Control points onto the screen and draw the nurbs on

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Unformatted text preview: design Pi : control points Bi,k: Bspline basis of order k wi : weights Benefits of using NURBS • More degrees of freedom to control the curve (can control the weights) • Invariant under perspective transformation – Can project the control points onto the screen and draw the NURBS on the screen ■ Don’t need to apply the perspective transformation to all the sample-points on the curve • Can model conic sections such as circles, ellipses and hyperbolas Example of changing weights • Increasing the weight will bring the curve closer to the corresponding control point Bspline Surfaces • Given the following information: • a set of m+1 rows and n+1 control points pi,j, where 0 <= i <= m and 0 <= j <= n; • Corresponding knot vectors in the u and v direction, Clamping, Closing B-spline Surfaces • The B-spline surfaces can be clamped by repeating the same knot values in one direction of the parameters (u or v) • We can also close the curve / surface by recycling the control points Closed B-spline Surfaces • If a B-spline surface is closed in one direction, then the surface becomes a tube. • Closed in two direction : torus – Problems handling objects of arbitrary topology, such as a ball, double torus Today – More about Bezier and Bsplines ■ de Casteljau’s algorithm ■ BSpline : General form ■ de Boor’s algorithm ■ Knot insertion – NURBS – Subdivision Surface Subdivision Surface • A method to model smooth surfaces 3D subdivi...
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This document was uploaded on 03/26/2014.

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