The commonly used analytic bidirectional reflectance distribution functions (BRDFs) do not model goniochromatism, that is, angle-dependent material color. The material color is usually defined by a diffuse reflectance spectrum or RGB vector and a specular part based on a spectral complex index of refraction. Extension of the commonly used BRDFs based on wave theory can help model goniochromatism, but this comes at the cost of significant added model complexity. We measured the goniochromatism of structual color pigments used for additive color printing and found that we can fit the observed spectral angular dependence of the bidirectional reflectance using a simple modification of the standard microfacet BRDF model. All we need to describe the goniochromatism is an empirically-based spectral parameter, which we use in our model together with a specular reflectance spectrum instead of the spectral complex index of refraction. We demonstrate the ability of our model to fit the measured reflectance of red, green, and blue commercial structural color pigments. Our BRDF model enables straightforward implementation of a shader for interactive preview of 3D objects with printed spatially and angularly varying texture.

Recent advances in pigment production resulted in the possibility to print with RGBW primaries instead of CMYK and performing additive color mixing in printing. The RGBW pigments studied in this work have the properties of structural colors, as the primary colors are a result of interference in a thin film coating of mica pigments. In this work, we investigate the angle-dependent gamut of RGBW primaries. We have elucidated optimal angles of illumination and observation for each primary ink and found the optimal angle of observation under diffuse illumination. We investigated dot off dot halftoned screen printing with RGBW inks on black paper and in terms of angle-dependent dot gain. Based on our observations, optimal viewing condition for the given RGBW inks is in a direction of around 30◦ to the surface normal. Here, the appearance of the resulting halftoned prints can be estimated well by Neugebauer formula (weighted averaging of the individual reflected spectra). Despite the negative physical dot gain during the dot off dot printing, we observe angularly dependent positive optical dot gain for halftoned prints. Application of interference RGBW pigments in 2.5D and 3D printing is not fully explored due to the technological limitations. In this work, we provide colorimetric data for efficient application of the angle-dependent properties of such pigments in practical applications.

The iridescent effect produced by structural color is difficult (if not impossible) to capture and print using traditional CMYK pigments. The so called RGB reflective pigments, nonetheless, generate angle-dependent colors by light interference. A layered surface structure generated by the pigments’ particles on a substrate reflects light waves of different wavelengths at different viewing angles according to the optical principle known as the Bragg Law. In this work, we have studied the influence of different halftone structures on printed images, produced with RGB reflective inks via screen printing. The main goal was to enhance the iridescence of a printed reproduction by studying the performance of different halftone algorithms on a screen printing process. We investigated the influence of different halftone structures in creating different spatial combinations of inks on a print to reproduce the image of an iridescent feathered headdress. We applied first-order, second-order, and structure-aware FM halftones to compare how they influence the reproduction of the material appearance of the object represented in the original image. The results show that the structure-ware halftones improve the representation of the image structures and details. Therefore, it could better convey the 3D surface features that produce iridescence in real feathers.

Halftoning is a crucial part of image reproduction in print. For large format prints, especially at higher resolutions, it is important to have very fast and computationally feasible halftoning methods of good quality. The authors have already introduced an approach to obtain image-independent threshold matrices generating both first- and second-order frequency modulated (FM) halftones with different clustered dot sizes. Predetermined and image-independent threshold matrices make the proposed halftoning method a point-by-point process and thereby very fast. In this article, they report a comprehensive quality evaluation of first- and second-order FM halftones generated by this technique and compare them with each other, employing several quality metrics. These generated halftones are also compared with error diffusion (ED) halftones employing two different error filters. The results indicate that the second-order FM halftoning with small clustered dot size performs best in almost all studied quality aspects than the first- and second-order FM halftoning with larger clustered dot size. It is also shown that the first- and second-order FM halftones with small clustered dot sizes are of almost the same quality as ED halftones using Floyd–Steinberg error filter and of higher quality than halftones generated by ED employing Jarvis, Judice, and Ninke error filter.

The appearance of 3D-printed objects is affected by numerous parameters. Specifically, the colour of each point on the surface is affected not only by the applied material, but also by the neighbouring segments as well as by the structure underneath it. Translucency of the 3D printing inks is the key property needed for reproduction of surfaces resembling natural materials. However, the prediction of colour appearance of translucent materials within the print is a complex task that is of great interest. In this work, a method is proposed for studying the appearance of translucent 3D materials in terms of the surface colour. It is shown how the thickness of the printed flat samples as well as the background underneath affect the colour. By studying diffuse reflectance and transmittance of layers of different thicknesses, apparent, spectral optical properties were obtained, i.e., extinction and scattering coefficients, in the case of commercially available polylactic acid (PLA) filaments for Fused Deposition Modelling (FDM) printers. The coefficients were obtained by fitting a simplistic model to the measured diffuse reflectance as a function of layer thickness. The results were verified by reconstructing reflected spectra with the obtained parameters and comparing the estimated colour to spectrophotometer measurements. The resulting colour differences in terms of the CIEDE2000 standard are all below 2.

Many image reproduction devices, such as printers, are limited to only a few numbers of printing inks. Halftoning, which is the process to convert a continuous-tone image into a binary one, is, therefore, an essential part of printing. An iterative halftoning method, called Iterative Halftoning Method Controlling the Dot Placement (IMCDP), which has already been studied by research scholars, generally results in halftones of good quality. In this paper, we propose a structure-based alternative to this algorithm that improves the halftone image quality in terms of sharpness, structural similarity, and tone preservation. By employing appropriate symmetrical and non-symmetrical Gaussian filters inside the proposed halftoning method, it is possible to adaptively change the degree of sharpening in different parts of the continuous-tone image. This is done by identifying a dominant line in the neighborhood of each pixel in the original image, utilizing the Hough Transform, and aligning the dots along the dominant line. The objective and subjective quality assessments verify that the proposed structure-based method not only results in sharper halftones, giving more three-dimensional impression, but also improves the structural similarity and tone preservation. The adaptive nature of the proposed halftoning method makes it an appropriate algorithm to be further developed to a 3D halftoning method, which could be adapted to different parts of a 3D object by exploiting both the structure of the images being mapped and the 3D geometrical structure of the underlying printed surface.

Managing the final appearance of 3D surfaces is an interesting and essential topic in 3D printing applications. Knowledge about the parameters which influence the 3D surface reproduction quality enables engineers to achieve the final appearance as accurately as designed. Many studies have been conducted to explore numerous parameters that affect the quality of 3D surface reproduction. This work contributes to verifying the role of halftoning in increasing the 3D surface visual quality and the control over the surface appearance of a 3D printed object. The results show that applying different halftones according to the geometrical characteristics of the 3D surface could emphasize or diminish the perceived 3D geometrical structures of a shape. The experimental results are in line with the simulated outputs reported in previous work. Our findings might introduce a new approach towards having more control over 3D appearance reproduction without changing the material or printer settings.

Realistic appearance reproduction is of great importance in 3D printing’s applications. Halftoning as a necessary process in printing has a great impact on creating visually pleasant appearance. In this article, we study the aspects of adapting and applying Iterative Method Controlling Dot Placement (IMCDP) to halftone three-dimensional surfaces. Our main goal is to extend the 2D algorithm to a 3D halftoning approach with minor modifications. The results show high-quality reproduction for all gray tones. The 3D halftoning algorithm is not only free of undesirable artifacts, it also produces fully symmetric and wellformed halftone structures even in highlight and shadow regions.

As 3D printing is becoming increasingly popular, the demand for high quality surface reproduction is also increasing. Like in 2D printing, halftoning plays an important role in the quality of the surface reproduction. Developing advanced 3D halftoning methods for 3D printing and adapting them to the structure of the surface is therefore essential for improving surface reproduction quality. In this paper, an extension of an iterative 2D halftoning method to 3D is used to apply different halftone structures on 3D surfaces. The results show that using different halftones based on the 3D geometrical structure of the surface and/or the viewing angle in combination with the structure of the texture being mapped on the surface can potentially improve the quality of the appearance of 3D surfaces.

The spatial resolution of 3D printing is finite. The necessary discretisation of an object before printing produces a step-like surface structure that influences the appearance of the printed objects. To study the effect of this discretisation on specular reflections, we print surfaces at various oblique angles. This enables us to observe the step-like struc- ture and its influence on reflected light. Based on the step-like surface structure, we develop a reflectance model describing the redistribution of the light scattered by the surface, and we study dispersion effects due to the wavelength dependency of the refractive index of the material. We include preliminary verification by comparing model predictions to photographs for different angles of observation.