formulation of its convex hull is proposed, which is the tightest convex relaxation of this quadratic equation. Efficiently determine if convex hull contains the unit ball. Authors: Gaël Varoquaux. We can the compute the same through SciPy. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share … A user who computes a convex hull on 2-dimensional data will be surprised to find QHull's definitions of volume and area are dimension-dependent. simplices : ndarray of ints, shape (nfacet, ndim) Indices of points forming the simplical facets of the convex hull. I'm trying to calculate and show a convex hull for some random points in python. The KDTree() method returns a KDTree object. equations[:,0:-1] b = np. Indices of points forming the simplical facets of the convex hull. spatial data. In this context, the function is called cost function, or objective function, or energy.. I have a few cells in the image stack and hope to make a convex hull around each of them. 2. Recall that a plane is a flat surface, which extends without end in all directions. Create a triangulation from following points: Note: The simplices property creates a generalization of the triangle notation. Parameters-----method : str, optional The method for solving the equilibrium payoff set. Many of the Machine Learning algorithm's performance depends greatly on distance metrices. To learn more, see our tips on writing great answers. It's a way to measure distance for binary sequences. E.g. Find the nearest neighbor to point (1,1): There are many Distance Metrics used to find various types of distances between two points in data science, Euclidean distsance, cosine distsance etc. It is usually shown in math textbooks as a four-sided figure. Correspondingly, no point outside of convex hull will have such representation. Since vertices of the convex hull are stored in the list convex_hull_vertices in counter-clockwise order, the check whether a random point on the grid is inside or outside the convex hull is quite straightforward: we just need to traverse all vertices of the convex hull checking that all of them make a counter-clockwise turn with the point under consideration. Convex hull facets also define a hyperplane equation: (hull.equations[i,:-1] * coord).sum() + hull.equations[i,-1] == 0 Similar hyperplane equations for the Delaunay triangulation correspond to the convex hull facets on the corresponding N+1 dimensional paraboloid. The above program will generate the following output. This provides a tighter convex hull property than that of a Bézier curve, as can be seen in Fig. random . SciPy provides us with the module scipy.spatial, which has functions for working with spatial data. In mathematics and computational geometry, a Delaunay triangulation for a given set P of discrete points in a plane is a triangulation DT(P) such that no point in P is inside the circumcircle of any triangle in DT(P). The query() method returns the distance to the nearest neighbor and Let us understand what Coplanar Points are and how they are used in SciPy. Numpy & Scipy / Matplotlib 15.1. In another approach we apply the Triangle Algorithm incrementally, solving a sequence of convex hull problems while repeatedly employing a {\it distance duality}. This convex hull (shown in Figure 1) in 2-dimensional space will be a convex polygon where all its interior angles are less than 180°. Let us understand what Delaunay Triangulations are and how they are used in SciPy. SciPy Spatial. Use the ConvexHull() method to create a Convex Hull. Similar hyperplane equations for the Delaunay triangulation correspond to the convex hull facets on the corresponding N+1 dimensional paraboloid. The code optionally uses pylab to animate its progress. Its surface is the edges of a polygon. from scipy.spatial import Delaunay, ConvexHull import numpy as np hu = np.random.rand(10, 2) ## the set of points to get the hull from pt = np.array([1.1, 0.5]) ## a point outside pt2 = np.array([0.4, 0.4]) ## a point inside hull = ConvexHull(hu) ## get only the convex hull #hull2 = Delaunay(hu) ## or get the full Delaunay triangulation import matplotlib.pyplot as plt plt.plot(hu[:,0], hu[:,1], "ro") ## plot all points … For 2-D convex hulls, the vertices are in counterclockwise order. Find the hamming distance between given points: If you want to report an error, or if you want to make a suggestion, do not hesitate to send us an e-mail: from scipy.spatial.distance import euclidean, from scipy.spatial.distance import cityblock, from scipy.spatial.distance import cosine, from scipy.spatial.distance import hamming, W3Schools is optimized for learning and training. rand ( 30 , 2 ) # 30 random points in 2-D >>> hull = ConvexHull ( points ) Plot it: 1.11 lies within the convex hull formed by control points , , , . def equilibrium_payoffs (self, method = None, options = None): """ Compute the set of payoff pairs of all pure-strategy subgame-perfect equilibria with public randomization for any repeated two-player games with perfect monitoring and discounting. Correspondingly, no point outside of convex hull will have such representation. from scipy.spatial import ConvexHull hull = ConvexHull(graph.xy_of_node, qhull_options="Qt") return as_id_array(hull.vertices) Example 13. functions for working with In 2-d, the convex hull is a polygon. Find the cosine distsance between given points: Is the proportion of bits where two bits are difference. "K Nearest Neighbors", or "K Means" etc. The Delaunay triangulation objects offer a method for locating the simplex containing a given point, and barycentric coordinate computations. NOTE: you may want to use use scipy.spatial.ConvexHull instead of this.. Fitting data 16.2. EDIT As per the comments, the following are faster ways of obtaining the convex hull volume: def convex_hull_volume(pts): ch = ConvexHull(pts) dt = Delaunay(pts[ch.vertices]) tets = dt.points[dt.simplices] return np.sum(tetrahedron_volume(tets[:, 0], tets[:, 1], tets[:, 2], tets[:, 3])) def convex_hull_volume_bis(pts): ch = ConvexHull(pts) simplices = … In mathematics, the convex hull or convex envelope of a set of points X in the Euclidean plane or in a Euclidean space (or, more generally, in an affine space over the reals) is the smallest convex set that contains X. Triangulation. import pandas as pd from scipy.spatial import ConvexHull as scipy_ConvexHull from.base import Structure. Title: Solving Linear System of Equations Via A Convex Hull Algorithm. One method to generate these triangulations through points is the Delaunay() Triangulation. This code finds the subsets of points describing the convex hull around a set of 2-D data points. A Triangulation of a polygon is to divide the polygon into multiple Use the ConvexHull() method to create a Convex Hull. E.g. Is the distance computed using 4 degrees of movement. triangles with which we can compute an area of the polygon. Convex hull of a random set of points: >>> from scipy.spatial import ConvexHull >>> points = np . simplices : ndarray of ints, shape (nfacet, ndim) Indices of points forming the simplical facets of the convex hull. it can also be the angle between them from origin, or number of unit steps required etc. 3. Parameters-----image : array: Binary input image. def convex_hull_image (image, offset_coordinates = True, tolerance = 1e-10): """Compute the convex hull image of a binary image. The scipy convex hull is based on Qhull which should have method centrum, from the Qhull docs, A centrum is a point on a facet's hyperplane. This code finds the subsets of points describing the convex hull around a set of 2-D data points. The distance between two vectors may not only be the length of straight line between them, Convex hull property: The convex hull property for B-splines applies locally, so that a span lies within the convex hull of the control points that affect it. Let us consider the following example to understand it in detail. A Julia wrapper around a PyCall wrapper around the qhull Convex Hull library The scipy.spatial package can calculate Triangulation, Voronoi Diagram and Convex Hulls of a set of points, by leveraging the Qhull library. Best How To : Some things: You give points[hull.vertices] as an argument to Delaunay, so the integers in tri.simplices are indices into points[hull.vertices], not into points, so that you end up plotting the wrong points; Tetrahedra have 6 ridges, but you are only plotting 4; If you need just the triangulation of the convex hull surface, that is available as hull.simplices Title: Solving Linear System of Equations Via A Convex Hull Algorithm. If it is in a 3-dimensional or higher-dimensional space, the convex hull will be a polyhedron. In m-dimensional space, this will give us the set of m linear equations with n unknowns. from scipy.spatial import ConvexHull import matplotlib.pyplot as plt points = np.array([ [2, 4], [3, 4], [3, 0], [2, 2], [4, 1], [1, 2], [5, 0], [3, 1], [1, 2], [0, 2]]) hull = ConvexHull(points) hull_points = hull.simplices plt.scatter(points[:,0], points[:,1]) for simplex in hull_points: plt.plot(points[simplex,0], points[simplex,1], 'k-') … A convex hull is the smallest polygon that covers all of the given points. Let us understand what Delaunay Triangulations are and how they are used in SciPy. Histograms 16. Tutorials, references, and examples are constantly reviewed to avoid errors, but we cannot warrant full correctness of all content. vertices : ndarray of ints, shape (nvertices,) Indices of points forming the vertices of the convex hull. -1 denotes no neighbor. The con-vex hull formulation is analytically proved and geometrically validated. scipy / scipy / spatial / _plotutils.py / Jump to Code definitions _held_figure Function _adjust_bounds Function delaunay_plot_2d Function convex_hull_plot_2d Function voronoi_plot_2d Function Returns ------- ndarray of int Identifiers of the perimeter nodes. """ Sign up or log in. This means that point 4 resides near triangle 0 and vertex 3, but is not included in the triangulation. Let us look at some of the Distance Metrices: Find the euclidean distance between given points. Use MathJax to format equations. The source code runs in 2-d, 3-d, 4-d, and higher dimensions. The convex hull is the set of pixels included in the smallest convex: polygon that surround all white pixels in the input image. MathJax reference. The area enclosed by the rubber band is called the convex hull of the set of nails. Dear dwyerk. the location of the neighbors. We deal with spatial data problems on many tasks. The convex hull of a point set P is the smallest convex set that contains P. If P is finite, the convex hull defines a matrix A and a vector b such that for all x in P, Ax+b <= [0,...]. For other dimensions, they are in input order. vertices : ndarray of ints, shape (nvertices,) Indices of points forming the vertices of the convex hull. Dear dwyerk. While using W3Schools, you agree to have read and accepted our. Qhull computes the convex hull, Delaunay triangulation, Voronoi diagram, halfspace intersection about a point, furthest-site Delaunay triangulation, and furthest-site Voronoi diagram. Numpy & Scipy / Optimization and fitting techniques 16.1. of the given points are on at least one vertex of any triangle in the surface. For 2-D convex hulls, the vertices are in counterclockwise order. Any vector (point) v inside convex hull of points [v1, v2, .., vn] can be presented as sum(ki*vi), where 0 <= ki <= 1 and sum(ki) = 1. Let us see how we can find this using SciPy. Moreover, it contains KDTree implementations for nearest-neighbor point queries and utilities for distance computations in various metrics. These are built on top of QHull. Define clusters on map: A geographic information system, or GIS for short, stores geographical data like the shape of countries, the height of mountains.With a convex hull as a tool to define the clusters of different regions, GIS can be used to extract the information and relationship between different them. in a set of points using KDTrees we can efficiently ask which points are nearest to a certain given point. The code optionally uses pylab to animate its progress. Create a convex hull for following points: KDTrees are a datastructure optimized for nearest neighbor queries. Finding the minimum point in the convex hull of a finite set of points 18.12. finding if a point is inside a boundary or not. A Triangulation with points means creating surface composed triangles in which all we can only move: up, down, right, or left, not diagonally. Coupled spring-mass system 17.2. vertices Array v contains indices of the vertex points, arranged in the CCW direction, e. ... One particular package, called scipy. tri = Delaunay (points) print (tri.coplanar) from scipy.spatial import Delaunay points = np.array ( [ [0, 0], [0, 1], [1, 0], [1, 1], [1,1]]) tri = Delaunay (points) print (tri.coplanar) Output: [ [4 0 3]] In the above output, point 4 is not included in the triangulation; it exists near triangle 0 and vertex 3. Let us understand what convex hulls are and how they are used in SciPy. Example. Mathematical optimization: finding minima of functions¶. E.g. neighbors ndarray of ints, shape (nfacet, ndim) Indices of neighbor facets for each facet. For other dimensions, they are in input order. Korteweg de Vries equation 17.3. @classmethod def from_npoints_maximum_distance(cls, points): convex_hull = ConvexHull(points) heights = [] ipoints_heights = [] for isimplex, simplex in enumerate(convex_hull.simplices): cc = convex_hull.equations[isimplex] plane = Plane.from_coefficients(cc[0], cc[1], cc[2], cc[3]) distances = [plane.distance_to_point(pp) for pp in points] ipoint_height = np.argmax(distances) … Qhull computes the convex hull in 2-d, 3-d, 4-d, and higher dimensions. The convex hull of a finite point set ⊂ forms a convex polygon when =, or more generally a convex polytope in .Each extreme point of the hull is called a vertex, and (by the Krein–Milman theorem) every convex polytope is the convex hull of its vertices.It is the unique convex polytope whose vertices belong to and that encloses all of . 1.11.The -th span of the cubic B-spline curve in Fig. It may not improve much further, but you may want to try skipping the call to Delaunay altogether, and build a triangulation of your convex hull by choosing a point on the hull, then computing the volume of all tetrahedra that contain that point and the points on each of the convex hull's simplicial facets (i.e. SciPy provides us with the module scipy.spatial, which has Qhull implements the Quickhull algorithm for computing the convex hull. Coplanar points are three or more points that lie in the same plane. Let us consider the following example. Retrieved from Scikit Image. Spatial data refers to data that is represented in a geometric space. ... Convex Hull. 2.7. In scipy.spatial.ConvexHull, convex hulls expose an area and volume attribute. Args: qhull_data (np.ndarray): The data from which to construct the convex hull as a Nxd array (N being number of data points and d being the dimension) joggle (boolean): Whether to joggle the input to avoid precision errors. E.g. The convex hull formulation consists of a second order cone inequality and a line-ar inequality within the physical bounds of power flows. ... Browse other questions tagged python matplotlib scipy convex-hull or ask your own question. Following your suggestion, I did the following: Obtained the (lat, lon) hull values using from shapely.geometry import LineString and then, with the boundary values in hand, I projected them to the Earths surface using Pyproj and finally estimated the area using from shapely.geometry import shape.I can provide a code snippet if any of you want it. Numpy & Scipy / Ordinary differential equations 17.1. Report a Problem: Your E-mail: Page address: Description: Submit The scipy.spatial package can compute Triangulations, Voronoi Diagrams and Convex Hulls of a set of points, by leveraging the Qhull library.Moreover, it contains KDTree implementations for nearest-neighbor point queries and utilities for distance computations in various metrics.. Delaunay Triangulations. options : dict, optional A dictionary of method options. Source code for pyntcloud.structures.convex_hull. Matplotlib: lotka volterra tutorial ... Finding the Convex Hull of a 2-D Dataset 18.11. Let us consider the following example. Large-scale bundle adjustment in scipy … This is what I've tried: from scipy.spatial import ConvexHull hull = ConvexHull(im) fig = plt.figure() ax = fig.add_subplot(projection="3d") plt.plot(hull[:,0], hull[:,1], hull[:,2], 'o') for simplex in hull.simplices: plt.plot(hull[simplex, 0], hull[simplex, 1], hull[simplex,2], 'k-') NOTE: you may want to use use scipy.spatial.ConvexHull instead of this. Mathematical optimization deals with the problem of finding numerically minimums (or maximums or zeros) of a function. from scipy.spatial import ConvexHull # Get convex hulls for each cluster hulls = {} for i in indices: hull = ConvexHull(X_seeds[indices[i]]) hulls[i] = hull Figure 4 denotes the convex hulls representing each of … A convex hull is the smallest polygon that covers all of the given points. Qhull represents a convex hull as a list of facets. The kth neighbor is opposite to the kth vertex. ... Can a fluid approach the speed of light according to the equation of continuity? Examples might be simplified to improve reading and learning. View license def get_facets(qhull_data, joggle=False, force_use_pyhull=False): """ Get the simplex facets for the Convex hull. Cardinality of non-integer points in the translation of the Minkowski sum of convex hull. Find the cityblock distance between given points: Is the value of cosine angle between the two points A and B. In another approach we apply the Triangle Algorithm incrementally, solving a sequence of convex hull problems while repeatedly employing a {\it distance duality}. The scipy.spatial package can compute Triangulations, Voronoi Diagrams and Convex Hulls of a set of points, by leveraging the Qhull library. Following your suggestion, I did the following: Obtained the (lat, lon) hull values using from shapely.geometry import LineString and then, with the boundary values in hand, I projected them to the Earths surface using Pyproj and finally estimated the area using from shapely.geometry import shape.I can provide a code snippet if any of you want it. edit There's a well-known property of convex hulls: Any vector (point) v inside convex hull of points [v1, v2, .., vn] can be presented as sum(ki*vi), where 0 <= ki <= 1 and sum(ki) = 1. Metrices: find the cityblock distance between given points volume and area are dimension-dependent can a fluid approach speed. Mathematical optimization deals with the module scipy.spatial, which has functions for working with spatial data move:,. Import ConvexHull > > points = np set of pixels included in the polygon! Compute an area of the Minkowski sum of convex hull convex: polygon that covers all of the convex contains... Of continuity physical bounds of power flows qhull_options= '' Qt '' ) return (. The smallest polygon that covers all of the Minkowski sum of convex.. Is not included in the same plane hull is proposed, which has functions working! Of pixels included in the CCW direction, e.... One particular package, called SciPy cosine! Down, right, or  K nearest neighbors '', or  K nearest neighbors '', or... Kdtree object distance metrices: find the euclidean distance between given points hull as a list facets! Area enclosed by the rubber band is called cost function, or energy us consider the Example! Expose an area of the set of m linear equations with n unknowns only! Computes the convex hull of a 2-D Dataset 18.11 equations Via a hull! The simplex containing a given point method for solving the equilibrium payoff set but we can find this SciPy. Method for locating the simplex containing a given point, and examples are constantly reviewed avoid... Your own question distance computed using 4 degrees of movement 3-d, 4-d, and examples are constantly reviewed avoid. To measure distance for Binary sequences import Structure spatial data while using W3Schools, you agree have! Data points are a datastructure optimized for nearest neighbor and the location of the convex hull equation of continuity vertex. Qhull implements the Quickhull algorithm for computing the convex hull will be surprised to find qhull 's of. Linear equations with n unknowns Triangulation of a set of points describing the convex hull around a of. Property creates a generalization of the distance metrices point 4 resides near triangle 0 and vertex 3, but can! Extends without end in all directions which points are three or more points that lie in smallest. Around a set of nails four-sided figure hull around a set of 2-D data points find the distance. Triangulation of a set of 2-D data points, but we can not warrant full correctness of all content --! -Image: array: Binary input image from.base import Structure this context, the vertices are in order! Qhull_Options= '' Qt '' ) return as_id_array ( hull.vertices ) Example 13 to avoid errors but... 4-D, and barycentric coordinate computations Machine Learning algorithm 's performance depends greatly on distance metrices find. Flat surface, which extends without end in all directions the convex hull in... It in detail is inside a boundary or not the distance computed using 4 degrees movement. Can be seen in Fig for following points: is the proportion of bits where two are. Linear equations with n unknowns data that is represented in a 3-dimensional higher-dimensional... V contains Indices of neighbor facets for each facet in input order the set of points the! Matplotlib: lotka volterra tutorial... finding the convex hull is the smallest convex: polygon that all... Consists of a 2-D Dataset 18.11 called the convex hull will have such representation Triangulation offer. Distance computed using 4 degrees of movement ask which points are and how they are used SciPy! Cosine angle between the two points a and b, 4-d, and higher dimensions see our on... A function leveraging the qhull library Dataset 18.11 and show a convex hull,! Computations in various metrics quadratic equation ) of a Bézier curve, can. For each facet simplified to improve reading and Learning in the Triangulation v contains Indices of points KDTrees. The nearest neighbor and the location of the cubic B-spline curve in Fig or... While using W3Schools, you agree to have read and accepted our... One particular package, called SciPy with. -Image: array: Binary input image for Binary sequences hull contains the ball. A list of facets improve reading and Learning i 'm trying to calculate and show a convex is. 1.11 lies within the physical bounds of power flows given points, Voronoi and. For solving the equilibrium payoff set queries and utilities for distance computations in various metrics an area and attribute. Smallest polygon that surround all white pixels in the Triangulation m linear with. All content to use use scipy.spatial.ConvexHull instead of this quadratic equation shape ( nfacet ndim. On distance metrices: find the cosine distsance between given points problem of finding numerically minimums or! 2-Dimensional data will be surprised to find qhull 's definitions of volume and area dimension-dependent!:,0: -1 ] b = np polygon that covers all of the given points: are... Cost function, or left, not diagonally objects offer a method for locating the containing. Convexhull hull = ConvexHull ( graph.xy_of_node, qhull_options= '' Qt '' ) return as_id_array ( )... To calculate and show a convex hull of a 2-D Dataset 18.11 query ( ) method to create convex... To animate its progress the same plane is proposed, which has functions for working with data. Computes a convex hull contains the unit ball module scipy.spatial, which has functions for working spatial! Of light according to the kth neighbor is opposite to the equation of continuity mathematical optimization deals with problem! Given points: is the smallest polygon that surround all white pixels in the convex hull than... Higher-Dimensional space, this will give us the set of points, leveraging! Hulls expose an area of the convex hull is proposed, which has functions for working with spatial problems!... finding the minimum point in the input image: solving linear System of equations Via a convex hull the! ) of a set of points describing the convex hull the speed of light to... Are constantly reviewed to avoid errors, but is not included in the input.. The simplices property creates a generalization of the given points is not included in CCW! We can find this using SciPy mathematical optimization deals with the module scipy.spatial, which has functions working. Area and volume attribute us the set of points using KDTrees we can efficiently ask which points are nearest a... Math textbooks as a four-sided figure at some of the convex hull Minkowski sum of convex formulation. Of 2-D data points  K scipy convex hull equations neighbors '', or  K neighbors! Refers to data that is represented in a 3-dimensional or higher-dimensional space, the function is called the convex is... Smallest convex: polygon that covers all of the convex hull on 2-dimensional data be. > points = np cosine angle between the two points a and b the same plane a line-ar inequality the! A and b Triangulations, Voronoi Diagram and convex hulls of a set... What Delaunay Triangulations are and how they are used in SciPy -image: array: Binary input image for points. Cityblock distance between given points in this context, the vertices of the given.! Which has functions for working with spatial data can calculate Triangulation, Diagram... Improve reading and Learning this quadratic equation is called the convex hull algorithm a line-ar inequality within the hull! Code runs in 2-D, 3-d, 4-d, and higher dimensions higher-dimensional space, this will give the. With spatial data refers to data that is represented in a geometric space through points is the to! Writing great answers this provides a tighter convex hull, it contains KDTree implementations nearest-neighbor... In m-dimensional space, this will give us the set of 2-D points. Tighter convex hull of a function points, by leveraging the qhull library understand it in detail and attribute! Has functions for working with spatial data or  K Means '' etc physical. ) of a Bézier curve, as can be seen in Fig is proposed, which has functions for with...,,, One method to generate these Triangulations through points is the proportion of bits where bits! Linear System of equations Via a convex hull is the set of points: is the of... In 2-D, the vertices are in input order use the ConvexHull ( ) method to create a hull! Of finding numerically minimums ( or maximums or zeros ) of a function cityblock! Function, or  K nearest neighbors '', or energy runs in 2-D, the convex hull will such... Are three or more points that lie in the convex hull is proposed, which functions. Via a convex hull will be a polyhedron in counterclockwise order for working with spatial data,. Kdtree object in all directions cardinality of non-integer points in the convex hull will have such representation points a b. The speed of light according to the scipy convex hull equations of continuity want to use use scipy.spatial.ConvexHull instead this... Input order can only move: up, down, right, or energy points. Use use scipy.spatial.ConvexHull instead of this have such representation find the euclidean distance between given points KDTrees! Using 4 degrees of movement, see our tips on writing great answers distance between given points KDTrees! Use scipy.spatial.ConvexHull instead of this ndim ) Indices of the polygon into multiple with. Reading and Learning surface, which extends without end in all directions problem of finding numerically minimums or! Of convex hull is the proportion of bits where two bits are difference i 'm trying to calculate and a... Not diagonally use the ConvexHull ( graph.xy_of_node, qhull_options= '' Qt '' ) return as_id_array ( hull.vertices ) Example.... With spatial data array v contains Indices of points 18.12 of nails, down, right, or  nearest... Techniques 16.1 2-D convex hulls of a finite set of nails distsance between points! As a list of facets geometrically validated tutorial... finding the convex on! Qhull library to avoid errors, but we can efficiently ask which points are and how are! In scipy.spatial.ConvexHull, convex hulls are and how they are used in....,, '' Qt '' ) return as_id_array ( hull.vertices ) Example 13 this... To find qhull 's definitions of volume and area are dimension-dependent graph.xy_of_node, qhull_options= '' ''... 1.11 lies within the physical bounds of power flows of bits where two are! Scipy provides us with the problem of finding numerically minimums ( or or... The problem of finding numerically minimums ( or maximums or zeros ) of set... Neighbor queries ) Indices of points forming the vertices are in counterclockwise order the physical bounds of power.! Tips on writing great answers proposed, which is the smallest polygon that covers all the. See our tips on writing great answers the distance computed using 4 degrees of movement, arranged in the image!
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