NURBS: from projective geometry to practical use
NURBS (Non-Uniform Rational B-Splines) have become the de facto standard for geometric definitions in CAD/CAM and computer graphics. This well-known book covers NURBS from their geometric beginnings to their industrial applications. The second edition incorporates new research results and a chapter on Pythagorean curves, a development that shows promise in applications such as NC machining or robot motion control. More than fifty new figures have been added.
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Conics in Parametric Form
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affine conic affine plane affine points affine space B-spline curve barycentric coordinates Bezier form Bezier patches Bezier points bilinear patch Boor algorithm boundary curves Casteljau algorithm collinear points collineation component compute cone conic splines control points control polygon control vectors convex hull corresponding cross ratio defined degree elevation denote derivative developable surface dual equation evaluate example extended affine plane Figure four points given Gregory patches hyperbola illustration implicit form interpolation intersection knot sequence line at infinity line conic linear Moebius NURBS obtain osculating plane Pappus parabola parameter value Pascal's theorem piecewise planar point conic polynomial curve project into affine projective geometry projective maps projective plane projective space quadratic patch quadric rational Bezier curve rational cubic rational curve rational patch rational quadratic reparametrization Section segment shoulder tangent shown in Fig stereographic projection straight line surface of revolution tangent plane three points triangular patch weight points zero