Convex hull computation in SciPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to import the convex hull function from scipy.spatial.

SciPy

from scipy.spatial import [1]

points = [[0, 0], [1, 1], [1, 0], [0, 1]]
hull = ConvexHull(points)

Drag options to blanks, or click blank then click option'

Ahull

Bconvex_hull

CConvex_Hull

DConvexHull

Attempts:

3 left

💡 Hint

Common Mistakes

Using lowercase or incorrect casing for ConvexHull

Trying to import a non-existent function like convex_hull

The correct function to import is ConvexHull with exact casing from scipy.spatial.

2fill in blank

medium

Complete the code to create a convex hull object from the points array.

SciPy

import numpy as np
from scipy.spatial import ConvexHull

points = np.array([[0, 0], [1, 1], [1, 0], [0, 1]])
hull = [1](points)

Drag options to blanks, or click blank then click option'

AHull

Bconvex_hull

CConvexHull

DconvexHull

Attempts:

3 left

💡 Hint

Common Mistakes

Using incorrect casing or misspelled class names

Trying to call a function that does not exist

The convex hull object is created by calling ConvexHull(points).

3fill in blank

hard

Fix the error in accessing the convex hull vertices.

SciPy

import numpy as np
from scipy.spatial import ConvexHull

points = np.array([[0, 0], [1, 1], [1, 0], [0, 1]])
hull = ConvexHull(points)
vertices = hull.[1]

Drag options to blanks, or click blank then click option'

Apoints

Bvertices

Cvertex

Dverts

Attempts:

3 left

💡 Hint

Common Mistakes

Using singular 'vertex' instead of 'vertices'

Trying to access non-existent attributes like 'verts'

The convex hull vertices are accessed using hull.vertices.

4fill in blank

hard

Fill both blanks to create a dictionary of hull vertices and their coordinates.

SciPy

vertex_coords = {hull.[1][i]: points[hull.[2][i]] for i in range(len(hull.vertices))}

Drag options to blanks, or click blank then click option'

Avertices

Bpoints

Cvertex

Dverts

Attempts:

3 left

💡 Hint

Common Mistakes

Using different or incorrect attribute names for the two blanks

Using singular 'vertex' instead of 'vertices'

Both blanks should be vertices to access the indices of hull vertices.

5fill in blank

hard

Fill all three blanks to compute the perimeter of the convex hull polygon.

SciPy

import numpy as np
perimeter = 0
for i in range(len(hull.[1])):
    start = points[hull.[2][i]]
    end = points[hull.[3][(i + 1) % len(hull.vertices)]]
    perimeter += np.linalg.norm(end - start)

Drag options to blanks, or click blank then click option'

Avertices

Dpoints

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'points' instead of 'vertices' in the blanks

Not using modulo to wrap around the last vertex

All blanks should be vertices to iterate over the hull vertex indices and compute distances between consecutive points.

Practice

1. What does the scipy.spatial.ConvexHull function compute for a set of points?

easy

A. The smallest convex shape enclosing all points

B. The average distance between points

C. The maximum value among the points

D. The sum of all point coordinates

Solution

1. Step 1: Understand the purpose of ConvexHull

   The ConvexHull function finds the smallest convex polygon that contains all given points.

2. Step 2: Compare options with definition

   Only The smallest convex shape enclosing all points describes this smallest convex shape enclosing all points.

3. Final Answer:

   The smallest convex shape enclosing all points -> Option A

4. Quick Check:

   Convex hull = smallest convex shape [OK]

Hint: Convex hull wraps points tightly in a convex boundary [OK]

Common Mistakes:

• Confusing convex hull with average or sum calculations
• Thinking it finds maximum or minimum coordinate values
• Assuming it returns all points instead of boundary points

2. Which of the following is the correct way to import the ConvexHull class from scipy?

easy

A. from scipy.spatial import ConvexHull

B. import scipy.ConvexHull

C. from scipy import ConvexHull

D. import ConvexHull from scipy.spatial

Solution

1. Step 1: Recall correct import syntax in Python

   To import a class from a submodule, use 'from module.submodule import Class'.

2. Step 2: Match with scipy.spatial.ConvexHull

   The correct import is 'from scipy.spatial import ConvexHull'. Other options have syntax errors or wrong paths.

3. Final Answer:

   from scipy.spatial import ConvexHull -> Option A

4. Quick Check:

   Correct import = from scipy.spatial import ConvexHull [OK]

Hint: Use 'from module.submodule import Class' for importing classes [OK]

Common Mistakes:

• Using 'import scipy.ConvexHull' which is invalid syntax
• Trying 'import ConvexHull from ...' which is wrong order
• Importing directly from 'scipy' without 'spatial'

3. What will be the output of the following code?

import numpy as np
from scipy.spatial import ConvexHull
points = np.array([[0, 0], [1, 0], [1, 1], [0, 1], [0.5, 0.5]])
hull = ConvexHull(points)
print(hull.vertices)

medium

A. [1 2 3]

B. [0 1 2 3 4]

C. [4]

D. [0 1 2 3]

Solution

1. Step 1: Identify points forming the convex hull

   The points at indices 0,1,2,3 form the square boundary; point 4 is inside.

2. Step 2: Understand hull.vertices output

   hull.vertices returns indices of points forming the hull boundary, excluding interior points.

3. Final Answer:

   [0 1 2 3] -> Option D

4. Quick Check:

   Vertices exclude inside points = [0 1 2 3] [OK]

Hint: Hull vertices exclude points inside the shape [OK]

Common Mistakes:

• Including interior points in hull vertices
• Expecting all points as hull vertices
• Misunderstanding output as coordinates instead of indices

4. The following code throws an error. What is the likely cause?

import numpy as np
from scipy.spatial import ConvexHull
points = np.array([[0, 0], [1, 1]])
hull = ConvexHull(points)
print(hull.vertices)

medium

A. Missing import statement

B. Points are not in ascending order

C. Not enough points to form a convex hull

D. Points array has wrong data type

Solution

1. Step 1: Check minimum points needed for convex hull

   Convex hull in 2D requires at least 3 points to form a polygon.

2. Step 2: Analyze given points

   Only 2 points are given, so ConvexHull cannot compute a polygon, causing an error.

3. Final Answer:

   Not enough points to form a convex hull -> Option C

4. Quick Check:

   Minimum 3 points needed for 2D hull [OK]

Hint: Convex hull needs at least 3 points in 2D [OK]

Common Mistakes:

• Assuming any number of points works
• Thinking order of points matters for hull computation
• Ignoring error message about input size

5. You have a set of 2D points representing city locations. You want to find the smallest fence enclosing all cities. Which steps correctly use scipy.spatial.ConvexHull to find the fence points?

hard

A. Import ConvexHull, sort points by x-coordinate, use hull.simplices to get fence points

B. Import ConvexHull, create numpy array of points, compute hull, use hull.vertices to get fence points

C. Import ConvexHull, compute hull, use hull.area to get fence points

D. Import ConvexHull, compute hull, use hull.points to get fence points

Solution

1. Step 1: Prepare data and compute hull

   Import ConvexHull, convert city coordinates to numpy array, then compute hull = ConvexHull(points).

2. Step 2: Extract fence points using hull.vertices

   hull.vertices gives indices of points forming the convex hull boundary (fence).

3. Final Answer:

   Import ConvexHull, create numpy array of points, compute hull, use hull.vertices to get fence points -> Option B

4. Quick Check:

   hull.vertices = fence points [OK]

Hint: Use hull.vertices for boundary points, not hull.area or hull.points [OK]

Common Mistakes:

• Using hull.area which is a number, not points
• Using hull.points which is all points, not boundary
• Sorting points manually instead of using hull.vertices