math-based-animations.md

layout	title	parent
page	Math-based Animations	Concepts

Math-based Animations

Table of contents

{: .text-delta } 1. TOC {:toc}

Intermediate {: .label .label-yellow }

Math animations are a powerful alternative to key-frame animations. Generally speaking, math based animations is the concept of using Molang expressions to animate entity geometry. All vanilla animations are math-based:

Here is an example:

"leftarm" : {
    "rotation" : [ "((-0.2 + 1.5 * (math.abs(math.mod(query.modified_distance_moved, 13) - 6.5) - 3.25) / 3.25) * query.modified_move_speed) * 57.3 - variable.agent.armxrotationfactor", 0.0, "-variable.agent.armzrotation" ]
},

As you can see, Math-based animations are complicated, and hard to understand. For this reason, they should be treated as a specialized-alternative to key-frames -not a full replacement.

Writing math-animations

By Hand

Math-based animations can be written by hand. Simply create a new animation file, and write the math expressions. The format is fundamentally similar to key-frame animations. The vanilla resource files can be a valuable source of inspiration, and you should definitely download the vanilla resource pack!

In Blockbench

You can write and preview math-based animations in Blockbench. If you just want to create a math powered animation, just create a keyframe at 0 seconds in your timeline and edit the MoLang expressions in the keyframe panel on the left sidebar. You can also mix and match numeric keyframes with math-based keyframes. Omit quotation marks around the expression, they are only required in raw JSON editing!

Not all queries are supported in Blockbench due to missing context. If you want to preview an animation that uses a specific query, you can add it to the "Variable Placeholders" section right under the keyframe panel to simulate a value. For example, adding query.modified_distance_moved = time*8 simulates the modified_distance_moved query with a speed of 8 blocks per second.

Using queries

The biggest tool you have access to when writing math-based animations, is using queries. Queries can be used to add outside-information into your math expression.

Common ones include:

• query.modified_distance_moved
• query.modified_move_speed
• query.anim_time
• query.life_time

The reason we want to use queries is it allows us to directly drive animations from gameplay. Things like the attack time, or distance moved, allows us to drive gameplay directly, and allows animations to match the speed of the action.

Avoiding animation controllers

By using queries, you can avoid the need to create animation controllers. If the speed of the entity is directly related to the speed of the walk animation, then by default an entity that isn't moving won't be animated.

Example

A specific example is using animations to drive the wheels of a car based on the modified_distance_moved:

{
	"format_version": "1.12.0",
	"animations": {
		"animation.car.wheel_spin": {
			"loop": true,
			"animation_length": 1.0,
			"bones": {
				"front_wheels": {
					"rotation": [ "query.modified_distance_moved * -30", 0, 0  ]
				},
				"back_wheels": {
					"rotation": [ "query.modified_distance_moved * -30", 0, 0  ]
				}
			}
		}
	}
}

In this example, the bones/groups front_wheels and back_wheels are rotated based on the query.modified_distance_moved, multiplied by some 30.

This means

• A car at rests will not spin
• A car that is driving will spin proportionally fast to the speed of the car