Why use Screw Linear Interpolation instead of standard SLERP?

While SLERP handles rotations, Screw Linear Interpolation (ScLERP) provides a true geodesic on the motor manifold, ensuring perfectly smooth and constant velocity for both rotation and translation simultaneously.

What is a 'Motor' in the context of PGA?

A motor is an algebraic object in Projective Geometric Algebra (PGA) that unifies rotation and translation into a single geometric operator, allowing for more efficient and robust 3D transformations compared to matrices.

Which programming languages and libraries does this skill support?

The skill provides implementation patterns and logic for ganja.js (JavaScript/Web), klein (high-performance C++), and Grassmann.jl (Julia), covering a wide range of development environments.

How does PGA help with skeletal animation?

PGA simplifies the math behind bone weighting and joint movement by treating rotations and translations as a single geometric entity, which helps avoid common issues like gimbal lock and 'candy-wrapper' artifacts.

PGA Motor Interpolation

Name: PGA Motor Interpolation
Author: plurigrid

byplurigrid

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Game Development

Provides smooth rigid body transformations and motor interpolation using Projective Geometric Algebra for 3D animations and trajectories.

This skill implements advanced interpolation techniques—including NLERP, SLERP, and Screw Linear Interpolation—within the framework of Projective Geometric Algebra (PGA). By leveraging motor logarithms and exponential maps via libraries like ganja.js and klein, it enables seamless transitions between rotations and translations in 3D space. It is particularly effective for skeletal animation, robotics trajectory planning, and any application requiring unified, singularity-free rigid body motion without the complexities of traditional dual quaternions.

Key Features

01Unified rotation and translation interpolation via PGA Motors

02Exponential and Logarithmic mapping for motor manifolds

03GF(3) trit-aligned motor decomposition and conservation verification

04Implementation of NLERP, SLERP, and Screw Linear Interpolation (ScLERP)

05Cross-library support for ganja.js, klein (C++), and Grassmann.jl

068 GitHub stars

Use Cases

01Calculating precise robotic arm trajectories and path planning for industrial automation

02Developing smooth skeletal animations for 3D character models and rigged assets

03Implementing cinematic camera movements with unified rigid body physics in game engines

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi pga-motor-interpolation

For use in Claude.ai and ChatGPT

Download Skill