A Study on Subdivision and Displacement for Higher-Order Lagrange Elements in 3D Printing

In today’s digital world, technologies are constantly evolving. Technology has also evolved in the creative field, giving a boost to technologies like 3D printing, Augmented Reality, High Graphics Computer Games, Virtual Reality, and many more. In these technologies, visual quality plays an important role. To improve accuracy and visual quality, one needs high polygon counts to realize smoothly curved surfaces. In the contex of 3D printing, when increasing the size of the print, the number of polygons needed to represent smoothly curved surfaces to within the printer’s accuracy increases too. This thesis conducts and analyzes an experimental comparison between two techniques to realize curved surfaces represented as curved high-order triangular Lagrange elements: A displacement-based implementation [3] and an adaptive subdivision approach, which is also implemented as part of this thesis. This thesis mainly focuses on the approximation of the cubic surface by subdividing a curved triangle into smaller triangles. By adapting the subdivision to the tessellation error locally, while maintain proper mesh connectivity, an accurate, smooth surface is produced while avoiding unnecessarily high triangle counts.