Data Domains in Grasshopper
In this short tutorial, I am showing the essentials of data domains in Grasshopper. A domain is a data type in Grasshopper that represents a portion of the 1d or 2d number space. This requires a starting and ending point in those spaces. In 1d, these points are two numbers. Then, the domain represents all the numbers between them. In 2d, a data domain is represented by two coordinates (u, v). This presentation illustrates this concept with the area defined by the rectangle with two opposite corners at these two coordinates. Besides, I gave several examples from Grasshopper components that require domain data type.
This tutorial shows the fundamental utilization of data domains in Grasshopper’s parametric curve and surface operations. For example, when we reparameterize a curve, we remap its domain into another domain between 0 and 1. This is related to curve and surface evaluations and I find it useful in teaching the necessity of reparameterization in several design conditions. The animations show how Grasshopper calculates the parametric points on curves and surfaces. Therefore, we can extend the concept of data domains into its mathematical meaning. When we trim or extend a parametric curve, we change its domain according to the criteria we define. I hope I will be explaining these in my new book on design mathematics.
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