This paper presents a novel object-space line drawing algorithm that can depict shapes with view-dependent feature lines in real time. Strongly inspired by the Laplacian-of-Gaussian (LoG) edge detector in image processing, we define Laplacian lines as the zero-crossing points of the Laplacian of the surface illumination. Compared to other view-dependent feature lines, Laplacian lines are computationally efficient because most expensive computations can be preprocessed. We further extend Laplacian lines to volumetric data and develop the algorithm to compute volumetric Laplacian lines without isosurface extraction. We apply the proposed Laplacian lines to a wide range of real-world models and demonstrate that Laplacian lines are more efficient than the existing computer generated feature lines, and can be used in interactive graphics applications.

Designing rotational symmetry fields on surfaces is an important task for a wide range of graphics applications. This work introduces a rigorous and practical approach for automatic N-RoSy field design on arbitrary surfaces with user-defined field topologies. The user has full control of the number, positions, and indexes of the singularities (as long as they are compatible with necessary global constraints), the turning numbers of the loops, and is able to edit the field interactively. We formulate N-RoSy field construction as designing a Riemannian metric such that the holonomy along any loop is compatible with the local symmetry of N-RoSy fields. We prove the compatibility condition using discrete parallel transport. The complexity of N-RoSy field design is caused by curvatures. In our work, we propose to simplify the Riemannian metric to make it flat almost everywhere. This approach greatly simplifies the process and improves the flexibility such that it can design N-RoSy fields with single singularity and mixed-RoSy fields. This approach can also be generalized to construct regular remeshing on surfaces. To demonstrate the effectiveness of our approach, we apply our design system to pen-and-ink sketching and geometry remeshing. Furthermore, based on our remeshing results with high global symmetry, we generate Celtic knots on surfaces directly.

This paper presents a novel object-space line drawing algorithm that can depict shape with view dependent feature lines in real-time. Strongly inspired by the Laplacian-of-Gaussian (LoG) edge detector in image processing, we define Laplacian Lines as the zero-crossing points of the Laplacian of the surface illumination. Compared to other view dependent features, Laplacian lines are computationally efficient because most expensive computations can be pre-processed. Thus, Laplacian lines are very promising for interactively illustrating large-scale models.

Conveying shape using feature lines is an important visualization tool in visual computing. The existing feature lines (e.g., ridges, valleys, silhouettes, suggestive contours, etc.) are solely determined by local geometry properties (e.g., normals and curvatures) as well as the view position. This paper is strongly inspired by the observation in human vision and perception that a sudden change in the luminance plays a critical role to faithfully represent and recover the 3D information. In particular, we adopt the edge detection techniques in image processing for 3D shape visualization and present Photic Extremum Lines (PELs) which emphasize significant variations of illumination over 3D surfaces. Comparing with the existing feature lines, PELs are more flexible and offer users more freedom to achieve desirable visualization effects. In addition, the user can easily control the shape visualization by changing the light position, the number of light sources, and choosing various light models. We compare PELs with the existing approaches and demonstrate that PEL is a flexible and effective tool to illustrate 3D surface and volume for visual computing.