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Tech neck is a modern affliction caused by the bent head position many use when looking at their electronic devices, like phones or tablets. Extended use of these devices can cause progressive deterioration and pain in your neck, back, and shoulders. Advances in minimally invasive spine surgery MISS have made the prospects of undergoing back surgery a bit less daunting.

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Find out what makes a microsurgical lumbar laminoplasty different from traditional open surgery, and how it can benefit you. Sahni is such an excellent Dr.


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He made me so comfortable when I was incredibly nervous. His team is the best and they take very great care of their parents. Sahni is very up front about options and his staff is friendly and makes you feel very welcome. Sahni and his staff are extremely nice, helpful, and very knowledgeable. He is very concerned about my needs as a patient and took his time with me I had my back surgery and was able to heal quickly.

Thanks again. A doctor that knows his stuff and is super friendly! Sahni and his staff were super helpful and very friendly.

He is very professional yet warm and friendly. I would recommend him highly to anyone. Sahni is an exceptional surgeon, highly intellectual and very professional. He also has a very compassionate and attentive bedside manner that I appreciated. Monday am - pm Tuesday am - pm Wednesday am - pm Thursday am - pm Friday am - pm Saturday Closed Sunday Closed.

Sahni is a fantastic and wonderful doctor. Carol A.


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Jump to a Section Chapter Low Back Pain Chapter Facet Syndrome Chapter Failed Back Surgery Syndrome. Sign In. They also provide the ability to add control points without increasing the degree of the curve.


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  • B-spline Curves: Definition;

B-spline curves have the ability to interpolate or approximate a set of given data points. Interpolation is useful in displaying design or engineering results such as stress or displacement distribution in a part while approximation is good to design free-form curves. Interpolation is also useful if the designer has measured data points in hand that must lie on the resulting curve. Use your CAD software to draw several B-spline curves. Use the same control points to draw both approximation curves and interpolation curves. Report your observations.

The theory of B-spline curves separates the degree of the resulting curve from the number of the given control points. First, the parameter k controls the degree k -1 of the resulting B-spline curve and is usually independent of the number of control points. The B-spline functions have the following properties:. Partition of unity:.

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The first property ensures that the relationship between the curve and its defining control points is invariant under affine transformations. The second property guarantees that the curve segment lies completely within the convex hull of P i. Assume a set of 4 two-dimensional control points P i in the x - y plane, the B-spline curve defined by this set of control points is. Assume the following affine transformation discussed in Chapter 1 to transform P u to get :. Use the same affine transformation to transform P i to get , and the B-spline curve defined by this set of control points is.

This also ensures that the relationship between the curve and its defining control points is invariant under affine transformations. This is a hard question. You do not have to? You just have to assume a set of control points and coefficients for the affine transformation, and? Use your CAD software to draw curves similar to those in Figure 1.