# What is parametric modeling?

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Here is a simple shape with parameters. Image: Scan2CAD.

In computer-aided design (CAD), parametric modeling is a technique for creating and modifying drawings (2D) and models (3D) by specifying parameters. For example, with parametric modeling, you define a box with the parameters L for length, W for Width and H for height instead of using numbers. Parameters can be filled in with numbers or formulae. For example, for L (length), you could use L=2*W, making the length of the box twice the width. Parameters can define distance, angle, quantities, and more.

When you change a parameter, the entire model updates automatically to reflect the change.

### Benefits of Parametric Modeling

• Flexibility: It’s easy to make changes to a model after it has been created. You simply adjust the parameters and the model will update automatically. For example, if a client wants to see how it will look if all the ceilings in a high-rise are changed from 8 feet to 8.5 feet, the architect needn’t tear their hair out—if the height of the ceiling was defined with a single parameter, say H. The architect only has to make H equal to 8.5 feet in one place and all the floors in the building will immediately be at the new height. The architect would not have to manually change each ceiling height manually.

• Complexity: Parametric models can be more complex to create than traditional models, especially for beginners. Defining a model parametrically means more up-front work in the design. Users may protest having to use parametric design, especially on simple models. A complicated model will require significantly more effort than just plugging in numbers, especially if formulae are used.
• Constraint hell: Parameters first come into play when creating the sketch that will serve as the basis of a solid model, for example, the profile of an extrusion. A parametric modeler that requires a fully constrained model before the solid is created may put the user in “constraint hell,” a condition in which the user cannot find how the sketch is under- or overconstrained, and the modeling can go no further.

A sport wheelchair is defined parametrically. Image: Onshape.

### A Little History

The first parametric model? Weights used as parameters in Antoni Gaudi’s analysis of the Sagrada Familia. Image: Paul Heney.

Parametric modeling has been around since the 19th century when the famous Barcelona architect Antoni Gaudi explored early concepts of parametric design in his physical models for the Church and the iconic Sagrada Familia. Gaudi used strings and weights (effectively parameters) to create complex, interconnected structures that could be modified by adjusting the weights.

Parametric modeling, as we know it today, came into being with a company that had “parametric” as its first name: Parametric Technology Corporation. The company now just goes by its initials. PTC burst onto the scene in 1988 with Pro/ENGINEER and was immediately popular with mechanical designers and engineers, competing against CATIA by Dassault Systèmes, I-DEAS by SDRC, Applicon by Schlumberger, CADDS 4X by Computervision, Matra Datavision, Intergraph, Unigraphics and Alias—all capable mechanical CAD programs but all lacking the emphasis on parametric modeling.

Pro/ENGINEER was the first built-from-the-ground-up-feature-based solid modeler, which may be the cause of its popularity, rather than its parametric capability, the cause of its popularity.

### How Much?

Parametric modeling software is typically more expensive to acquire than traditional 2D CAD and takes longer to learn, increasing training costs.

David Weisberg.