Drawing Curved Lines and Surfaces from Points

Splines

• Hermite spline - requires starting and ending point slopes for each pair of points, allows local control
• Cardinal Spline - slopes interpolated from point proceeding and follow current points [does not require knowing slopes as for Hermite]
• Kochanek Bartels splines - add parameters of tension and bias
  tension - how close to go to the polyline going through the points
  bias - bending at the end points of the curve

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• Bezier - spline approximate - Bezier splines (Bezier curves use a blending function)

Bezier Surface

             m     n
             __   __
             \    \
P(u,v)     = /    /   p   BEX     BEZ    (u)
             --   --   jk    jm      kn
            j=0   k=0

B-Spline curves and surfaces

• degree can be set independent of # of control points
• allow local control over the shape [but more complex]

Beta Splines

Rational Splines