EAN: 9783031795152

SYNTHESIS LECTURES ON COMPUTER GRAPHICS AND ANI...

In this lecture  we study Bézier and B-spline curves and surfaces  mathematical representations
for free-form curves and surfaces that are common in CAD systems and are used to design
aircraft and automobiles  as well as in modeling packages used by the computer animation
industry. Bézier B-splines represent polynomials and piecewise polynomials in a geometric
manner using sets of control points that define the shape of the surface. The primary analysis
tool used in this lecture is blossoming  which gives an elegant labeling of the control points
that allows us to analyze their properties geometrically. Blossoming is used to explore both
Bézier and B-spline curves  and in particular to investigate continuity properties  change of
basis algorithms  forward differencing  B-spline knot multiplicity  and knot insertion
algorithms. We also look at triangle diagrams (which are closely related to blossoming)  direct
manipulation of B-spline curves  NURBS curves  and triangular and tensor product surfaces.

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