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README.md

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[![License: MIT](https://img.shields.io/badge/License-MIT-yellow.svg)](https://opensource.org/licenses/MIT)
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## Table of Contents
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- [Overview](#overview)
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- [Key Features](#key-features)
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- [Spline Interpolation](#spline-interpolation)
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## Installation
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### Using pip
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```bash
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pip install InterpolatePy
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```
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### From Source
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To install the latest development version with all dependencies:
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# For testing dependencies only
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pip install -e ".[test]"
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# For documentation dependencies only
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pip install -e ".[doc]"
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# For development tools only
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pip install -e ".[dev]"
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```
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InterpolatePy implements several key mathematical concepts for trajectory generation:
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### B-splines
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Piecewise parametric curves defined by control points and a knot vector. B-splines offer local control (changes to a control point only affect the curve locally) and customizable continuity.
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### Cubic Splines
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Piecewise polynomials with C² continuity (continuous position, velocity, and acceleration) that interpolate a given set of points.
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### Smoothing Splines
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### Smoothing Splines
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Splines with a controllable balance between accuracy (passing through points exactly) and smoothness (minimizing curvature). The μ parameter controls this tradeoff.
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### Trapezoidal Velocity Profiles
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Trajectories with linear segments of constant acceleration and velocity, creating a trapezoidal shape in the velocity profile.
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### Double-S Trajectories
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Motion profiles with bounded jerk, acceleration, and velocity, creating smooth S-curves in the acceleration profile. These are ideal for robotic motion to reduce stress on mechanical systems.
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### Frenet Frames
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Local coordinate systems defined by tangent, normal, and binormal vectors along a curve, useful for tool orientation and trajectory tracking.
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## Requirements

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