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You can change the direction of a curve by choosing Edit Curves |
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Reverse Curve Direction Knowing the direction of a curve is especially important during certain operations, especially those that involve connecting and merging curves You ll see an example showing why knowing the direction of curves is important later in this chapter in the section Cutting and Filleting Curves
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Parameterization of Curves and Surfaces
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Parameterization describes how the numeric values are assigned to each point on a NURBS surface or curve Each of these points has a numerical value known as a parameter that describes the point s location On a curve, this parameter gives a point s location in the curve s U direction
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FIGURE 5-5 A curve displaying its CVs and curve direction
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Basic NURBS Modeling
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A surface has two parameters, one in U and the other in V Any point on a surface can be queried or described using this coordinate system You can find the parameter value of any curve by right-clicking the curve and choosing Curve Point from the marking menu Then click any point on the curve, and its parameter value will appear on the title bar at the top of your main Maya window, as shown here:
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You can also use the Parameter tool to find the parameter of any point on a curve (choose Create | Measure Tools | Parameter Tool) by clicking any point along a curve The parameter value for this point appears next to the point and remains onscreen, as shown in Figure 5-6 This is perhaps a bit more convenient and useful than looking in the title bar
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Methods of Parameterization
The parameterization, or how a parameter value is calculated across the curve, is determined by one of two methods: the uniform method or the chord-length method, both shown in Figure 5-6 When drawing a curve, the method of parameterization can be set in Knot Spacing attributes of the CV (or EP) Curve tool s settings window (choose Create | CV Curve Tool r) With uniform parameterization, integral parameter values are assigned at each edit point To demonstrate, let s consider a curve with four spans, in which the edit points are not evenly spaced In the uniform parameterized FIGURE 5-6 Two- and four-span curves: the top curve uses curve shown in Figure 5-6, the first four uniform parameterization and the bottom curve uses chordedit points fall in the first half of the length parameterization curve and the last edit point is at the end of the curve The first edit point has a parameter value of 0, the next edit point has a value of 1, the next is 2, then 3, and the last point has a value of 4 We can use the Arc Length tool (choose Create | Measure Tools | Arc Length Tool) and the Parameter tool (Create | Measure Tools | Parameter Tool) to find a parameter value for any point on the curve by clicking it Say, for example, you wanted to find the parameter value for the middle of the curve Clicking at the center of the curve will return a value of 2589839, also shown in Figure 5-6
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Using uniform parameterization, you can match parameterization between two curves just by figuring the total number of spans However, determining parameters based on the length of the curves is not so straightforward By clicking at the approximate midpoint of the four-span curve shown in Figure 5-6, the midpoint parameter shows 2589839 This is not so intuitive if you want to insert knots at specific lengths, however like halfway, a quarter of the way, or three-quarters of the way down the curve When these types of calculations are necessary, it s probably more useful to use chord-length parameterization Using chord-length parameterization, the parameter values are assigned to the edit points based on the distance of a straight line, expressed in Maya units, extended between the edit points While this method gives the curves irregular parameter values at their edit points, the values do reflect information that is relative to a point s position along the curve So, for example, since this curve is 12 units long, it has a U parameter of 12 The middle of this curve could then be easily determined by dividing the parameterization in half A U value of 6, then, would be the middle of the curve
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