# TL Clothoid

## Description

An Euler spiral is a curve whose curvature changes linearly with its curve length (the curvature of a circular curve is equal to the reciprocal of the radius). Euler spirals are also commonly referred to as spiros, clothoids, or Cornu spirals. Clothoids have applications to diffraction computations. They are also widely used as transition curves in railroad engineering/highway engineering for connecting and transitioning the geometry between a tangent and a circular curve. A similar application is also found in photonic integrated circuits. The principle of linear variation of the curvature of the transition curve between a tangent and a circular curve defines the geometry of the Euler spiral.

This app provides various commands allowing you to work with stand-alone spiral curves as polylines inside AutoCAD. Note that similar functionality exists out of the box in some Autodesk® AutoCAD® vertical products such as Autodesk® Civil 3D®. However:

- this app works in any AutoCAD based application, it does not require Civil 3D

- this app is designed not to replace, but to extend existing functionality found in Civil 3D, particularly while working with stand alone spirals

A Clothoid has various parameters (refer to the included diagram) such as:

<Parameter A>: A scale value, also known as 'flatness'

<Length>: The distance from sta 0 to the end of the curve. (Actual mathematical curve has a distance of +-Infinity and radius of zero at the end)

<Radius>: The radius at the end of the computed curve at station +-<Length>

<Tangent>: The value of the first derivative at the end of the curve at station +-<Length>. Range is 0 to Pi

Each set of two parameters uniquely defines a Clothoid for a total of six possible combinations. The app provides six drawing modes for all possible combinations.

Point coordinates (x,y) along a normalized Clothoid curve are expressed by the Fresnel Integrals. These integrals don't have closed form solutions and are in turn approximated as power series. The app computes up to 75 terms of the Fresnel integral series approximations for each Clothoid point. The actual number of iterations vary, depending on the achieved accuracy, which the program track internally.

command (as far as the MaxError parameter value is reached)

Features:

Six clothoid creation modes

- Length & Radius
- Length & Tangent/Theta
- Parameter A & Radius
- Tangent/Theta & Radius
- Parameter A & Tangent/Theta
- Parameter A & Length

Five clothoid curve-fitting transition commands

- Spiral-Curve-Spiral
- Spiral-Line-Spiral
- Spiral-Spiral (Curves)
- Spiral-Spiral (Tangents)
- Segmental Spiral

Four miscelineous manipulation/inquiry commands

- Locate Elements
- Clothoid Info
- Redraw Last
- Draw Segment

Dynamic preview of the computed curve(s) with on-screen info and mouse scroll button parameter adjustments

Custom UCS support

Automatic internal error checking and accuracy control of the computed clothoid points

Control of the number of polyline points/distance between computed points

Clothoid parameters report for each computed curve

XData with Clothoid definition parameters for all generated polylines

A "Copy" curve functionality to quickly copy the clothoid parameters from an Autocad polyline clothoid

Customizable "Draw Flags" settings to turn on/off various clothoid elements when generating the curve in Autocad