Cg17_2013

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Unformatted text preview: oint and ai is computed by The polyline Pj-k+1, Pj-k+2, ..., Pj-1, Pj is replaced with Pj-k+1, Qj-k+2, ..., Qj-1, Qj ,Pj. Example • A Bspline curve of degree 3 (k=4) having the following knots • t=0.5 inserted t0 to t3 t4 t5 t6 t7 t8 to t11 0 0.2 0.4 0.6 0.8 1 t0 to t3 t4 t5 t6 t7 t8 t9 to t12 0 0.2 0.4 0.5 0.6 0.8 1 http://i33www.ira.uka. de/applets/mocca/html/noplugin/curves.html Example • A bspline curve of degree 3 (k=4) having the following knots • t=0.5 inserted t0 to t3 t4 t5 t6 t7 t8 to t11 0 0.2 0.4 0.6 0.8 1 t0 to t3 t4 t5 t6 t7 t8 t9 to t12 0 0.2 0.4 0.5 0.6 0.8 1 Example • A bspline curve of degree 3 (k=4) having the following knots • t=0.5 inserted http://geom.ibds.kit. edu/applets/mocca/html/noplugin/IntBSpline/ AppInsertion/index.html t0 to t3 t4 t5 t6 t7 t8 to t11 0 0.2 0.4 0.6 0.8 1 t0 to t3 t4 t5 t6 t7 t8 t9 to t12 0 0.2 0.4 0.5 0.6 0.8 1 http://i33www.ira.uka. de/applets/mocca/html/noplugin/curves.html Summary of B-splines • • • • Knot vector defines the domain Evaluation by de Boor’s algorithm Controlling the shape by the control points Clamping the points by increasing the multiplicity of the knots at the end points • Increase the resolution by knot insertion Today – More about Bezier and Bsplines ■ de Casteljau’s algorithm ■ BSpline : General form ■ de Boor’s algorithm ■ Knot insertion – NURBS – Subdivision Surface NURBS (Non-uniform rational B-spline) • Standard curves/surface representation in computer aided...
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This document was uploaded on 03/26/2014.

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