Whether you're a programmer, technical director, or an artist who wishes to have a better understanding of computer graphics applications, a strong mathematical foundation is essential. Under the hood, almost everything in computer graphics is based on a relatively small set of mathematical principles.
3DBuzz's "Mathematics" training series focuses on exactly those principles that we believe provide a solid foundation for anyone working in - or hoping to work in - the fields of programming or computer graphics. Each topic covered is related and applied to a variety of computer graphics problems.
Mathematics Bundle, Volumes I-III strives to recreate as close to a traditional learning environment as possible. Mathematical theories are presented and explained while being drafted out on the whiteboard. Example questions are then presented, and solved by the instructor, using practical examples to help lock those theories into place. Finally, you, the viewer, are asked to answer a series of questions. With the ability to pause each video, you can attempt to answer each question in your own time, referring back to earlier videos if necessary. Once you have a solution, you can then resume the video and see the instructor work through the solution on the white board, explaining each step along the way.
Volume I begins by introducing a number of essential concepts of algebra, including the order of operations, the algebraic laws, and rearranging equations. There are countless scenarios in computer graphics, and programming in general, where an equation might state a rule (or set of rules) that govern something that you're trying to work with. Therefore, the ability to work with and manipulate equations, using the algebraic topics covered in this volume, will be a huge boost to your skill set, whether a programmer or a technical artist.
• Order of operations
• Algebraic laws
• Rearranging of equations
• Cartesian coordinates
• Equation of a straight line
• Quadratic equations
• Pythagorean theorem in 2D and 3D
• Area of an isosceles triangle
• Equations for circles
• Line-circle intersections
Volume II focuses on trigonometry, which is incredibly useful for solving problems relating to triangles. Many visual and geometric problems can be constructed as triangle problems. Therefore, knowledge of trigonometry is extremely beneficial for programmers and technical computer graphics artists alike, and this volume will run you through a variety of topics from beginner level to more in-depth triangle calculations.
• Measuring in Degrees and Radians
• Trigonometric ratios
• Inverse trigonometric functions
• Triangle area
• The Pythagorean Identity
• Sine rule
• Cosine rule
• Complementary angle and negative angle identities
• Compound angle identities
Volume III focuses on vectors. Vectors have facilitated the development and advancement of theories in physics, engineering, computer graphics, programming, and many other areas of research!
The key to vectors, as you will discover in this DVD, is that they allow us to represent a direction in our 3D space. Because of this, vectors can be applied to just about any area of computer graphics. They're used in modelling, rigging, animation, physics calculations, lighting, shading, and these are just a handful of examples. Vectors are so fundamental to any program that involves some 2D and/or 3D space that they are one of the most important areas of mathematics that a graphics programmer can know.
• 2D vectors defined
• Adding and subtracting 2D vectors
• Magnitude of a 2D vector
• Multiplying a 2D vector by a scalar
• 2D unit vectors
• 2D position vectors
• 3D vectors defined
• Adding and subtracting 3D vectors
• Magnitude of a 3D vector
• Multiplication of a 3D vector by a scalar
• 3D unit vectors
• 3D position vectors
• Cartesian vectors
• Dot product of two vectors
• Cross product of two vectors
• Vector equations of a line
• Perpendicular distance of a point from a line
Best of all, you get all 3 of these volumes all on one disc! This is a great way for you to get up to speed on critical mathematics skills, especially those that are absolutely essential for a graphics programmer!
Please note that each volume builds upon topics presented in the previous videos, so viewers without an understanding of certain areas may have problems following along if they skip ahead.