Book | Visualizing Equations

The most common equations in video games and CG.

• The Dot Product’s behaviour.
• The nature of Cross Product.
• Quaternions and vertices.
• Euler angles and gimbal lock.
  

If you are a student, a technical artist or a Unity enthusiast, the Visualizing Equations book can be helpful! Elevate your understanding of mathematical equations by creating visualization tools using Unity’s ‘EditorWindow’ class.

This book is designed to assist Unity developers in creating effective software tools for visualizing equations in their projects. Through a combination of theory and practical examples, readers will learn how to apply mathematical concepts and programming tools to create dynamic and engaging visualizations that illustrate mathematical concepts in a clear and accesible way.

1. Understanding Dot Product.

• It covers all the math needed to understand the geometry of the dot product in a simple and easy-to-understand way.
• Offers a C# implementation for visualizing the geometry of the dot product, along with straightforward examples.
• Create a versatile tool for comprehending the relationships between vectors.
• Enhance your comprehension of the EditorWindow and its methods.

2. Understanding Cross Product.

• It explains the mathematical properties of the cross product, enhancing your understanding of three-dimensional geometry.
• Offers a C# implementation that enables a profound understanding of vector relations and linear applications.
• Provides a versatile tool for comprehending the geometry of the cross product and serves as a cornerstone for developing more advanced tools.
• Elevate your utilization of EditorWindow with more advanced examples.

3. Understanding Quaternions.

• Simple and comprehensive introduction to quaternions and complex numbres with easy-to-follow examples, so you can apply them immediately.
• C# implementation to properly comprehend algebraic results that simplify the application of rotations in 3D space.
• Provides a tool to directly visualize the usage of rotation quaternions on group of vectors.
• Offers an intuitive understanding of how we can use EditorWindow methods to perform transformation on objects.

4. Understanding Rotation matrices and Euler angles.

• Explore rotation matrices and Euler angles with our intuitive and visually engaging introduction!
• Achieve precision and Control: Harness the C# implementation for crafting impeccable rotation sequences to transform object orientations in space.
• Elevate your understanding: Visualiza rotations with unparalleled clarity using Gimbal-enabled tool.
• Explore how EditorWindow Masters the art of projecting objects in space!