Contents
What is planar polygon?
A polygon face is planar when: all of its vertices lie in a certain plane. For example, a triangle face is always planar, because its three points define a plane.
How do you know if a ring is planar?
When you look at the structure of a six-membered ring, if all the molecular geometries around each atom in the ring are sp2 -hybridized, then the whole molecule is planar.
How do you know if a molecule is planar?
If the atoms arrange themselves around the central molecule so that they exist on a single two-dimensional plane, the molecule is planar. The molecule may otherwise form any of several three-dimensional shapes, including tetrahedrons, octahedrons or bipyramids.
Is K5 planar?
A graph is called planar if it can be drawn in the plane (R2) with vertex v drawn as a point f(v) ∈ R2, and edge (u, v) drawn as a continuous curve between f(u) and f(v), such that no two edges intersect (except possibly at the end-points). In fact, K5 is not planar.
Can You triangulate two non planar polygons at once?
Although the algorithm can be applied to triangulate two non-planar polygons, it does not explore those triangles whose vertices belong solely to one ofthepolygons,yetsuchtrianglesareoftenimportanttopro- duce a fairsurface for non-planar inputs (e.g,the car bumper in Figure 1). Also, the algorithm does not generalize to mul- tiple polygons.
Which is the best algorithm for triangulating a polygon?
The algorithm, based on dy- namic programming, constructs the optimal triangulation of a larger domain from the optimal triangulations of smaller sub-domains. The algorithm was extended by Barequet and Sharir [BS95] to find an optimal triangulation of a 3D polygon that minimizes the sum of per-triangle weights (e.g., area), with the same complexity.
How to triangulate a pool of closed polygons?
Single polygon We consider a closed 3D polygonPand a pool of “candi- date” trianglesTconnecting vertices ofP. Tcan be the set of all triples of vertices ofP, or some subset (see more dis- cussions in the next section).
What’s the best way to surfacing a polygon?
For a single boundary polygon, a common practice for surfacing is to first generate an initial mesh, usually atrian- gulationinvolvingonly theverticesonthepolygon, and then to refine this initial surface to achieve better smoothness or mesh quality.