objective-c判断两条线段相交

转载自：http://blog.csdn.net/yang3wei/article/details/7375013

参考自：http://zhidao.baidu.com/question/146717333

//

//  LineIntersect.h

//  HungryBear

//

//  Created by Bruce Yang on 12-3-12.

//  Copyright (c) 2012年 EricGameStudio. All rights reserved.

//


#import <cstdio>

#import "Box2D.h"


#define zero(x) (((x)>0?(x):-(x))<b2_epsilon)


@interface LineIntersect : NSObject


#pragma mark-

#pragma mark 适用于 b2Vec2 的版本~



// 判两线段相交,包括端点和部分重合

+(int) intersect_in:(b2Vec2)u1 u2:(b2Vec2)u2 v1:(b2Vec2)v1 v2:(b2Vec2)v2;



// 计算两线段交点,请判线段是否相交(同时还是要判断是否平行!)

+(b2Vec2) intersection:(b2Vec2)u1 u2:(b2Vec2)u2 v1:(b2Vec2)v1 v2:(b2Vec2)v2;


#pragma mark-

#pragma mark 适用于 CGPoint 的版本~



+(int) intersect_in2:(CGPoint)u1 u2:(CGPoint)u2 v1:(CGPoint)v1 v2:(CGPoint)v2;



// 计算两线段交点,请判线段是否相交(同时还是要判断是否平行!)

+(CGPoint) intersection2:(CGPoint)u1 u2:(CGPoint)u2 v1:(CGPoint)v1 v2:(CGPoint)v2;


#pragma mark-

#pragma mark 验证上述几个方法的移植是否存在什么问题~



+(void) validateAlgorithm;


@end








//

//  LineIntersect.mm

//  HungryBear

//

//  Created by Bruce Yang on 12-3-12.

//  Copyright (c) 2012年 EricGameStudio. All rights reserved.

//


#import "LineIntersect.h"


@implementation LineIntersect



// 计算交叉乘积 (P1-P0)x(P2-P0)

+(double) xmult:(b2Vec2)p1 p2:(b2Vec2)p2 p3:(b2Vec2)p0 {

    return (p1.x-p0.x)*(p2.y-p0.y)-(p2.x-p0.x)*(p1.y-p0.y);

}


// 判点是否在线段上,包括端点

+(int) dot_online_in:(b2Vec2)p l1:(b2Vec2)l1 l2:(b2Vec2)l2 {

    return zero([self xmult:p p2:l1 p3:l2]) && 

            (l1.x-p.x)*(l2.x-p.x) < b2_epsilon && 

            (l1.y-p.y)*(l2.y-p.y) < b2_epsilon;

}


// 判两点在线段同侧,点在线段上返回0

+(int) same_side:(b2Vec2)p1 p2:(b2Vec2)p2 l1:(b2Vec2)l1 l2:(b2Vec2)l2 {

    return [self xmult:l1 p2:p1 p3:l2] * [self xmult:l1 p2:p2 p3:l2] > b2_epsilon;

}


// 判两直线平行

+(int) parallel:(b2Vec2)u1 u2:(b2Vec2)u2 v1:(b2Vec2)v1 v2:(b2Vec2)v2 {

    return zero((u1.x-u2.x)*(v1.y-v2.y)-(v1.x-v2.x)*(u1.y-u2.y));

}


// 判三点共线

+(int) dots_inline:(b2Vec2)p1 p2:(b2Vec2)p2 p3:(b2Vec2)p3 {

    return zero([self xmult:p1 p2:p2 p3:p3]);

}


// 判两线段相交,包括端点和部分重合

+(int) intersect_in:(b2Vec2)u1 u2:(b2Vec2)u2 v1:(b2Vec2)v1 v2:(b2Vec2)v2 {

    if (![self dots_inline:u1 p2:u2 p3:v1] || ![self dots_inline:u1 p2:u2 p3:v2]) {

        return ![self same_side:u1 p2:u2 l1:v1 l2:v2] && ![self same_side:v1 p2:v2 l1:u1 l2:u2];

    } else {

        return [self dot_online_in:u1 l1:v1 l2:v2] || 

                [self dot_online_in:u2 l1:v1 l2:v2] || 

                [self dot_online_in:v1 l1:u1 l2:u2] || 

                [self dot_online_in:v2 l1:u1 l2:u2];

    } 

}



// 计算两线段交点,请判线段是否相交(同时还是要判断是否平行!)

+(b2Vec2) intersection:(b2Vec2)u1 u2:(b2Vec2)u2 v1:(b2Vec2)v1 v2:(b2Vec2)v2 {

    b2Vec2 ret=u1;

    double t=((u1.x-v1.x)*(v1.y-v2.y)-(u1.y-v1.y)*(v1.x-v2.x))

    /((u1.x-u2.x)*(v1.y-v2.y)-(u1.y-u2.y)*(v1.x-v2.x));

    ret.x+=(u2.x-u1.x)*t;

    ret.y+=(u2.y-u1.y)*t;

    return ret;

}



#pragma mark-

#pragma mark 适用于 CGPoint 的版本~


// 计算交叉乘积 (P1-P0)x(P2-P0)

+(double) xmult2:(CGPoint)p1 p2:(CGPoint)p2 p3:(CGPoint)p0 {

    return (p1.x-p0.x)*(p2.y-p0.y)-(p2.x-p0.x)*(p1.y-p0.y);

}


// 判点是否在线段上,包括端点

+(int) dot_online_in2:(CGPoint)p l1:(CGPoint)l1 l2:(CGPoint)l2 {

    return zero([self xmult2:p p2:l1 p3:l2]) && 

    (l1.x-p.x)*(l2.x-p.x) < b2_epsilon && 

    (l1.y-p.y)*(l2.y-p.y) < b2_epsilon;

}


// 判两点在线段同侧,点在线段上返回0

+(int) same_side2:(CGPoint)p1 p2:(CGPoint)p2 l1:(CGPoint)l1 l2:(CGPoint)l2 {

    return [self xmult2:l1 p2:p1 p3:l2] * [self xmult2:l1 p2:p2 p3:l2] > b2_epsilon;

}


// 判两直线平行

+(int) parallel2:(CGPoint)u1 u2:(CGPoint)u2 v1:(CGPoint)v1 v2:(CGPoint)v2 {

    return zero((u1.x-u2.x)*(v1.y-v2.y)-(v1.x-v2.x)*(u1.y-u2.y));

}


// 判三点共线

+(int) dots_inline2:(CGPoint)p1 p2:(CGPoint)p2 p3:(CGPoint)p3 {

    return zero([self xmult2:p1 p2:p2 p3:p3]);

}


+(int) intersect_in2:(CGPoint)u1 u2:(CGPoint)u2 v1:(CGPoint)v1 v2:(CGPoint)v2 {

    if (![self dots_inline2:u1 p2:u2 p3:v1] || ![self dots_inline2:u1 p2:u2 p3:v2]) {

        return ![self same_side2:u1 p2:u2 l1:v1 l2:v2] && ![self same_side2:v1 p2:v2 l1:u1 l2:u2];

    } else {

        return [self dot_online_in2:u1 l1:v1 l2:v2] || 

        [self dot_online_in2:u2 l1:v1 l2:v2] || 

        [self dot_online_in2:v1 l1:u1 l2:u2] || 

        [self dot_online_in2:v2 l1:u1 l2:u2];

    } 

}



// 计算两线段交点,请判线段是否相交(同时还是要判断是否平行!)

+(CGPoint) intersection2:(CGPoint)u1 u2:(CGPoint)u2 v1:(CGPoint)v1 v2:(CGPoint)v2 {

    CGPoint ret=u1;

    double t=((u1.x-v1.x)*(v1.y-v2.y)-(u1.y-v1.y)*(v1.x-v2.x))

    /((u1.x-u2.x)*(v1.y-v2.y)-(u1.y-u2.y)*(v1.x-v2.x));

    ret.x+=(u2.x-u1.x)*t;

    ret.y+=(u2.y-u1.y)*t;

    return ret;

}



#pragma mark-

#pragma mark 验证上述几个方法的移植是否存在什么问题~


+(void) validateIntersect:(b2Vec2)u1 u2:(b2Vec2)u2 v1:(b2Vec2)v1 v2:(b2Vec2)v2 {

    b2Vec2 answer;

    if ([self parallel:u1 u2:u2 v1:v1 v2:v2] || ![self intersect_in:u1 u2:u2 v1:v1 v2:v2]){

        printf("无交点!\n");

    } else {

        answer = [self intersection:u1 u2:u2 v1:v1 v2:v2];

        printf("交点为:(%lf,%lf)\n", answer.x, answer.y);

    }

}


+(void) validateAlgorithm {

    [LineIntersect validateIntersect:b2Vec2(0,1) u2:b2Vec2(1, 0) v1:b2Vec2(0, 0) v2:b2Vec2(1,1)];

    [LineIntersect validateIntersect:b2Vec2(0,10) u2:b2Vec2(10, 0) v1:b2Vec2(0, 0) v2:b2Vec2(10,10)];

    [LineIntersect validateIntersect:b2Vec2(-2,0) u2:b2Vec2(2, 0) v1:b2Vec2(-1, 3) v2:b2Vec2(-1, -1)];

    [LineIntersect validateIntersect:b2Vec2(-2,0) u2:b2Vec2(2, 0) v1:b2Vec2(-1, 3) v2:b2Vec2(1, -2)];

}



@end