Category Archives: Math

Game Math: Dot Product, Rulers, And Bouncing Balls

本文之中文翻譯在此 Prerequisites Trignometry Basics – Sine & Cosine Trigonometry Basics – Tangent, Triangles, And Cannonballs Inverse Trigonometric Functions, Slope Angles, And Facing Objects Overview The dot product is a simple yet extremely useful mathematical tool. It encodes the relationship between … Continue reading

Posted in Gamedev, Math, Uncategorized | 2 Comments

Game Math: Inverse Trigonometric Functions, Slope Angles, And Facing Objects

本文之中文翻譯在此 Prerequisites Trignometry Basics – Sine & Cosine Trigonometry Basics – Tangent, Triangles, And Cannonballs Overview At this point, we have learned about the three basic trigonometric functions: sine, cosine, and tangent. Now, we are going to take a look … Continue reading

Posted in Gamedev, Math, Unity | 1 Comment

Game Math: Trigonometry Basics – Tangent, Triangles, And Cannonballs

本文之中文翻譯在此 Prerequisite Trignometry Basics – Sine & Cosine Overview In the previous tutorial, we have learned about two basic trigonometric functions: sine & cosine. This time, we are going to look at another basic trigonometric function: tangent. Together, these three … Continue reading

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Game Math: Trigonometry Basics – Sine & Cosine

本文之中文翻譯在此 Overview Trigonometry is a very essential building block to a huge portion of game math. That’s why I’ve chosen this topic for the first tutorial of my new Gamedev Tutorials series. Having a solid understanding of basic of trigonometry … Continue reading

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Game Math: Deriving the Slerp Formula

This post is part of my Game Math Series. It occurred to me that the entire time I’ve been working with quaternions, I have never read or learned about the derivation of the formula for slerp, spherical linear interpolation. I … Continue reading

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Game Math: Swing-Twist Interpolation (…Sterp?)

This post is part of my Game Math Series. Source files are on GitHub. Shortcut to sterp implementation. Shortcut to code used to generate animations in this post. An Alternative to Slerp Slerp, spherical linear interpolation, is an operation that … Continue reading

Posted in Gamedev, Math, Programming, Unity | 2 Comments

Game Math: Curve Approximation via Curve “Projection”

This post is part of my Game Math Series. Also, this post is part 2 of a series (part 1) leading up to a geometric interpretation of Fourier transform and spherical harmonics. Drawing analogy from vector projection, we have seen … Continue reading

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Game Math: “Projecting” a Curve onto Another

This post is part of my Game Math Series. Also, this post is part 1 of a series (part 2) leading up to a geometric interpretation of Fourier transform and spherical harmonics. Fourier transform and spherical harmonics are mathematical tools … Continue reading

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Game Math: More on Numeric Springing

This post is part of my Game Math Series. Source files are on GitHub Previously, I talked about numeric springing and provided some examples. I have been saving up miscellaneous topics I would like to discuss about numeric springing, and … Continue reading

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Game Math: Numeric Springing Examples

This post is part of my Game Math Series. Source files are on GitHub So, you have seen how to precisely control numeric springing in my previous post. I showed this animation as an example. Manually fine-tuning the animation with … Continue reading

Posted in Gamedev, Math, Physics | 7 Comments