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A well of algorithms

September 27, 2006

Paul Bourke has a web site with a well of information on technical issues mainly related to computers video and graphics. Here’s some of the information that has caught my attention so far:

  • A few days ago I added a new external to Jamoma based on the algorithm he provides for cubic interpolation.
  • The inside/outside polygon test might be combined with theory of convex hulls to define a convex hull for an array of arbitrarily positioned loudspeakers in two-dimensional space to determine if a virtual source is positioned inside or outside the convex hull. AndrÈ Sier has ported the method for Distance based amplitude panning (DBAP) proposed by me on the Max list some years ago to C as Max externals. One of the challenges remaining to be solved is what to do with the virual source once it moves outside the convex hull defined by the speakers. This test might bring us one step closer to approaching that.
  • In this context it might also be relevant to be able to determine whether a line segment intersects a 3 vertex facet calculate the distance from a point to a line and from a point to a plane not to speak of combining clipping a line segment to a complex polygon in combination with finding the centroid of a polygon.
  • The above can also be applied for another problem that preoccupies me at the moment: If one define a subspace of RGB colorspace defined by a limited number of colors (points in RGB-space) and the convex hull defined by these points how can one map any point in RGB-space onto the nearest point on this convex hull? This will equal a painterly probem of saying that you are to use a limited palett made up of only a few colors and the possible mixes of these colors. How do you best manage to represent the true colors of a photo using this limited palett? I’ve been able to solve the problem using two colors only but once I expand to three colors it grows much more complex and I have to find a different more general approach to the problem.
  • Two-dimensional Fourier transforms als fascinates me and I would like to be able to explore some of the potential for treatment of photos of video this could offer.