Basic NURBS Modeling in Software

Generate QR Code 2d barcode in Software Basic NURBS Modeling

and is an industry staple in building models for high-end film productions and industrial design While NURBS are very technical in nature, taking the time to understand how they work is worthwhile because you can benefit by using them in certain modeling scenarios

Non-Uniform Rational B-Splines is a mathematical term that sounds complicated To understand NURBS, you should know that a NURBS object is a mathematical description of a curve or surface Any point on a NURBS curve or surface has an exact coordinate value, in contrast to a polygonal surface, where only the locations of the vertices can be returned When comparing NURBS to polygons, a good analogy to consider is the difference between vector-based graphics used in Adobe Illustrator and Flash and pixel-based images used in Adobe Photoshop and many digital video and photography applications Because vector lines are drawn on your screen based on a mathematical description, they always remain smooth, no matter how close you zoom in on them or how big the window is in which they are played back Pixelbased images, on the other hand, are made up of finite rectangles, called pixels While these may not be visible when you re viewing an image at its normal resolution, the image starts to break up as you zoom in and see that the image is made up of thousands, or even millions, of rectangular pixels Polygonal geometry, which we ve been working with over the last two chapters, is made up of finite segments (faces) Since a NURBS surface is mathematically described, it can be rendered to appear infinitely smooth, no matter how close up the camera gets Figure 5-1 shows a NURBS sphere (left) and a polygonal sphere (right) Look at the edges of the spheres and notice that the polygonal sphere is FIGURE 5-1 A close-up of a NURBS sphere (left) versus a made up of segments polygonal sphere (right) and is not smooth like the NURBS sphere In this chapter, we ll cover the components of NURBS geometry, discuss some advantages and disadvantages of NURBS compared to polygonal modeling, and demonstrate how to work with NURBS curves and surfaces

Both NURBS curves and surfaces have similar components that control how they are edited Understanding how these components relate to each other and how they are used to calculate curves and surfaces will provide you with a good foundation for transforming your simple surfaces into more complex shapes while maintaining a clean geometry that is easy to edit

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We ll first examine curves, since they have similar, but fewer, components than surfaces You ll then learn how these components relate to surfaces and how some other components are unique to surfaces

Figure 5-2 shows a NURBS curve displaying its components, described next:

polynomial curve segments, called spans The points where these segments join are called edit points (sometimes called knots) An edit point lies on a curve and is represented by a small that you can select and move to edit the shape of the curve Edit points can be added to a curve by using the Insert Knot command (Edit Curves | Insert Knot)

between edit points CVs basically define the shape of a curve or surface The number of CVs between edit points depends on the degree of the curve (See Surface or Curve Degree later in this chapter) CVs often lie above or below a curve, in space, and are the components most commonly edited to control the shape of the curve CVs cannot be inserted directly into the curve but rather are added when an edit point is inserted