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All main topics / Informatik / Computergrafik / Schwerpunktkolloquium: Basic Techniques, Geometry Processing, Global Illumination
77
What are spline curves? How are spline curves constructed from Bézier curves?
Spline curves: Piecewise polynomial curves which are maximally smooth:
Polynomial degree continuous

Constructing Spline curves
  • Degree 1: Linear segments.
  • Connect endpoints for continuity.
  • Degree 2: Quadratic segments.
  • Connect endpoints for continuity.Use identical vector for first and last edge of subsequent segments for continuity.
  • Degree 3: Cubic segments.
  • Connect endpoints for continuity.Use identical vector for first and last edge of subsequent segments for continuity.Extend the middle edges of both segments and find the intersection point: If the so-created A-frame splits each pair of collinear edges in a 1:1 ratio, the connection between the segments is continuous.


This allows to create a cubic spline curve by only specifying A-frame vertices:
  • Connect A-frame vertices by edges and split 1:1:1
  • Add edges between each first and last vertex between neighboring edges and split 1:1
  • Connect each 4 vertices with one cubic spline
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Flashcard info:
Author: janisborn
Main topic: Informatik
Topic: Computergrafik
School / Univ.: RWTH Aachen
City: Aachen
Published: 18.05.2022

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