Small post today covering something I just finished working on, discrete geodesics. "A geodesic [ jee-oh-des-ik, -dee-sik ] is a generalization of the notion of a "straight line" to "curved spaces".(Wikipedia) "Discrete" simply means I'm looking at non-continuous lines along the surface of a 3D object. There are plenty of applications for Geodesics such as surface parameterization, segmentation, and surface measurements.

For my purposes geodesics help with finding curved lines on the surface of a 3D mesh. At the end of the day it all boils down to: "Well what can you actually do with the data." 3D scanning isn't rocket science, the tech. has been around for years and there are even homebrew lego made laser scanners. (There are better examples that don't require the milk, you just need a way to measure each level.) So it always comes down to what you can do with the data.

Enter my side project. Basically what the function does is it takes a start point and an end point and, using front wave propagation, parses the 3D mesh in to distance values from the start point.


The photo color range is yellow to purple, purple being the farthest away. If you look closely at Optimash's behind you'll see a small dot, this is the start location. Notice how the distances emanate from that position. Once the whole surface has been parameterized it's a simple matter of taking the end point and then backtracking through the mesh locating the paths with the smallest distance. This is due to the start point distance propagating outward. When you look at the colors each value is actually a representation of how far that point is from our start point.

The pathing algorithm is still in the works. Using a discrete function gives us a very jagged path, a continuous method will need to be used in order to mitigate the jagged problem.

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