Abstract: Perlin noise is the most widely used tool in procedural texture synthesis. It is a simple and fast method to enhance the quantity of detail or to render natural materials with no use of storage resources. However, this technique is very sensitive to aliasing artifacts, especially when composed with shape and color functions. Moreover, it is computationally intensive and can become slow, especially when generating procedural volumes of density in real time. This study aims at analyzing Perlin noise properties in order to control the apparition of artifacts and optimize the computational cost. We present a method for computing a maximum and minimum frequency threshold per noise component, we propose an idea to handle the case of non linear transforms of the noise, and show an optimization method for volume generation.

Abstract: In this paper, procedural texture mapping based on Perlin noise is firstly implemented and simulated in Matlab. And then the design is converted from float-point to fix-point in Simulink. Using the system modeling tool, System Generator from Xilinx company, the noise function can be directly mapped into FPGA hardware. From the experimental results, various graphical textures can be implemented in real time and with realistic effects in FPGA hardware.

Abstract: This study intends to propose a new drawing algorithm which generates procedural texture of decorative ornate patterns. Since it takes much time and energy to draw a lot of exquisite ornaments by hand drawing, it is expected that procedural generation of such a complicated pattern is beneficial in the field of CGI (Computer Generated Imagery). Based on this viewpoint, a construction of the algorithm was attempted. Further, producing an animation work based on the resultant algorithm was also attempted as an application of the algorithm. Ornaments are formative arts based on highly regularized patterns. They usually have a distinct formative rule such as symmetry and repetition, and they have been developed and sophisticated by humans along with the rule. Since it is often the case that formative rules in ornaments such as repetition, symmetry, and rhythm are clear, it is expected that we can extract the rule from some decorative styles, and represent the rule as an algorithm. Over the past few decades, several studies have been made on a procedural generation of decorative ornaments. It ranges from a primitive tiling pattern to complicated floral patterns found on illuminated manuscripts. However, unlike these previous works, this study does not intend to simulate an existing style of ornaments, but attempts to generate "ornament￢like" shapes efficiently. This research specifically focuses on carved ornaments called "medallions" which are widely found in various styles of Western traditional architectural ornaments. A medallion is a floral or geometrical decor based on a rule of rotational symmetry. Although expressions of medallions vary based on the number of axes and the type of motifs, they usually consist of relief-like elements whose cross-section has an acute angle. On the basis of these characteristics of medallions, a construction of a method which generates complicated relief-like objects is attempted. This study uses metaballs as elements of a medallion. Metaball is a modeling method to represent a smooth curved shape by using density distributions defined in a space. Although metaballs are commonly used for generating a 3D smooth object, 2D metaballs are used in this study to generate a procedural texture. Unlike 3D metaballs, a drawing procedure of 2D metaballs is simple, and it can be drawn by calculating a density value of each pixel directly on the screen. Then, it is determined whether the density value satisfies an optional threshold value or not. Especially, an algorithm called "stepwise threshold detection" was used for drawing 2D metaballs in this research. This algorithm can generate complicated and unexpected curves contingently. In this procedure, a threshold process is performed for all metaballs on the 2D plane. The repetition of this process leads to the generation of complicated curves like a rice terrace. On the basis of the morphological characteristic, this type of metaballs is used as elements of medallions. Incidentally, although the resultant textures are 2D, a luminance calculation can be performed to represent a pseudo 3D relief-like effect by applying normal vectors to the shape. Also, by arranging metaballs symmetrically, generation of medallion-like objects was attempted. Further, since medallions usually consist of a combination of curves and straight lines, metaballs with regular polygonal density distributions were used in addition to conventional circular metaballs. Further, it is expected that generating the similar textures in a 3D space is also beneficial. Therefore, as a normal mapping to define convexity, applying the 2D metaball texture to the surface of Jl) objects were also attempted. Finally, on the basis of the above-mentioned techniques, application of the above-mentioned algorithm to an artwork was attempted, and an animation piece "Orb" was produced. A custom software program written in C was used for producing this animation. Since the resultant algorithm can draw complicated and elaborated shapes by using only a small amount data, further technical development can be expected.

Abstract: A variety of animation effects such as herds and fluids contain detailed motion fields characterized by repetitive structures. Such detailed motion fields are often visually important, but tedious to specify manually or expensive to simulate computationally. Due to the repetitive nature, some of these motion fields (e.g. turbulence in fluids) could be synthesized by procedural texturing, but procedural texturing is known for its limited generality.We apply example-based texture synthesis for motion fields. Our technique is general and can take on a variety of user inputs, including captured data, manual art, and physical/procedural simulation. This data-driven approach enables artistic effects that are difficult to achieve via previous methods, such as heart shaped swirls in fluid animation. Due to the use of texture synthesis, our method is able to populate a large output field from a small input exemplar, imposing minimum user workload. Our algorithm also allows the synthesis of output motion fields not only with the same dimension as the input (e.g. 2D to 2D) but also of higher dimension, such as 3D volumetric outputs from 2D planar inputs. This cross-dimension capability supports a convenient usage scenario, i.e. the user could simply supply 2D images and our method produces a 3D motion field with similar characteristics. The motion fields produced by our method are generic, and could be combined with a variety of large-scale low-resolution motions that are easy to specify either manually or computationally but lack the repetitive structures to be characterized as textures. We apply our technique to a variety of animation phenomena, including smoke, liquid, and group motion.

Abstract: Noise is an essential tool for texturing and modeling. Designing interesting textures with noise calls for accurate spectral control, since noise is best described in terms of spectral content. Texturing requires that noise can be easily mapped to a surface, while high-quality rendering requires anisotropic filtering. A noise function that is procedural and fast to evaluate offers several additional advantages. Unfortunately, no existing noise combines all of these properties.In this paper we introduce a noise based on sparse convolution and the Gabor kernel that enables all of these properties. Our noise offers accurate spectral control with intuitive parameters such as orientation, principal frequency and bandwidth. Our noise supports two-dimensional and solid noise, but we also introduce setup-free surface noise. This is a method for mapping noise onto a surface, complementary to solid noise, that maintains the appearance of the noise pattern along the object and does not require a texture parameterization. Our approach requires only a few bytes of storage, does not use discretely sampled data, and is nonperiodic. It supports anisotropy and anisotropic filtering. We demonstrate our noise using an interactive tool for noise design.