There are many books and references for those of you interested in an in-depth reading about NURBS. Figure (36): Non-uniform rational B-splines and their control structure. It is easy to represent free-form curves using NURBS and the control structure makes it easy and predictable to edit. NURBS is an accurate mathematical representation of curves that is highly intuitive to edit. \(a\), \(b\), and \(c\) define the slope of the line, such that the vector \(\mathbf\). \(x’\), \(y’\), and \(z’\) are the coordinates of a point on the line segment. \(x\), \(y\), and \(z\) are functions of t where t represents a range of real numbers. We saw earlier that the parametric equation of a line in terms of parameter \(t\) is defined as: In general, we can describe the \(x\), \(y\), and \(z\) location of a parametric curve in terms of some parameter \(t\) as follows: The time interval you spend from start to end (8 to 9) is called the curve domain or interval. Congratulations, you have just defined your first parametric curve! You have used time as a parameter to define your path, and hence you can call your path curve a parametric curve.
Assuming you travel the exact same speed every day, at 8:00 you would be at home (start location), at 9:00 you would be at work (end location) and at 8:40 you would at the exact same location on the path as the 40th plot point. If you plot your location every minute during your trip, you can define the path between home and work by connecting the 60 points you plotted.
At each point in time between 8:00 and 9:00, you would be at some location along the way. You leave at 8:00 in the morning and arrive at 9:00. Suppose you travel every weekday from your house to your work. This guide is an in-depth review of parametric curves with special focus on NURBS curves and the concepts of continuity and curvature.
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