DRCH: A Method for 3D Convex Hull

2014 ◽  
Vol 571-572 ◽  
pp. 721-724
Author(s):  
Xiu Xun Huang ◽  
Ji Ting Zhou ◽  
Chen Ling ◽  
Wen Jun Zhang
Keyword(s):  
Convex Hull ◽  
Dimensionality Reduction ◽  
Time Complexity ◽  
Three Dimensional ◽  
Higher Dimensional ◽  
Point Set ◽  
Convex Hull Algorithm ◽  
Convex Hull Method

A novel three-dimensional (3D) convex hull method is proposed, which is called dimensionality reduction convex hull method (DRCH).Through having 3d point set map to 2d plane, most initial 3D points in the convex hull are removed. Then, the remaining points are to generate 3D convex hull using any convex hull algorithm. The experiment demonstrates 3D DRCH is faster than general 3D convex hull algorithms. Its time complexity is O(r log r), where r is the number of points not in the hull. And DRCH can be generalized to higher-dimensional problems.

A Randomized Parallel Three-Dimensional Convex Hull Algorithm for Coarse-Grained Multicomputers

1997 ◽  
Vol 30 (6) ◽  
pp. 547-558 ◽  
Author(s):  
F. Dehne ◽  
X. Deng ◽  
P. Dymond ◽  
A. Fabri ◽  
A. A. Khokhar
Keyword(s):  
Convex Hull ◽  
Three Dimensional ◽  
Coarse Grained ◽  
Convex Hull Algorithm

A Fast Convex Hull Algorithm of Planar Point Set

2013 ◽  
Vol 706-708 ◽  
pp. 1852-1855
Author(s):  
Hong Fei Jiang
Keyword(s):  
Convex Hull ◽  
Planar Point ◽  
Point Set ◽  
Convex Hull Algorithm

In this paper ,a new algorithm is proposed for improving speed of calculating convex hull of planar point set .The algorithm creates a square mesh to manage points ,when eliminating points which are obviously in convex hull ,selecting or eliminating of points can be converted to that of grid , work of calculation depends on points near edges of convex hull and density of grid but not the number of points ;at the meantime ,remainder points are sorted roughly .When calculating convex hull of remainder points ,a method is presented which can take advantage of order of remainder points ,it calculates boundaries of convex hull segment by segment ,then ,combines the boundaries to form convex hull.

An Efficient Convex Hull Algorithm Using Affine Transformation in Planar Point Set

2014 ◽  
Vol 39 (11) ◽  
pp. 7785-7793 ◽  
Author(s):  
Changyuan Xing ◽  
Zhongyang Xiong ◽  
Yufang Zhang ◽  
Xuegang Wu ◽  
Jingpei Dan ◽  
...  
Keyword(s):  
Convex Hull ◽  
Affine Transformation ◽  
Planar Point ◽  
Point Set ◽  
Convex Hull Algorithm

A FAST AND COMPLETE CONVEX-HULL ALGORITHM ARCHITECTURE BASED ON ELLIPSE AND ELASTIC ELLIPSE METHODS

2013 ◽  
Vol 27 (08) ◽  
pp. 1354008
Author(s):  
XUE GANG WU ◽  
BIN FANG ◽  
YUAN YAN TANG ◽  
PATRICK SHEN-PEI WANG
Keyword(s):  
Convex Hull ◽  
Affine Transformation ◽  
Circle Method ◽  
Extreme Points ◽  
Transformation Method ◽  
Data Sets ◽  
Planar Point ◽  
Point Set ◽  
Convex Hull Algorithm ◽  
Better Than

The number of inner points excluded in an initial convex hull (ICH) is vital to the efficiency getting the convex hull (CH) in a planar point set. The maximum inscribed circle method proposed recently is effective to remove inner points in ICH. However, limited by density distribution of a planar point set, it does not always work well. Although the affine transformation method can be used, it is still hard to have a better performance. Furthermore, the algorithm mentioned above fails to deal with the exceptional distribution: the gravity centroid (GC) of a planar point set is outside or on the edge formed by the extreme points in ICH. This paper considers how to remove more inner points in ICH when GC is inside of ICH and completely process the case which mentioned above. Further, we presented a complete algorithm architecture: (1) using the ellipse and elasticity ellipse methods (EM and EEM) to remove more inner points in ICH and process the cases: GC is inside or outside of ICH. (2) Using the traditional methods to process the situation: the initial centroid is on the edge in ICH. It is adaptive to more data sets than other algorithms. The experiments under seven distributions show that the proposed method performs better than other traditional algorithms in saving time and space.

scholarly journals ON GOOD TRIANGULATIONS IN THREE DIMENSIONS

1992 ◽  
Vol 02 (01) ◽  
pp. 75-95 ◽  
Author(s):  
TAMAL KRISHNA DEY ◽  
CHANDERJIT L. BAJAJ ◽  
KOKICHI SUGIHARA
Keyword(s):  
Convex Hull ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Convex Polyhedra ◽  
Finite Precision ◽  
Robust Implementation ◽  
Guaranteed Quality ◽  
Point Set ◽  
Finite Precision Arithmetic ◽  
Special Case

In this paper, we give an algorithm that triangulates the convex hull of a three dimensional point set with guaranteed quality tetrahedra. Good triangulations of convex polyhedra are a special case of this problem. We also give a bound on the number of additional points used to achieve these guarantees and report on the techniques we use to produce a robust implementation of this algorithm under finite precision arithmetic.

scholarly journals An Improved Convex Hull Algorithm Considering Sort in Plane Point Set

2013 ◽  
Vol 17 (1) ◽  
pp. 29-35 ◽  
Author(s):  
Byeong-Ju Park ◽  
Jae-Heung Lee
Keyword(s):  
Convex Hull ◽  
Point Set ◽  
Convex Hull Algorithm ◽  
Plane Point
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