How can you ensure that geometric intersection algorithms are reliable?

1 Understand the problem

Before you start coding, you need to understand the problem you are trying to solve and the assumptions you are making. What are the types and properties of the geometric objects you are dealing with? Are they convex or concave, simple or complex, planar or spatial, static or dynamic? How do you represent them in your data structures and algorithms? How do you define and measure intersection? Do you need to find all the intersection points, segments, or regions, or just some of them? Do you need to handle special cases, such as collinear, parallel, or coincident objects? By clarifying these questions, you can avoid unnecessary confusion and errors later on.

2 Choose the right algorithm

Depending on the problem, you may have different options for choosing the algorithm that computes the intersection. Some common factors to consider are the accuracy, efficiency, simplicity, and generality of the algorithm. Accuracy refers to how well the algorithm handles numerical errors and rounding issues, which can affect the correctness and stability of the results. Efficiency refers to how fast the algorithm runs and how much memory it uses, which can affect the performance and scalability of your application. Simplicity refers to how easy the algorithm is to understand, implement, and debug, which can affect the development and maintenance costs. Generality refers to how well the algorithm works for different types and combinations of geometric objects, which can affect the versatility and adaptability of your solution.

3 Test and debug thoroughly

Once you have implemented your algorithm, you need to test and debug it thoroughly to ensure that it works as expected and handles all the possible cases. You can use various tools and techniques to help you with this process, such as unit testing, visual debugging, boundary testing, and randomized testing. Unit testing is a method of verifying that each function or module of your code performs correctly and consistently, by comparing the actual output with the expected output for a given input. Visual debugging is a method of inspecting and manipulating the graphical representation of your geometric objects and their intersection, by using interactive tools such as drawing software, graphics libraries, or online platforms. Boundary testing is a method of checking that your algorithm handles the edge cases and extreme values of your input, such as zero, infinity, or very large or small numbers. Randomized testing is a method of generating and testing random or pseudo-random input for your algorithm, by using tools such as random number generators, probabilistic distributions, or geometric random walks.

5 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?