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MT 21_CAD/CAM 3(1-2)

Than Lin, Ph.D. Instructor, Undergraduate Program

Asian Institute of Technology

Lecture: Week 7 NURBS

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NONUNIFORM RATIONAL B-SPLINE (NURBS)

A nonuniform rational B-spline curve, or simply a NURBS curve. It’s similar to a nonuniform B-spline curve in that it uses the same blending functions derived from the nonuniform knots as those of nonuniform B-spline curves.

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Properties

- A NURBS curve (Eq 6.51) passes through the first and last control

points if nonperiodic knots are used.

-The tangent vector at the starting point is in the same direction as

P1 – P0 and at the ending point it is in the same directions as

Pn – Pn-1.

-The NURBS equation is a general form that can represent both

B-spline and Bezier curves.

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Advantages over a B-spline equation

- Increasing the value of the homogenerous coordinate of a control

point has the effect of drawing a curve toward the control point.

-The conic curves – circles, ellipses, parabolas and hyperbolas can

be exactly represented by NURBS equations.

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Fig 6.8 Control points of a NURBS curve equivalent to a circular arc.

To demonstrate how to derive the NURBS representation of conic curves, An example is shown for presenting order, the coordinates of the control points (including the homogeneous coordinates), and the knot values of the NURBS curve equivalent to a circular arc.

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Example 6.6

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Example 6.7

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