Geometric Algorithms

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Practice Problems on Geometric Algorithms

What are Geometric Algorithms?

Geometric algorithms are a type of algorithm that deal with solving problems related to geometry. These algorithms are used to solve various geometric problems such as computing the area of a polygon, finding the intersection of geometric shapes, determining the convex hull of a set of points, and many other tasks related to geometric objects and their properties. Geometric algorithms are important in various fields such as computer graphics, computer-aided design, robotics, and geographical information systems.

Pattern Printing:

• Print lower triangle with alternate ‘*’ and ‘#’
• Print the pattern 1*2*5*6 –3*4
• Python Program to print the pattern ‘G’
• Pascal’s Triangle
• Program to print pyramid pattern
• Program to print the diamond shape
• Hour-glass Pattern
• Program to print V and inverted-V pattern
• Program to print hollow pyramid, diamond pattern and their modifications
• Code to Generate the Map of India (With Explanation)

Lines:

• Program to find the mid-point of a line
• Section formula (Point that divides a line in given ratio)
• Program to find slope of a line
• Program to find line passing through 2 Points
• Program for Point of Intersection of Two Lines
• Reflection of a point about a line in C++
• Find points at a given distance on a line of given slope
• Given n line segments, find if any two segments intersect
• Count maximum points on same line
• Minimum lines to cover all points

Triangle:

• Check whether triangle is valid or not if sides are given
• Check whether a given point lies inside a triangle or not
• Program to find area of a triangle
• Check if right triangle possible from given area and hypotenuse
• Count Integral points inside a Triangle
• Find all angles of a given triangle
• Program to find Circumcenter of a Triangle
• Number of Triangles that can be formed given a set of lines in Euclidean Plane
• Program to calculate area of Circumcircle of an Equilateral Triangle
• Program to find third side of triangle using law of cosines

Rectangle | Square | Circle:

• Check whether a given point lies inside a rectangle or not
• Program for Area And Perimeter Of Rectangle
• Find if two rectangles overlap
• How to check if given four points form a square
• Number of rectangles in N*M grid
• Program to find Circumference of a Circle
• Program to find area of a circle
• Check whether a point exists in circle sector or not
• Check if two given circles touch or intersect each other
• Program to find area of a Circular Segment
• Check if a line touches or intersects a circle
• Area of a Circumscribed Circle of a Square
• Find minimum radius such that atleast k point lie inside the circle
• Angular Sweep (Maximum points that can be enclosed in a circle of given radius)

Quadrilateral:

• Number of parallelograms when n horizontal parallel lines intersect m vertical parallellines
• Program for Circumference of a Parallelogram
• Program to calculate area and perimeter of Trapezium
• Program to find area of a Trapezoid
• Find all possible coordinates of parallelogram
• Maximum area of quadrilateral
• Check whether four points make a parallelogram
• Find the Missing Point of Parallelogram

3D Objects:

• Find the perimeter of a cylinder
• Program for Volume and Surface area of Frustum of Cone
• Program to calculate volume of Ellipsoid
• Program for volume of Pyramid
• Calculate volume and surface area of a cone
• Calculate Volume and Surface area Of Sphere
• Program for Volume and Surface Area of Cuboid
• Program for Volume and Surface Area of Cube
• Pythagorean Quadruple
• LS3/NS3 sphere generation algorithm and its implementation

Polygon and Convex Hull:

• How to check if a given point lies inside or outside a polygon?
• Area of a polygon with given n ordered vertices
• Tangents between two Convex Polygons
• Find number of diagonals in n sided convex polygon
• Convex Hull using Jarvis’ Algorithm or Wrapping
• Quickhull Algorithm for Convex Hull
• Deleting points from Convex Hull
• Minimum area of a Polygon with three points given

Standard Problems on Geometric Algorithm:

• Finding the vertex, focus
• and directrix of a parabola
• Find Simple Closed Path for a given set of points
• Number of Integral Points between Two Points
• Optimum location of point to minimize total distance
• Find perimeter of shapes formed with 1s in binary matrix
• Draw geometric shapes on images using OpenCV
• Find if it’s possible to rotate the page by an angle or not
• Equable Shapes

Quick Links :

• Learn Data Structure and Algorithms | DSA Tutorial
• ‘Practice Problems’ on Geometric Algorithms
• Recent Articles on Geometric Algorithms