Vectorization for Fast, Analytic, and Differentiable Visibility

In Computer Graphics, the two main approaches to rendering and visibility involve ray tracing and rasterization. However, a limitation of both approaches is that they essentially use point sampling. This is the source of noise and aliasing, and also leads to significant difficulties for differentiable rendering. In this work, we present a new rendering method, which we call vectorization, that computes 2D point-to-region integrals analytically, thus eliminating point sampling in the 2D integration domain such as for pixel footprints and area lights. Our vectorization revisits the concept of beam tracing, and handles the hidden surface removal problem robustly and accurately. That is, for each intersecting triangle inserted into the viewport of a beam in an arbitrary order, we are able to maintain all the visible regions formed by intersections and occlusions, thanks to our Visibility Bounding Volume Hierarchy structure. As a result, our vectorization produces perfectly anti-aliased visibility, accurate and analytic shading and shadows, and most important, fast and noise-free gradients with Automatic Differentiation or Finite Differences that directly enables differentiable rendering without any changes to our rendering pipeline. Our results are inherently high-quality and noise-free, and our gradients are one to two orders of magnitude faster than those computed with existing differentiable rendering methods.

A Space-Optimal Hidden Surface Removal Algorithm for Iso-Oriented Rectangles

We investigate the problem of finding the visible pieces of a scene of objects from a specified viewpoint. In particular, we are interested in the design of an efficient hidden surface removal algorithm for a scene comprised of iso-oriented rectangles. We propose an algorithm where given a set of [Formula: see text] iso-oriented rectangles we report all visible surfaces in [Formula: see text] time and linear space, where [Formula: see text] is the number of surfaces reported. The previous best result by Bern [Journal of Computer and System Sciences 40 (1990) 49–69], has the same time complexity but uses [Formula: see text] space.

Different Ray-Casting Algorithm Implementations for Volume Rendering

Volume Rendering is the way to achieve 3D visualization. Volume Rendering is used for visualization of 2D projections of 3D data. In volume rendering techniques, direct volume rendering techniques (DVR) can be divided into image order and object order. Image order technique can be achieved by ray-casting algorithm. Ray-casting algorithm is used for raysurface interaction tests to solve problems in computer graphics like collision detection and hidden surface removal. In DVR, the ray is pushed through the object and 3D scalar field of interest is sampled along the ray inside the object. Over the years, different approaches towards this algorithm took place. This paper represents the review and analysis of different approaches of raycasting algorithm

Hidden Surface Removal in Augmented Reality: Hand Region Extraction using PCA

Recently, augmented Reality (AR) is growing rapidly and much attention has been focused on interaction techniques between users and virtual objects, such as the user directly manipulating virtual objects with his/her bare hands. Therefore, the authors believe that more accurate overlay techniques will be required to interact more seamlessly. On the other hand, in AR technology, since the 3-dimensional (3D) model is superimposed on the image of the real space afterwards, it is always displayed on the front side than the hand. Thus, it becomes an unnatural scene in some cases (occlusion problem). In this study, this system considers the object-context relations between the user's hand and the virtual object by acquiring depth information of the user's finger using a depth sensor. In addition, the system defines the color range of the user's hand by performing principal component analysis (PCA) on the color information near the finger position obtained from the depth sensor and setting a threshold. Then, this system extracts an area of the hand by using the definition of the color range of the user's hand. Furthermore, the fingers are distinguished by using the Canny method. In this way, this system realizes hidden surface removal along the area of the user's hand. In the evaluation experiment, it is confirmed that the hidden surface removal in this study make it possible to distinguish between finger boundaries and to clarify and process finger contours.

High Resolution Computer-Generated Rainbow Hologram

We have developed an output device for a computer-generated hologram (CGH) named a fringe printer, which can output a 0.35- μ m plane-type hologram. We also proposed several CGH with a fringe printer. A computer-generated rainbow hologram (CGRH), which can reconstruct a full color 3D image, is one of our proposed CGH. The resolution of CGRH becomes huge (over 50 Gpixels) due to improvement of the fringe printer. In the calculation, it is difficult to calculate the whole fringe pattern of CGRH at the same time by a general PC. Furthermore, since the fine pixel pitch provides a wide viewing angle in CGRH, object data, which are used in fringe calculation, should be created from many viewpoints to provide a proper hidden surface removal process. The fringe pattern of CGRH is calculated in each horizontal block. Therefore, the object data from several view points should be organized for efficient computation. This paper describes the calculation algorithm for huge resolution CGRH and its output results.