[0].getFeatures().next()

line_points = [ feat.geometry().asPolyline() for feat in trajectory[0].getFeatures() ]

feats_trajectory = [ feat for feat in trajectory[0].getFeatures() ]

convex_hull_trajectory = [ feat.geometry().convexHull() for feat in trajectory[0].getFeatures() ]

centroid_convex_hull = convex_hull_trajectory[0].centroid().asPoint()

distances = [ point.distance(centroid_convex_hull) for point in line_points[0] ]

max_distance = max(distances)

new_extent = feat_extent_trajectory.geometry().buffer(-max_distance, -1)
xmin, ymin, xmax, ymax = new_extent.boundingBox().toRectF().getCoords()

points = []
rotations = []

n = 10 #number of trajectories

for i in range(n):
    xRandom = random.uniform(xmin, xmax)
    yRandom = random.uniform(ymin, ymax)
    points.append(QgsPoint(xRandom, yRandom))
    rotation = random.uniform(0,360)
    rotations.append(rotation)

lines = []

for i in range(len(rotations)):
    feats_trajectory = [ feat for feat in trajectory[0].getFeatures() ]

    feats_trajectory[0].geometry().rotate(rotations[i], centroid_convex_hull)

    convex_hull_trajectory = [ feat.geometry().convexHull() for feat in trajectory[0].getFeatures() ]
    centroid_convex_hull = convex_hull_trajectory[0].centroid().asPoint()

    x = points[i].x() - centroid_convex_hull.x()  
    y = points[i].y() - centroid_convex_hull.y()

    feats_trajectory[0].geometry().translate(x, y)

    lines.append(feats_trajectory[0].geometry().exportToWkt())

epsg = trajectory[0].crs().postgisSrid()

uri = "LineString?crs=epsg:" + str(epsg) + "&field=id:integer""&index=yes"

mem_layer = QgsVectorLayer(uri,
                           'random_trajectories',
                           'memory')

prov = mem_layer.dataProvider()

feats = [ QgsFeature() for i in range(len(lines)) ]

for i, feat in enumerate(feats):
    feat.setAttributes([i])
    feat.setGeometry(QgsGeometry.fromWkt(lines[i]))

prov.addFeatures(feats)

QgsMapLayerRegistry.instance().addMapLayer(mem_layer) 

It produces a memory layer with all considered trajectories (in this case 10) randomly rotated and moved.

After running the code at Python Console of QGIS I got:

When n is changed by 1000, it was obtained result of next image . It can be observed that any trajectory intersects the outer edge.