Some Cool Tricks

 We can consider the screen as high school graph paper.  Each sprite or object is located somewhere in the coordinate system.

 Remember our screen is not like the school mathematical graph paper! The origin is at the top-left!  That means the bottom of our object is at a higher y position than the top!

 Moving things around is called translation.  Usually we translate our object to the origin before we perform rotation and scaling.

 Move every point in one object to another location.

 For rotation, lets visit the Siggraph web page: accessed August

 We use Pythagoras to find the distance between two points.

 Using (x, y) positions is common.  However, you may use (r, Θ)  r = distance from origin  Θ = angle.  Converting between the two systems is easy.  Just remember the name!

 Beware, we need a little bit more sophistication to calculate the angle… as this gives us ambiguity.

 We can use circle to circle collision as an example.  We find the centre of each circle and use Pythagoras to discover the distance between the two.  The equations to the right tell us when there has been a collicsion! We can possibly do this with square distances to avoid using expensive sqrt operations. We must be careful to avoid interpenetration as the entities will indefinite collide with each other.

 Interpenetration of objects.  Interlocking of objects.  Quantum Tunnelling Effects.

 Once again in scaling we need to translate our object’s origin to the origin of the world, we then perform the scaling operation.  Remember to translate back!

 We use logic all the time in coding.  We will use logic for our AI and decision making in games.  We will explicitly cover some rudimentary logic.

 And  Or  Not  Xor  Implies  Tautologies—Saying the same thing more than once.  Associative Laws—Order does not matter.  Distributive Laws—We can say things in different ways that mean the same thing.  Identity Laws

 Sets can be used to make decisions.  Sets indicate belongingness.

 Venn Diagrams  Union  Intersection  Difference.  Sets  Subsets  Compliment  Universal Set  Identity Laws

 What is in A, B and C?  What is in A?  What is in not A?  Useful for games.  Useful for determining strategies.

 Yes!  std::set!  How awesome is that?

 Vectors and matrices are mathematically convenient tools.  They are used in games for graphical mathematics.  So annoying that std::vector is named in such a way to make things a little confusing.

I like to call this Quantum Tunnelling. We miss the detection of a collision as the bullet passes through the wall.

Bounding box collision detection in 2D.

 Tricks  One’s Compliment

 The distance between two points can be calculated using Pythagoras.  This can be used for simple collision detection.  Movie, E13Y, accessed August E13Y

 OvVep2uSg, accessed August OvVep2uSg

 Analytical Geometry is concerned with points and the relationships between points.  We can find angles between two points to determine interesting relationships.

 Useful for determining:  (a) If a collision would take place.  (b) If a collision has taken place.

 Let’s look at the diagrams!  geometry/perpendicular-distance-point- line.php, accessed August geometry/perpendicular-distance-point- line.php

 Vectors can represent acceleration, velocity and displacement and any sort of force, which is essential to any physics orientated game.  It allows for you to calculate paths, trajectories and many aspects of physics within code.

 A vector is a point.  For two dimensional mathematics:  (x, y).  These vectors have interesting operations.  They make it easier to do mathematics.

 We can simply calculate the resulting vector when combining multiple forces…

 A matrix is a column by row matrix of values.  The matrix has defined operations so we can perform mathematical operations efficiently on a collection of points.

 Read the wikipage on 2D Graphics.  This will help you understand more about your programming project. 