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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 samplepoints 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 Bspline Surfaces
• The Bspline 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 Bspline Surfaces
• If a Bspline 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.
 Spring '14

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