Curves

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For the next programming assignment (as stated on #4 ) we need to implement a basic curves editor with shape extruding. Two kinds of curves must be supported:

• [x] BSplines (see Fundamentals of Computer Graphics, Shirley - Chapter 15 - curves)
• [x] NURBS
• [x] RaGs (see: Geometric modelling using rational Gaussian curves and surfaces)

I also suggest a third as it's a very common choice among pen tools:

• Bezier Curve Redundant. We can easily create bezier curves from BSplines if we allow (and we will) the user specify the knots vector

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Extra

noise-reduction: Ramer-Douglas-Peucker and Visvaligam's algorithm

• [x] Try to take advantage of instancing and glSubBufferData-a-like stuff for perf.

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We need to find the derivatives so that we're capable of determining surface normals. see Implementation of NURBS Curve Derivatives in Engineering Practice

[cirocosta]

Implementation

In terms of Interface

• [x] Number of subdivisions to be made
• [x] Type of curve to be made
• [x] Specify specific curve params
  • [x] RaGs: variance
  • [x] BSplines: degree of base polynomials
  • [x] validate the input. It must be at most the same as the number of control points
• [x] Specify curve's control points
• [x] knots vector
  • [x] default: uniform

[cirocosta]

Demo

[cirocosta]

http://dl.acm.org/citation.cfm?id=2658575 - Parametric Circles and Spheres --> uses NURBS for that (as we can do conics with it)