Geometric Algorithms

Geometric algorithms are a type of algorithm that deal with solving problems related to geometry.

• Solve problems involving, distances, intersections, arrangements, and transformations.
• Used in graphics, computer-aided design, robotics, and geographical information systems. medical imaging, and astronomy for spatial computation and analysis.
• Popular algorithms include Convex Hull, Closest Pair, Line Intersection, Point-in-Polygon, Sweep Line, Voronoi Diagram, Delaunay Triangulation, and Rotating Calipers.

Lines:

• Mid-point of a line
• Section formula (Point that divides a line in given ratio)
• Slope of a line
• Line passing through 2 Points
• Intersection of Two Lines
• Find if any two segments intersect
• Count maximum points on same line
• Minimum lines to cover all points

Triangle:

• Check triangle is valid or not
• Check if a given point lies inside a triangle
• Area of a triangle
• Check if right triangle possible from given area and hypotenuse
• Count Integral points inside a Triangle
• All angles of a given triangle
• Circumcenter of a Triangle
• Triangles formed from a set of lines in Euclidean Plane
• Area of Circumcircle of an Equilateral Triangle
• 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