Polyline Vertices Research Articles

Strokes2Surface: Recovering Curve Networks From 4D Architectural Design Sketches

AbstractWe present Strokes2Surface, an offline geometry reconstruction pipeline that recovers well‐connected curve networks from imprecise 4D sketches to bridge concept design and digital modeling stages in architectural design. The input to our pipeline consists of 3D strokes' polyline vertices and their timestamps as the 4th dimension, along with additional metadata recorded throughout sketching. Inspired by architectural sketching practices, our pipeline combines a classifier and two clustering models to achieve its goal. First, with a set of extracted hand‐engineered features from the sketch, the classifier recognizes the type of individual strokes between those depicting boundaries (Shape strokes) and those depicting enclosed areas (Scribble strokes). Next, the two clustering models parse strokes of each type into distinct groups, each representing an individual edge or face of the intended architectural object. Curve networks are then formed through topology recovery of consolidated Shape clusters and surfaced using Scribble clusters guiding the cycle discovery. Our evaluation is threefold: We confirm the usability of the Strokes2Surface pipeline in architectural design use cases via a user study, we validate our choice of features via statistical analysis and ablation studies on our collected dataset, and we compare our outputs against a range of reconstructions computed using alternative methods.

Generalized Approach to Optimal Polylinearization for Smart Sensors and Internet of Things Devices

This study introduces an innovative numerical approach for polylinear approximation (polylinearization) of non-self-intersecting compact sensor characteristics (transfer functions) specified either pointwise or analytically. The goal is to partition the sensor characteristic optimally, i.e., to select the vertices of the approximating polyline (approximant) along with their positions, on the sensor characteristics so that the distance (i.e., the separation) between the approximant and the characteristic is rendered below a certain problem-specific tolerance. To achieve this goal, two alternative nonlinear optimization problems are solved, which differ in the adopted quantitative measure of the separation between the transfer function and the approximant. In the first problem, which relates to absolutely integrable sensor characteristics (their energy is not necessarily finite, but they can be represented in terms of convergent Fourier series), the polylinearization is constructed by the numerical minimization of the L1-metric (a distance-based separation measure), concerning the number of polyline vertices and their locations. In the second problem, which covers the quadratically integrable sensor characteristics (whose energy is finite, but they do not necessarily admit a representation in terms of convergent Fourier series), the polylinearization is constructed by numerically minimizing the L2-metric (area- or energy-based separation measure) for the same set of optimization variables—the locations and the number of polyline vertices.

SurfaceBrush

Popular Virtual Reality (VR) tools allow users to draw varying-width, ribbonlike 3D brush strokes by moving a hand-held controller in 3D space. Artists frequently use dense collections of such strokes to draw virtual 3D shapes. We propose SurfaceBrush , a surfacing method that converts such VR drawings into user-intended manifold free-form 3D surfaces, providing a novel approach for modeling 3D shapes. The inputs to our method consist of dense collections of artist-drawn stroke ribbons described by the positions and normals of their central polylines, and ribbon widths. These inputs are highly distinct from those handled by existing surfacing frameworks and exhibit different sparsity and error patterns, necessitating a novel surfacing approach. We surface the input stroke drawings by identifying and leveraging local coherence between nearby artist strokes. In particular, we observe that strokes intended to be adjacent on the artist imagined surface often have similar tangent directions along their respective polylines. We leverage this local stroke direction consistency by casting the computation of the user-intended manifold surface as a constrained matching problem on stroke polyline vertices and edges. We first detect and smoothly connect adjacent similarly-directed sequences of stroke edges producing one or more manifold partial surfaces. We then complete the surfacing process by identifying and connecting adjacent similarly directed edges along the borders of these partial surfaces. We confirm the usability of the SurfaceBrush interface and the validity of our drawing analysis via an observational study. We validate our stroke surfacing algorithm by demonstrating an array of manifold surfaces computed by our framework starting from a range of inputs of varying complexity, and by comparing our outputs to reconstructions computed using alternative means.

Estimation of Road Centerline Curvature from Raw GPS Data

Development and wide use of route guidance systems lead to the need for suitable digital maps that can be used for some advanced applications. Sufficient accuracy of road geometry with emphasis on road centerline positions and curvature is crucial. In this paper is presented a method for finding road centerline curvature from raw GPS data. The approach consists of a few processing steps. First it is necessary to fit raw data of each road section using B-splines, and generate equidistant vertices of polyline of the fitted curve. Then follows the appliance of stereographic projection of chosen polyline segments onto the unit sphere. Using the least square method, the plane that best fits the points on the unit sphere is found and the circle that is the intersection of the plane and the unit sphere. Stereographic projection of this circle back to the equatorial plane gives the corresponding circular arc and curvature. The method is also applicable in higher dimensions. The 3D case is numerically presented and results show that the proposed procedure is efficient and yields accurate results.

Microcomputer stereotactic atlas.

A stereotactic atlas to determine thalamic target sites has been incorporated into a microcomputer. Variability studies of the thalamus with mean and standard deviations of nuclear borders are depicted graphically for overlay onto operative images. Internal landmarks traditionally used to reference target points for functional stereotaxis may be determined by conventional ventriculography or derived from magnetic resonance scans. Modeling of polyline vertices established from gray scale contour mapping and atlas reconstructions further enhance the spatial understanding of relationships to midline structures. Computer integration of anatomic reference points, graphically depicted images and stereotactic atlas data into head frame coordinates can be accomplished. This method is consistent with established stereotactic techniques and allows the visual conceptualization of imaged and graphic data for functional stereotaxis.