参考自:http://zhidao.baidu.com/question/146717333
LineIntersect.h
// // 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
// // 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
再提供一个判断两直线相交的方法,与上对比貌似更加高效一些~
/** * 判断两条线段是否相交,参见如下链接: * http://local.wasp.uwa.edu.au/~pbourke/geometry/lineline2d/ */ +(bool) checkLineIntersection:(b2Vec2)p1 :(b2Vec2)p2 :(b2Vec2)p3 :(b2Vec2)p4 { CGFloat denominator = (p4.y - p3.y) * (p2.x - p1.x) - (p4.x - p3.x) * (p2.y - p1.y); // In this case the lines are parallel so we assume they don't intersect~ if(denominator == 0.0f) { return false; } CGFloat ua = ((p4.x - p3.x) * (p1.y - p3.y) - (p4.y - p3.y) * (p1.x - p3.x)) / denominator; CGFloat ub = ((p2.x - p1.x) * (p1.y - p3.y) - (p2.y - p1.y) * (p1.x - p3.x)) / denominator; if(ua >= 0.0f && ua <= 1.0f && ub >= 0.0f && ub <= 1.0f) { return true; } return false; }