/* Create by zyzx
* Created 2008-11-4
* Modified 2008-11-4
*/?
?????? 在網(wǎng)上查了下，計(jì)算多邊形面積主要有2種方法：1、在多邊形內(nèi)部取一點(diǎn)，構(gòu)成三角形，再求三角形面積，此方法缺陷很多。2、矢量運(yùn)算法，這里主要介紹矢量運(yùn)算法。
???? 我們都知道已知A（x1,y1）B（x2,y2）C（x3,y3）三點(diǎn)的面積公式為 ?
??????????????? |x1? x2? x3| ?
???? S(A,B,C) = |y1? y2? y3| * 0.5 (當(dāng)三點(diǎn)為逆時(shí)針時(shí)為正，順時(shí)針則為負(fù)的)???
??????????????? |1?? 1?? 1 | ?
? ?
???? 對(duì)多邊形A1A2A3、、、An（順或逆時(shí)針都可以），設(shè)平面上有任意的一點(diǎn)P，則有： ?
? ?? S（A1，A2，A3，、、、，An） ?
? ?? = abs(S（P，A1，A2）+ S（P，A2，A3）+、、、+S（P，An，A1）)
???? P是可以取任意的一點(diǎn)，用（0，0）就可以了。 ?
????
代碼實(shí)現(xiàn)如下：
?1?
double?PolygonArea(const?Point_F*?p,?int?n);
?2?
double?Matrix3Pt(?Point_F?pt1,?Point_F?pt2,?Point_F?pt3?);
?3?
?4?
struct?Point_F?
?5?
{
?6?
???? Point_F()?{}
?7?
???? Point_F(double?x,?double?y)?:?x(x),?y(y)?{}
?8?
?9?
???? double?x;
10?
???? double?y;
11?
};
12?
13?
14?
/*?功能：計(jì)算多邊形面積
15?
?*?條件：非歧義多邊形
16?
?*?參數(shù)：
17?
?*???Point_F*??p?多邊形頂點(diǎn)序列：順時(shí)針，逆時(shí)針
18?
?*???int?n???????多邊形頂點(diǎn)個(gè)數(shù)
19?
?*?返回：面積
20?
*/
21?
double PolygonArea(?const?Point_F*?p，?int?n?)
22?
{
23?
????/*
24?
???????多邊形面積
25?
???????S(?A1,?A2,?A3,?
?,?An?)
26?
???????=?abs(?S(P,?A1,?A2)?+?S(P,?A2,?A3)?+?S(P,?A3,?A4)?+??+?S(P,?An,?A1)?)
27?
???????P?為任意點(diǎn)?(?默認(rèn)?P?=?(0,?0)?)
28?
????*/
29?
30?
????double?area?=?0;
31?
????int?iP?=?0;
32?
????Point_F*?pPt?=?(Point_F*)p;
33?
34?
????assert(?pPt?);
35?
????if(?n?<=?2?)?return?0.0;
36?
37?
????do?
38?
????{
39?
????????iP?+=?1;
40?
????????if(?n?>?iP?)
41?
????????{
42?
?????????????area?=?area?+?Matrix3Pt(?Point_F(0,0),?*pPt,?*(pPt?+?1)?);
43?
????????}else?if(?n?==?iP?){
44?
????????????area?=?area?+?Matrix3Pt(?Point_F(0,0),?*pPt,?*p?);
45?
????????}else{
46?
????????????break;
47?
????????}
48?
????????pPt?+=?1;
49?
????}?while?(?n?>=?iP?);
50?
51?
????area?=?fabs(?area?);
52?
53?
????return?area;
54?
}
55?
56?
/*?
57?
?*?功能：3點(diǎn)矢量行列式，算子->求面積
58?
*/
59?
double Matrix3Pt(?Point_F?pt1,?Point_F?pt2,?Point_F?pt3?)
60?
{
61?
????/*
62?
????????3點(diǎn)?行列式展開
63????????????????????
|?x1,?x2,?x3?|
64?
??????? S(A,B,C)?=??|?y1,?y2,?y3?|?*?0.5
65????????????????????
|?1,??1,? 1? |
66?
?? ? ?? =?(?x1*y2?-?x1*y3?-?x2*y1?+?x2*y3?+?x3*y1?-?x3*y2?)?*?0.5
67?
????*/
68?
????return?(?pt1.x?*?pt2.y?-
69?????????????
pt1.x?*?pt3.y?-
70?????????????
pt2.x?*?pt1.y?+
71?????????????
pt2.x?*?pt3.y?+
72?????????????
pt3.x?*?pt1.y?-
73?????????????
pt3.x?*?pt2.y
74???????????
)?*?0.5?;
75?
}
測(cè)試效果：
?1?
//?*?測(cè)試?yán)?/span>
?2?
?3?void?main()
?4?{
?5?????Point_F?pt[?4]?=?{
?6?????????Point_F(?0,?0?),
?7?????????Point_F(?100,?0?),
?8?????????Point_F(?100,?100?),
?9?????????Point_F(?0,?100?)
10?????};
11?
12?????double?area?=?PolygonArea(?pt,?4?);
13?
14?????
15?}