@MISC\{IMM2017-06964,
    author       = "L. Skovmand",
    title        = "Procedural modellering af regul{\ae}re strukturer",
    year         = "2017",
    publisher    = "Technical University of Denmark, Department of Applied Mathematics and Computer Science",
    address      = "Richard Petersens Plads, Building 324, {DK-}2800 Kgs. Lyngby, Denmark, compute@compute.dtu.dk",
    note         = "Supervised by Jeppe Revall Frisvad, jerf@dtu.dk, {DTU} Compute",
    url          = "http://www.compute.dtu.dk/English.aspx",
    abstract     = "In English: With additive layer manufactering (or {3D} printing) objects are created layer-by-layer, which results in a staircase effect. This staircase effect depends on the shape of the object and the direction in which it is printed. This report seeks to model this staircase effect, and to implement an interactive interface, which would make it possible for the user to control the layer thickness and printing direction.
The aim of this report is to study how regular structures, like this staircase effect, can be procedurally modelled by combining simple functions and by procedurally using bump or normal mapping, in a data-free way. It is sought to model photorealistic renderings of this staircase effect, which are compared to actual images of {3D-}printed objects.
The staircase effect is modelled by a simple algorithm, which assumes that the yaxis is the printing direction, such that the y-coordinate of a given point’s normal can be modified based on the placememt of the camera according to that point’s placement between 2 layers.
As these regular structures produce aliasing artifacts in excess, an anti-aliasing algorithm is implemented. This algorithm is a screen-space based super-sampling algorithm, which samples in an area of 2x2 pixels around the original fragment, and then invert the graphics pipeline transformations to get to the space where the procedural operations are performed, so that the color of the given sample can be computed. A shader which uses this anti-aliasing algorithm and the procedural modelling of the staircase effect is included in a paper about augmented reality interfaces for additive manufacturing, which can be found in the included zip-file [Eiriksson et al, 2017]."
}