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Being patient and observing how the different trendlines shift like this will give you con dence and help you understand how price action works Knowing the various trends at work in the market also helps a trader coordinate lower time frame charts If the short-term and intermediate-term trends are higher on the 240-minute chart, we don t have to look to know that it is very likely that the primary trend on the 60minute chart also will be higher If the intermediate-term trend is higher on the 240-minute chart, most likely the short-term trend on the daily chart will be higher The implications of this are very important for traders on both the lower and higher time frames Knowing when the trends started and in which direction they are pointed is also a simple way to determine whether the market we are analyzing is in a trending or countertrending mode If the majority of trends, particularly the long-term trends, are pointing in the same direction, we are in a trending market If the trends are in ux, we are very likely in a countertrend market It is also important to understand that once a short-term trendline is violated, it is likely that the market will migrate to the intermediate-term trendline, and once the intermediateterm trend is violated, it becomes more likely that the market will try to test the long-term trendline It is often at this point, after a closing penetration of the intermediate-term trend, that a market will show us whether it has real underlying strength or this is just another secondary move Note in Figure 9-11 how powerful the stochastic buy signal marked by the gray vertical line on November 24 turned out to be This was the case because we already had an intermediate-term trend shift in place This short-term stochastic signal was the equivalent of.

Summary

In this chapter, you have learned to lay out the structure of a model so that it deforms according to the anatomy of a real human face While we have only covered the face in this chapter, the same exact techniques can be applied to any organic structure It all starts by laying out the framework so that the edge loops flow in the direction of the muscles of the underlying anatomy Once you have placed the framework, you add and sculpt edge loops until the complete model has been realized

>> x = linspace(0,2*pi); >> plot(x,cos(x)),axis([0 2*pi 1 1])

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

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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

Figure 3-23 We overwrite the previous plot by typing plot[x, sin(x)]

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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:

Figure 3-24

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