Introduction

Throughout this course your instructor will use many conventions to denote mathematical properties and identifiers. Some of these are standard and in many published resources some of the notations used in this course differ from what is considered standard. As the intent of this course is to not make you an expert in Mathematics or Physics, the notations used simplify the understanding and, hopefully, make the programming aspect of video games easier for the programmer.

Accuracy

In actual game programming most data types are either Integer or Float data types. The rationale for this is the game loop, for whatever game engine you are using, must process all the calculations in each time slice in order to maintain a decent frames per second (fps) for game playability. While Integer data types are easy to process computationally by the computer floating point, or numbers with decimal places, are not so. In most computer programming, where accuracy is desired, programmers use the Double (double precision Float) data type. In game programming the trade-off between accuracy and speed generally sides with speed thus the use of the Float data type.

In this course, unless otherwise directed, students will round all answers to 4 decimal places. The best practice for this is to store all the calculated answers in the calculator’s memory then round only the final answer. (The computer calculator used by your instructor does this). As with any answer (calculated value) in game programming, close is close enough. When completing the online Knowledge Checks there is a rounding factor of 0.005 which should account for most of the rounding errors in your calculations.

Types of Numbers

There is a distinct difference between the data type of a number and its actual representation. The data type will store the value of the number, whereas the representation of the number will be something else entirely. There are two basic types of numeric representations, scalars and vectors. This introduction does not go into depth on the similarities and differences of these two representations, except how your instructor will represent each type. Scalar data will always be represented by lowercase alphabetical characters (i.e., s, m, or t), while vector data will be represented by UPPERCASE alphabetical characters (i.e., V, A, or F).

Doing any internet research, you may find different notations used for vectors such as ,, or v. While each type of notation has its place, your instructor has chosen to make it simpler.

Subscripts & Superscripts

Often there are not enough letters, or combination of letters, to identify a specific value in mathematics. It could be possible to use programming variable naming conventions but doing so would complicate the math equations and, in all likelihood, confuse the student. For this reason, certain subscripts and superscripts are used throughout the course.

Subscripts

Subscripts are used to denote different values of the same type, i.e., x1, x2, Fnet, and Fa. Another type of subscript is Eo which is used to denote energy loss.

Superscripts

Numeric superscripts are used quite often mathematically, such as in the equation a2 + b2 = c2. In addition to these standard superscripts certain superscript notations will be used in the course:

  • = normalizes A
  • = length of line segment between A and B

Other Notations

There are other notations used throughout this course, such as:

  • = magnitude of A
  • = determinant of A (where A is a matrix)

Greek Letters

It is standard to use the Greek alphabet to identify mathematical, or physical, properties. The following will be used throughout this course:

  • = change (i.e., )
  • The following symbols are used to denote angles:
    • = theta
    • = alpha
    • = beta
  • (pronounced mu) is used for the friction coefficient
  • (pronpuced epsilon) is used for the coefficient of elasticity
  • (pronounced tau) is used for torque
  • (pronounced omega) is used for angular velocity
  • (pronouced alpha) is also used for angular acceleration
  • I (pronounced iota) is used for inertia
  • (pronounced sigma) is used for summations
  • (pronounced zeta) is used in spring damping

Other Symbols

You may encounter some other symbols such as:

  • which is used for integration in calculus
  • which means approximately equal to
  • which is gemnerally used for therefore

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