Discrete 3D ModellingDiscrete LinesDiscrete PlanesDiscrete PolygonsDiscrete PolyhedraSupercoverA new discrete 3D line and 3D polygon, called Supercover 3D line and Supercover 3D polygon, are introduced. Analytical definitions are provided. The Supercover 3D polygon is a tunnel free plane segment ...
An edge is a Supercover 3D line segment. Two different polygons can share a common edge and if they do, the union of both polygons is tunnel free. This definition of discrete polygons has the "most" properties in common with the continuous polygons. It is particularly interesting for ...
CGPage: 1 東吳資訊科學 江清水 3.1 2D Geometry - points and polygons X Y A point in 2D is represented by two real numbers (X,Y) A line segment is represented by its two end points (X 1,Y 1 ) (X 2,Y 2 ), or a 2x2 matrix [ ] X 1 Y 1 X 2 Y 2 X Y CGPage: 2 東...
Purpose Contact detection for convex polygons/polyhedra has been a critical issue in discrete/discontinuous modelling, such as the discrete element method (DEM) and the discontinuous deformation analysis (DDA). The recently developed 3D contact theory for polyhedra in DDA depends on the so-called ...
Recently, there has been renewed interest in signed distance bound representations due to their unique properties for 3D shape modelling. This is especially the case for deep learning-based bounds. However, it is beneficial to work with polygons in most computer graphics applications. Thus, in ...
Keywords: 3D printing; point-in-polygon; boolean operations; code; probability; parallel 1. Introduction 1.1. The Point-in-Polygon Test Let P be a point and S a polygon on a plane. In computer graphics, finding whether P is inside, outside, or on the boundary of S is a fundamental ...
In the fields related to geometric modelling, it is fundamental to count on robust. In this work we present a new algorithm for testing the intersection between a segment and a polygon in 3D space. This algorithm is robust and efficient, and it is the basis of most operations developed in...
Purpose Contact detection for convex polygons/polyhedra has been a critical issue in discrete/discontinuous modelling, such as the discrete element method (DEM) and the discontinuous deformation analysis (DDA). The recently developed 3D contact theory for polyhedra in DDA depends on the so-called ...
solid modelling/ linear-time information-theoretically optimal compression algorithm2-manifold polygon meshes3D model representationtopological quantitiesgeometrical quantitiesconnection nodesnode positionsface colorsThe polygon mesh is an important primitive used in representing 3D models. Its specification consists ...