Gamedev Math on Godot 4 レシピ

Interpolation

Mon, 01 Jan 0001 00:00:00 +0000

Linear Interpolation, or its commonly-used abbreviation lerp, is a term that comes up often in game development. If you’ve never come across it before it can seem mysterious and highly-technical, but as you’ll see in this tutorial, it’s actually a straightforward concept with a wide variety of applications in game programming.

Numeric Interpolation

The core formula for linear interpolation is this:

func lerp(a, b, t):
 return (1 - t) * a + t * b

In this formula, a and b represent the two values and t is the amount of interpolation, typically expressed as a value between 0 (which returns a), and 1 (which returns b). The function finds a value the given amount between the two. For example:

Transforms

Tue, 09 Apr 2019 19:49:14 -0700

Before reading this, make sure you have an understanding of vectors and how they’re used in game development. If you don’t, I recommend you read this introduction I wrote for the Godot documentation: Vector Math.

2D Transforms

In 2D space, we use the familiar X-Y coordinate plane. Remember that in Godot, as in most computer graphics applications, the Y axis points downward:

To begin, let’s consider this spaceship floating in space:

Vectors: Using Dot and Cross Product

Mon, 01 Jan 0001 00:00:00 +0000

Problem

You’d like to understand what is meant by dot product and cross product.

Solution

In this recipe we’ll introduce the concept of vector dot product and cross product and how they might be used.

Dot product

Dot product is an operation on two vectors that returns a scalar. It is often visualized as the projection of vector A onto vector B:

This is the formula for calculating the dot product: