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 what it means to “project” a curve onto another in the previous post. This time, we’ll see how to find a the closest vector on a plane via vector projection, and then we’ll see how it translates to finding the best approximation of a curve via curve “projection”. This handy analogy can help us take another step closer to a geometric interpretation of Fourier transform and spherical harmonics later.

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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 that can be used to represent a function as a combination of periodic functions (functions that repeat themselves, like sine waves) of different frequencies. You can approximate a complex function by using a limited number of periodic functions at certain frequencies. Fourier transform is often used in audio processing to post-process signals as combination of sine waves of different frequencies, instead of single streams of sound waves. Spherical harmonics can be used to approximate baked ambient lights in game levels.

We’ll revisit these tools in later posts, so it’s okay if you’re still not clear how they can be of use at this point. First, let’s start somewhere more basic.

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Game Math: “Dot Product” of Curves

OK. Based on some feedback, turns out the wording of this post is logically loose and not entirely correct. Here is a revised version of this post.

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我的Uncharted 4開發雜記

Uncharted 4 logo

本文屬於My Career系列文

Here is the original English post.
本文之英文原文在此

註:為方便複製至PTT,本文排版採BBS格式,不習慣者請見諒

Uncharted 4已經發售,終於可以分享我負責開發的部分了
我主要是負責單人模式的夥伴AI、多人模式的戰友AI、還有一些遊戲邏輯
沒有收錄到最終遊戲的部分和一些瑣碎的細工我就略過不提

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A Brain Dump of What I Worked on for Uncharted 4

Uncharted 4 logo

This post is part of My Career Series.

Here is the Chinese translation of this post.
本文之中文翻譯在此

Now that Uncharted 4 is released, I am able to talk about what I worked on for the project. I mostly worked on AI for single-player buddies and multiplayer sidekicks, as well as some gameplay logic. I’m leaving out things that never went in to the final game and some minor things that are too verbose to elaborate on. So here it goes:

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我的秘境之旅

本文屬於My Career系列文

Here is the original English post.
本文之英文原文在此

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My Uncharted Journey

This post is part of My Career Series.

Here is the Chinese translation of this post.
本文之中文翻譯在此

Note: This post was written before Uncharted 4 went gold, so it might contain tones or implications that Uncharted 4 hasn’t gone gold yet. Sorry for the confusion.

I started working on Uncharted 4: A Thief’s End almost two years ago, and here we are, less than two months before release. This would be my first shipped title as a full-time game programmer (I shipped Planetary Annihilation during a summer internship). Looking back now, I realized that I’ve really come a long way since I first wanted to make games more than a decade ago. I would like to take this opportunity to write down this journey to share with you and as a note for myself.

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DigiPen: 我的遊戲學校

本文屬於My Career系列文

Here is the original English post.
本文之英文原文在此

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DigiPen: The Game School I Went To

This post is part of My Career Series.

Here is the Chinese translation of this post.
本文之中文翻譯在此

Disclaimer: This post is all about my personal experience with DigiPen and is in no way intended to represent anyone else’s experience or opinions.

I went to DigiPen Institute of Technology to learn how to make games in 2011, and graduated last year (2014). I graduated one year earlier than my fellow classmates in the same year, because I transferred in some credits I had already earned at my previous college in Taiwan.

I have written one post about my life at DigiPen every year on a game design forum in Taiwan. Also, many of my DigiPen friends just graduated and have started their jobs in the game industry. So I thought, why not write a dedicated post about my experience at DigiPen in English on my blog?

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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 now I have enough to write another post. Here are the topics:

  • Using The Semi-Implicit Euler Method
  • Numeric Springing vs. Tweening
  • Half-Life Parameterization

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