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Category Archives: Math
Game Math: Precise Control over Numeric Springing
This post is part of my Game Math Series. Source files are on GitHub Check out this post if you want to see more visual examples of numeric springing. Numeric springing is a very powerful tool for procedural animation. You … Continue reading
Posted in C/C++, Gamedev, Math
9 Comments
Game Math: Interpolating Quaternions with Circular Blending
This post is part of my Game Math Series. While processing data for skeletal animations, we are usually faced with a series of discrete samples of positions and orientations. The positional samples are typically stored as a series of 3D … Continue reading
Posted in Gamedev, Math
2 Comments
Game Math: Quaternion Implementations
This post is part of my Game Math Series. I have covered the basics of quaternions. In this post, I will show some examples of quaternion implementations. The Interface We want our quaternion class to handle basic arithmetics (addition, subtraction, … Continue reading
Posted in Gamedev, Math
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Game Math: Quaternion Basics
This post is part of my Game Math Series. A quaternion is a very useful mathematical object devised by Sir William Rowan Hamilton as an extension to complex numbers. It is often used to compactly represent 3D orientations with just … Continue reading
My Recommended Book List to Game Devs
Here’s a list of books I have read that I recommend to to game devs. I’ve divided the books into several categories: computer science, math & graphics, physics, and procedural animation. I intentionally did not include any “gem” or “pearl” … Continue reading
Posted in Design Patterns, Gamedev, Math, Physics, Programming
9 Comments
Game Math: Faster Re-Normalization of Unit Vectors.
This post is part of my Game Math Series. I first saw this technique in an article, Hacking Quaternions, written by Jonathan Blow (author of Braid). To normalize a vector, you divide its individual components by its length. The bottle … Continue reading
Posted in Gamedev, Math
4 Comments
Game Math: Faster Sine & Cosine with Polynomial Curves
This post is part of my Game Math Series. We have seen how to approximate a function using polynomials in this post. A good candidate for polynomial approximation would be the sine function, for it is used a lot in … Continue reading
Posted in Gamedev, Math
7 Comments
Game Math: Approximation with Polynomial Curves
This post is part of my Game Math Series. Polynomials A polynomial is an expression consisting of linear combination of products of variables raised to non-negative integer powers. In this post, I will specifically focus on polynomials of a single … Continue reading
Posted in Gamedev, Math
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Game Math: How to Eyeball the Inverse of a Matrix
This post is part of my Game Math Series. Matrix Multiplication as Linear Combinations of Columns/Rows As shown in this post, matrix multiplication can be viewed as linear combinations of columns from the left matrix or rows from the right … Continue reading
Posted in Gamedev, Math, Uncategorized
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Game Math: Block Matrices
This post is part of my Game Math Series. Splitting Matrices into Blocks When performing matrix multiplication, we can split matrices into “blocks”. The matrix multiplication can then be performed as if each block is a single matrix element, given … Continue reading
Posted in Gamedev, Math
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