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Adaptive slicing is a key step in three-dimensional (3D) printing as it is closely related to the building time and the surface quality. This study aims to develop a novel adaptive slicing method based on ameliorative area ratio and accurate cusp height for 3D printing using stereolithography (STL) models.

The proposed method consists of two stages. In the first stage, the STL model is sliced with constant layer thickness, where an improved algorithm for generating active triangular patches, the list is developed to preprocess the model faster. In the second stage, the model is first divided into several blocks according to the number of contours, then an axis-aligned bounding box-based contour matching algorithm and a polygons intersection algorithm are given to compare the geometric information between several successive layers, which will determine whether these layers can be merged to one.

Several benchmarks are applied to verify this new method. Developed method has also been compared with the uniform slicing method and two existing adaptive slicing methods to demonstrate its effectiveness in slicing.

Compared with other methods, the method leads to fewer layers whilst keeping the geometric error within a given threshold. It demonstrates that the proposed slicing method can reach a trade-off between the building time and the surface quality.

Metamodeling is an effective method to approximate the relations between input and output parameters when significant efforts of experiments and simulations are required to collect the data to build the relations. This paper aims to develop a new sequential sampling method for adaptive metamodeling by using the data with highly nonlinear relation between input and output parameters.

In this method, the Latin hypercube sampling method is used to sample the initial data, and kriging method is used to construct the metamodel. In this work, input parameter values for collecting the next output data to update the currently achieved metamodel are determined based on qualities of data in both the input and output parameter spaces. Uniformity is used to evaluate data in the input parameter space. Leave-one-out errors and sensitivities are considered to evaluate data in the output parameter space.

This new method has been compared with the existing methods to demonstrate its effectiveness in approximation. This new method has also been compared with the existing methods in solving global optimization problems. An engineering case is used at last to verify the method further.

This paper provides an effective sequential sampling method for adaptive metamodeling to approximate highly nonlinear relations between input and output parameters.