## Splines and Bézier Curves and their application in Video Games

The geometry of curves and surfaces is of fundamental importance in computer graphics and in video game programming. In this article we will describe the mathematics of interpolation curves, in particular splines and Bézier curves, with examples of use in the Unity 3D environment. 1) Mathematical representations of curves Definition Read more…

## Motion in a Plane and Unity’s 2D Physics Engine

This article gives a brief illustration of Newton’s laws of motion in the plane and analyzes the tools that the Unity 2D engine makes available to programmers to simulate the movement of bodies in the 2D environment.For the study of physics it’s essential to know the units of measurement of Read more…

## Euler Angles, Hamilton’s Quaternions and video games

Programming video games, as many areas of science and technology, requires computing the coordinates of an object in different reference systems, constructed by combining together translations, rotations or scale changes.The problem is particularly complex with the rotations. In a previous article we have studied the representation of rotations by means of matrices, Read more…

## Matrix Algebra and Game Programming

1) Algebra of matrices A matrix $$A(m,n)$$ defined on the field of real numbers $$\mathbb{R}$$ is a collection of real numbers $$(a_{ij})$$, indexed by natural numbers $$i, j$$, with $$1\le i\le m$$ and $$1\le j\le n$$. We can represent a matrix with a rectangular array of numbers arranged in Read more…

## Vector Algebra and Game Programming

Video game programming requires extensive use of mathematics and physics. Some typical examples are the following: controlling the motion of objects in space, drawing geometric shapes on the scene, computing the effects after a collision of objects in accordance with Newton’s laws of classical mechanics, etc.Geometry plays a fundamental role. The classic Read more…